FLAC3D 中多种因素对路基开挖过程稳定性的影响

IF 1.8 4区 地球科学 Q3 GEOCHEMISTRY & GEOPHYSICS
Li Danli, Dai Bing, Zhang Lei
{"title":"FLAC3D 中多种因素对路基开挖过程稳定性的影响","authors":"Li Danli, Dai Bing, Zhang Lei","doi":"10.2113/2024/lithosphere_2023_219","DOIUrl":null,"url":null,"abstract":"Appropriate simulation set parameters are the precondition to obtain accurate results; while the simulation results are affected by multiple factors, it is thus crucial to investigate the sensibility of different factors. This paper first analyses the application situation of numerical simulation software in the field of geotechnical engineering and finds that Fast Lagrangian analysis of continua in three dimensions (FLAC3D) has been widely used on roadways or tunnels. Then, taking the roadway excavation process as the engineering background, FLAC3D was used to create 171 schemes of different simulation parameters and analyze the influence of different factors on the simulation results. The findings show that there is a considerable difference in the degree of effect of different parameters on the simulation results. Most of the factors have a remarkable effect on the numerical simulation results (displacement and stress), and only some factors (parameter uniformity and density) have almost no effect on the results. Meanwhile, the trend of displacement and stress is opposite in most cases. In addition, some neglected factors can also have a considerable effect on the simulation results, such as the zone amount; therefore, it is necessary to avoid the variation of nonstudy factors as possible when carrying out the numerical simulation. This study may significantly assist concerned engineers and technicians in developing a more organized and thorough grasp of the impacts of various parameters on simulation outcomes.The challenges of mining underground mineral resources have grown increasingly difficult and dangerous due to the increasing depth of mining. Numerous researchers have conducted studies to address these challenges that limit the safe and effective production of mines, from the appearance [1, 2] to the essence [3, 4], from the Macro [5, 6] to the Microscopic [7, 8] to the Micro [9, 10] structures, and from the single physical field [11, 12] to multiple physical coupling field [13, 14], and there have been many outcomes. Nevertheless, the complex and variable environment of underground roadways makes it difficult for traditional theoretical analyses [15, 16] to resolve a specific complex engineering problem, and it is laborious and time-consuming to conduct scaled physical simulation tests [17, 18], and it is difficult to reproduce overly complex scenarios, and the accuracy of the obtained results cannot be guaranteed. As the understanding of the properties of geotechnical materials grows and computers continue to develop, computational mechanics [19] is in a flourishing stage. Considering the mutual coupling relationship between various fields, computational mechanics, an emerging interdisciplinary discipline, has significant advantages in processing practice engineering problems. Numerical simulation code based on computational mechanics can simulate approximate object comprehensions for almost any complex operating conditions. At present, the common numerical simulation methods are Finite Element Method [20] (FEM), Finite Difference Method [21] (FDM), Discrete Element Method [22], Boundary Element Method [23], and so on. Among them, due to its precision and speed, the Fast Lagrangian analysis of continua in three dimensions (FLAC3D) [24], a representative of the FDM, has emerged as one of the most popular numerical simulation software.Researchers and technicians have conducted a large number of simulation studies on roadway/tunnel excavation using FLAC3D. Unlu et al. [25] used FLAC3D to determine the variation rule of the radial boundary displacement along the longitudinal direction of a circular tunnel located in the initial stress field, and based on the deformation behavior of linear elastic materials, the expression for the radial displacement of the tunnel excavation surface was obtained by nonlinear curve fitting. Xiao et al. [26] based on the internal stress field distribution law of coal rock in the process of mine roadway excavation obtained by FLAC3D, combined with the force-electricity coupling relationship equation between the electromagnetic radiation intensity generated in the process of compression and deformation and rupture of the coal rock and the internal stress of the coal rock, and researched the change rule of the electromagnetic emission (EME) signals generated in the process of roadway excavation. Meng et al. [27, 28] used FLAC3D to simulate the rheological characteristics of a deep high-stress soft rock tunnel, analyzed the rheological deformation law of the top plate, bottom plate, and two gangs of the surrounding rock of the soft rock tunnel under the action of high stress, and obtained the depth of burial of the tunnel-time creep curve, lateral pressure coefficient-time creep curve, elasticity modulus-time creep curve, and hysteresis coefficient-time creep curve. Suo et al. [29] applied FLAC3D to analyze the plastic damage of the tunnel when the inner, overlapping, and outer staggered arrangement of the working face of the coal seam tunnel under the very close coal seam group, and the plastic damage of the tunnel, the vertical stress of the top plate, and the sinking displacement of the top plate. Niu et al. [30] established a strength attenuation model for the ruptured perimeter rock of a deep tunnel and implanted the model into FLAC3D to verify the reasonableness of the established model. Pongpanya et al. [31] used FLAC3D to study the damage behavior of the roadway at different depths of overburden and found that factors such as the depth of excavation, the bearing capacity of the support system, and the depth of overburden are closely related to the plastic zone of the roadway. Zuo et al. [32] used FLAC3D to obtain the distribution law of roof stress and displacement under anchor support and equal-strength beam support and found that the use of the concept of equal-strength beam support can significantly optimize the distribution of stress in the roadway so that the local stress in the roof plate shows a uniform state, and the deformation of the surrounding rock is effectively controlled, which verifies the feasibility of the equal-strength beam support technology. Xue et al. [33] proposed a comprehensive mining roadway over-support program using automatic support and anchor combination unit based on FLAC, described the structure and working principle of the support robot, and proposed a method for determining the working resistance of the over-support bracket based on the over-support bracket peripheral rock mechanics coupling model. Dibavar et al. [34] focused on the effect of longitudinal and transverse spacing on the stability of tunnels with “umbrella arch” support and proposed to keep the longitudinal and transverse spacing more than 2.5 times the diameter of the tunnel. Wang et al. [35] compiled a command flow for energy dissipation to realize the secondary development of FLAC3D strain softening constitutive model, which extends the energy calculation module of FLAC3D. Mahmoudi et al. [36] used FLAC3D to model tunnels adjacent to caverns and investigated the effect of location, size, distance, shape, and arrangement of the caverns on the displacements, bending moments, and axial forces in the tunnel lining. Wu et al. [37] used FLAC3D software to conduct stability analysis of five different section-shape tunnel models under the conditions of no support and different base-angle support angles and carried out simulation verification under the actual working conditions of the Sanshandao gold mine.In conclusion, although FLAC3D has been widely applied, most of the literature focuses on the use of the software to solve a specific problem but seldom focuses on the proper use of the tool itself. For beginners, how to set up various parameters in the simulation (not only geotechnical parameters) to obtain accurate and reliable simulation results has always been a problem for them. Therefore, in this paper, we designed 171 simulation scenarios based on the engineering background of roadway excavation (FLAC3D-based) and comprehensively and systematically explored the influence of twelve factors on the numerical simulation results, which can provide a careful reference for many FLAC3D users to design and adjust the parameters.FLAC3D was created by Cundall et al. and is widely applied in geotechnical and mining engineering analysis and design at present [24]. It is a 3D numerical analysis code that was developed based on continuous medium theory and explicit FDM. FLAC3D is especially well suited for dealing with FEM difficult-to-solve complex geotechnical subjects, typically such as complex multiconditions, large deformation, nonlinear material behavior, occurrence, and development of destabilization damage [38]. Therefore, FLAC3D is a well-suited numerical simulation software for underground subterranean works.The numerical simulation section of the China Geotechnical Forum (aka YanTuBBS) was surveyed, and the more active sections (those with more than 1000 posts) were statistically analyzed (Figure 1). FLAC is the most active section of them all (over 40% of the total). The literature search engines Google Scholar (GS), Web of Science (WOS), China National Knowledge Infrastructure (CNKI), and WanFang Academic Search System (WFASS) were used for keyword retrieval. Where WOS, an English literature search engine, only used the keywords “roadway” and “tunnel,” whereas CNKI and WFASS, Chinese literature search engines, only used the keywords “巷道” and “隧道” (i.e., “roadway” and “tunnel” in Chinese). GS is a literature search engine with mixed, and the outcomes are derived by applying logical operators like “AND/OR” to the search terms. Due to the different operating principles of each search engine, GS obtained the highest number of documents, while WOS obtained the least (Figure 2). The Large general numerical simulation software such as ANSYS, ABAQUS, MIDAS, and so on retrieves the papers in GS totaling more than 200,000. FLAC3D (about 34,500) is larger than FLAC2D (about 5950), so it can be seen that the 3D version is currently being used more frequently than its 2D counterpart in FLAC. Figure 3 demonstrates how FLAC is widely utilized in the field of “roadway” or “tunnel.”In summary, FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” and “tunnel” Therefore, it is of great engineering significance and theoretical value to study the influence of various factors (in FLAC3D) on the stability of the tunneling process and to provide guidance and help for the beginners of many simulation software.FLAC3D is a finite difference numerical program, which mathematically uses the fast Lagrangian method. Among them, the FDM is a method for finding numerical solutions to definite problems of partial differential equations and systems of equations [39, 40]. The basic idea of FDM is to discretize the problem’s defining domain into a mesh (zone) and then, at the gridpoints, replace the differential quotient in the definite problem with the difference quotient according to the appropriate numerical discretization formulas, thus discretizing the problem into a different format, which in turn leads to a numerical solution. This method is widely used because it is easy to implement on computers [41]. The fast Lagrangian method [42] is a stepwise solution based on explicit differencing to obtain all the equations of motion and constitutive equations of the model, whose constitutive equations are derived from the basic stress-strain definitions and Hooke’s law, while the equations of equilibrium of motion are directly applied to the Cauchy equations of motion (which are derived from Newton’s law of motion). Its computational model is generally composed of several different shapes of three-dimensional units, that is, the dissected spatial unit mesh area, and each unit is further divided into tetrahedra consisting of four nodes in the computation, and the stress-strain of the tetrahedra is only transferred to the other tetrahedra through the four nodes, which is then transferred to other units. When a load is applied to a node, the load acting at that point only affects several surrounding nodes (neighboring nodes) for a tiny period. Using the equations of motion, the relative displacements between the units can be calculated based on the change in velocity and time of the unit nodes, which in turn leads to the unit strains, and then using the constitutive model of the unit, the unit stresses can be calculated. In the process of calculating the strain, the Gaussian integral theory is utilized to simplify the three-dimensional problem by transforming it into a two-dimensional problem. In the equation of motion, the viscosity of the geotechnical body is also fully considered, which is regarded as damping attached to the equation.The “roadway” and “tunnel” (the follow-up is all called: roadway) excavation simulation can be broken down into the following phases, as indicated in Figure 4, depending on the “FLAC3D user help manual” and the author’s practical experience with the software. The simulation process of statics is roughly divided in the “FLAC3D user help manual” into fourteen phases. The “Project Planning and Setup” section contains another seven steps, and the “Tips and Advice” section also gives thirteen tips and advice. Without going into the details of each section, readers can refer to the “FLAC3D help” section of FLAC3D for more specific information.The models are generated by the built-in command flow of FLAC3D, and some special section-shaped roadway models are generated by Rhino. To study the influence of different factors on the stability of the roadway excavation process, a certain initial model and its initial parameters are used as the baseline group (control group). To avoid the interference of irrelevant factors, the following assumptions are made for the model of the benchmark group: (1) the phenomenon of rock mass layering is not considered; (2) rock mass defects, such as fracture zones, joints, and fissures, are ignored, and the model is a homogeneous geological body; and (3) the geostress is applied perpendicularly on the surface of the model. The bottom, left, right, front, and rear faces of the model were fixed, and a compressive stress of 30 MPa was uniformly applied to all the faces except the bottom, and the displacement and plastic zones were zeroed after the model converged. Subsequently, according to the content of the study, to carry out the corresponding excavation simulation, the maximum unbalanced force in the model is 1 × 10 − 5 (the default convergence conditions of the software) to stop the calculation (part of the simulation program under the model cannot be converged, the calculation of 5000 steps).A total of twelve primary types and 171 groups of simulation test scenarios were created based on the baseline group by changing various factors. Due to the large number of scenarios, this section does not provide a detailed description of each set of scenario parameters. The parameters of the baseline group model and the specific simulation scenarios are shown in Table 1, and the scenario parameters that are not specifically described are the baseline group model parameters for variable control in this study. In addition, the displacement and stress results of the analysis section are the maximum value in the model (or in different directions). The analysis of the results is carried out in terms of displacement and stress.The model size is the overall size (length, width, and height) of the numerical model created, and its value mainly relates to the influence of boundary effects. Figure 5 shows the simulation results in fourteen schemes of model size (with seven model sizes in two conditions of considering gravity and did not consider). The roadway could not converge when the model size is 10 × 10 × 10 m due to the roadway outline being too near to the model boundary. The displacement of the roadway tends to gradually decrease with the increase in model size. On the contrary, the stress in the model tends to gradually increase as the model size increases. Additionally, when gravity is considered, the displacement and stress in the model are slightly higher than gravity, which is not considered.In FLAC3D, the model is mainly composed of zones and gridpoints, and the more zones there are, the more time is needed for computation. Figure 6 exhibits the simulation results in four schemes of zone amount. The displacement and stress in the model tend to gradually increase with the increase in zone amount. It should be noted that the vertical stress is higher than the horizontal stress in terms of the magnitude of the increase.A common strategy used in simulations is to encrypt the mesh (zone) attached to the important region to improve computational accuracy. Here, the mesh gradient coefficient is the degree to which the mesh is gradually encrypted from the model boundary to the roadway outline. Figure 7 expresses the simulation results in seven schemes of mesh gradient coefficient. The displacement of the roadway tends to increase as the mesh gradient coefficient increases. The stress in the model is to decrease and then level off as the mesh gradient coefficient increases; the vertical stress is a little higher than the horizontal stress.Metallic materials have a uniform distribution of physical and mechanical parameters, whereas rock mass is a nonhomogeneous material. However, the usual simulation treats the rock mass as a homogeneous material and assigns it to uniform parameters. Here, the Gaussian distribution command was utilized to assign nonuniform values to the rock mass material. Figure 8 demonstrates the simulation results in five schemes of Gaussian distribution rate. As the Gaussian distribution rate increases (within 10%), the displacement and stress in the model remain essentially unchanged.There are two main ways to excavate a roadway in FLAC3D: one way is to use the “null” command to “excavate” the roadway, which is a kind of sudden change; the other way is to use the “relax excavate” command, which gradually reduces the physical–mechanical parameters in the region, which is a kind of slow change, which can avoid the interference of inertia effect on the result due to sudden change to a certain extent. In practical engineering, tunnel excavation is a “slow” process, but the “null” command is commonly used for simulation. Figure 9 displays the simulation results in two schemes of excavation mode. When “relax excavate” is used, the displacement in the model can be reduced by about 4.5%, and the stress can be increased by about 7.5% compared with “null.” The excavation mode has a slight effect on the simulation results.The cross-sectional area of the roadway is one of the direct factors concerning the stability of excavation. Therefore, many studies on the stability of the roadway directly focus on the roadway span and height (area) as the key considerations. Figure 10 manifests the simulation results in seven schemes of roadway area (rectangle). As the area of the roadway increases, the displacement in the roadway continues to grow in an approximately linear fashion. The stress is decreasing, the rate of stress decreases is also decreasing. In addition, the values of vertical and horizontal stresses converge as the area of the roadway increases.The shape of the roadway is a key factor affecting the state of geostress redistribution after excavation. Here, based on engineering experience, the study was carried out with typical six shapes of roadway sections. In addition, the model built in this section was generated by Rhino software (which also utilized the griddle plug-in to optimize the mesh), and the zone amount and so on were inevitably disturbed, so it was difficult to keep consistent with the baseline group. For this reason, the model size (changed to 50 × 50 × 5.5 m) and the cyclic footage (changed to 5.5 m) were also changed to speed up the simulation process. Figure 11 indicates the simulation results in six schemes of roadway shape. For the displacements, overall, the displacements of the sidewall of the roadway are generally larger than the other positions, while the horizontal displacements are generally slightly larger than the vertical displacements, in addition to the overall displacements: rectangle > trapezoid > straight wall semicircular arch > horseshoe > three-center arch > round. When the stress law is opposite to it, the stress of the roadway shape schemes with large displacement is relatively small.The cyclic footage is the length of the roadway or tunnel that is excavated at one time during the boring process. Figure 12 shows the simulation results for eight cyclic feed scenarios (four of the cyclic footage lengths under two stopping calculation conditions, the maximum imbalance force reaches 1 × 10−5, or a total of 2000 steps are calculated). The displacements in the model are generally greater when the maximum unbalanced force is used as the convergence condition than when the computational step is used as the convergence condition. This is because the model needs to be calculated after each excavation until equilibrium, so the cumulative steps for the convergence condition of maximum unbalanced force are significantly higher than 2000. Hence, the displacement values are larger for the scheme with maximum unbalanced force as the convergence condition. It should be noted that the stress values in the model are very little affected by this factor. In addition, the effect of cyclic footage on the simulation results is “fluctuating, not simply increasing or decreasing, suggesting that there may be an optimal value for cyclic footage within the simulation range. At the same time, the effect of cyclic footage on the results is relatively slight.The in situ stresses are natural stresses present in the earth’s crust that have not been disturbed by engineering, whose values are influenced by many factors (one of the main ones being the depth of burial) and are at the heart of underground engineering hazards, such as rockburst, collapse, and so on, which are also known as stress-induced hazards. Figure 13 illustrates the simulation results for twelve in situ stress values. The displacement of the roadway increases as the in situ stress increases (as the in situ stress increases, the increase in the rate of displacement is also growing), and the stress in the model also increases. A gentler phase exists at about 30 MPa and before a significant and sustained increase begins at about 40 MPa. In addition, as the in situ stresses exceed 40 MPa, the vertical stresses also begin to be significantly greater than the horizontal stresses.The formation of the in situ stress field is influenced by a variety of factors, such as self-gravity stress, tectonic stress, and residual stress, and presents an extremely complex state. Therefore, the values of horizontal and vertical stresses are often different. The lateral stress coefficient is defined as the ratio of horizontal stress to vertical stress. Figure 14 shows the simulation results for eight lateral stress coefficients. The overall displacement of the roadway roughly increases with the growth of the lateral stress coefficient. In particular, when the lateral stress coefficient is small, the displacement of the sidewall of the roadway is larger than that at the floor, and with the increase of the lateral stress coefficient ( >1.0), the displacement at the floor begins to be larger than that at the sidewall, the horizontal stress begins to be larger than that at the vertical stress, and the vertical stress and the maximum shear stress tend to be gradually stabilized.A constitutive model, also known as the mechanical constitutive equation of a material, or the stress-strain model of a material, is a mathematical expression that describes the mechanical properties of a material (stress-strain-strength-time relationship). Currently, the M-C and H-B constitutive models are the most commonly used regarding the simulation of engineering scales (geotechnical). To be able to compare the influence of these constitutive models on the simulation results to a certain extent, we have chosen to analyze only the constitutive models with some of the same parameters (Elastic/E, Mohr–Coulomb/M-C, and Mohr–Coulomb strain softening/MSC). Figure 15 shows the simulation results for three constitutive models. It can be seen that the effect of the constitutive model on the simulation results is prominent. Especially for the MSC constitutive model (using the softening coefficients commonly used in the FLAC3D case), the values of the channel displacements are significantly higher than those of other constitutive models, even though the parameters before softening are consistent with those of the M-C constitutive model.The physical–mechanical parameters of a geotechnical body (hereafter referred to as geotechnical parameters) are one of the most crucial factors to be considered in engineering design. In numerical simulation, different constitutive models require different geotechnical parameters, and different constitutive models can be selected according to different engineering characteristics and engineering requirements. The M-C constitutive model is one of the most commonly applied constitutive models for geotechnical bodies. The required parameters are elasticity modulus, tensile strength, dilatancy angle, cohesion, internal friction angle, and Poisson’s ratio in addition to the density of the surrounding rock is also necessary. Figure 16 displays the simulation results for a total of seven influencing factors and ninety-four sets of simulation scenarios.For the stress, some factors have essentially no effect on it, such as density, elasticity modulus, tensile strength, and dilatancy angle. The stress has increased gently and slowly with the Poisson’s ratio growth; additionally, the stress fluctuates but has a total rising trend with the cohesion and internal friction angle enlarging. For the displacement, the density also has essentially no effect on it. The growth of most factors (elasticity modulus, tensile strength, cohesion, and internal friction angle) causes the displacement to show a pattern of decreasing and then leveling off. In addition, an increase in dilatancy angle leads to an increase in displacement, while a growth in Poisson’s ratio causes the displacement to fluctuate within a small range.Numerical simulation has become an indispensable means to solve complex engineering problems, and reasonable setting parameters are the key to guaranteeing the reliability of numerical simulation results. In this paper, we take the tunnel excavation as the engineering background and FLAC3D as the research object to explore the effect of various factors on the simulation results. Although some studies have analyzed the influence of different factors on roadway excavation, for example, Peng et al. [43] studied the influence of the ground stress and the roadway area on the damage zone of the roadway excavation. Zhong-Cheng et al. [44] investigated the influence of different geotechnical parameters on roadway deformation and damage by carrying out orthogonal numerical simulation experiments and concluded that the influence of various factors on roadway deformation is in the following order of significance: cohesion > tensile strength > elasticity modulus > internal friction angle > Poisson’s ratio. In addition, there have been studies on the grid size effect [45-47], but they have not been extended to the engineering scale of the roadway excavation. Most of these studies focus on the effect of one or more factors, which may not provide readers with more comprehensive and intuitive help. To the best of our knowledge, nothing like this paper has been reported. Therefore, the results of this paper may provide researchers or engineers with more comprehensive guidance and reference for numerical simulation.The factors discussed in this paper are not only limited to geotechnical and construction parameters but also involve some modeling parameters (Figure 17). The results of this study show that the impacts of roadway excavation on rock mass are not only affected by “direct” parameters such as geotechnical and construction parameters but also by modeling parameters such as model size and zone amount. Even the effects of these modeling factors are as strong as those of geotechnical and construction parameters, but they are often “neglected.” For example, when the model size was increased from 20 × 20 × 20 m to 70 × 70 × 70 m, the displacement in the model decreased by 21%, and the stress increased by 38%, while all other parameters were kept constant (Figure 5). When the number of meshes was increased by about three times (from 320,000 to 972,000 considering the self-gravity), the displacement in the model increased by 31%, and the horizontal stress increased by 55% (Figure 6). When the mesh gradient coefficient was increased from 0.8 to 1.4, the displacement in the model doubled by about six times, and the horizontal and vertical stresses were reduced by 50% and 58%, respectively (Figure 7). The effect of such a change on the results is significant. Therefore, when using numerical simulation to study a particular problem, parameter calibration should be performed first, and once all parameters are calibrated, no further changes should be made to parameters other than those of the study objective, or this may lead to significant deviations in the results.The purpose of conducting numerical simulations is mostly to get regular conclusions (of course, there are some studies to get specific values, at which time it is necessary to try to guarantee that each simulation parameter is consistent with the actual parameter), so some parameters can be simplified appropriately. For example, in reality, the geotechnical body is a nonhomogeneous material, and its parameters cannot be as homogeneous as in common numerical models [48], but assuming its parameters as homogeneous, which has almost no effect on the simulation results (Figure 8). Similarly, the excavation of the roadway can be performed by using commands such as “assign null” and “relax excavation.” Theoretically, “relax excavation” is more in line with the actual excavation process, but “assign null” is more commonly used, and the results show that the effect of these two methods on the results is extremely slight, so the excavation pattern may not interfere with the results more significantly (Figure 9).In addition, the roadway area (Figure 10), roadway shape (Figure 11), in situ stress (Figure 13), and lateral stress coefficient (Figure 14) all have a more significant effect on the displacements and stresses of the model. The type of constitutive model, on the other hand, determines the various parameters required for the simulation and has an extremely significant effect on the results (Figure 15). At the same time, different geotechnical parameters based on the M-C constitutive model have different effects on the tunneling process and may even lead to a certain arching of the stress (horizontal) distribution characteristics (Figure 18), but this phenomenon has not been reported to the best of our knowledge, perhaps because the cohesion of the rock mass in practical engineering is difficult to reach 10 MPa.A variety of factors can have a significant impact on the simulation results, and the stress and displacement with the change of the influencing factors show different patterns, but in most cases, the change rule of displacement and stress is opposite (Figures 5,7,9-11,15,16(e), (f) and (g), and in a small number of cases, the change rule of displacement and stress is consistent (Figures 6, 13, 14 and 16(d)), and there are a few cases in which stress is not affected, only displacement changes (Figure 16(b) and (c)). This phenomenon still needs to be further analyzed.In this paper, a large number of simulation experiments are carried out to visualize the influence of different factors on the simulation results, which may be able to provide a reference for the parameter design and adjustment in numerical simulation research. Generally speaking, the simulation results are affected by many factors; even the zone amount and model size, which are often neglected, will have a great influence on the simulation results. Therefore, when the research is carried out through numerical simulation, it is very necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and at the same time, it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.In addition, the design of the schemes in the study is based on the author’s experience, and to further reflect the influence of the parameters on the results, the designed parameter values may exceed the limits that can be observed in practical engineering. Moreover, due to the rich variety of factors studied in the article, an in-depth and detailed analysis of each set of simulation results is difficult to be carried out; thus, the paper only briefly discusses the pattern of the results.Aiming at the challenges in the numerical simulation process, a brief survey and analysis of simulation software in the field of geotechnical engineering were carried out first, followed by designing more than 100 sets of research scenarios based on FLAC3D to analyze the influence of various factors on the stability of the roadway excavation with the roadway excavation as the engineering background. The main conclusions are as follows:Through searching and analyzing the literature, we found that FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” or “tunnel.” A brief introduction to the software is given, and the suggested steps to carry out the hydrostatic simulation are given.The simulation results show that there is a significant difference in the influence of different parameters on the simulation results. The ones with greater influence are model size, zone amount, mesh gradient coefficient, roadway area, roadway shape, lateral stress coefficient, constitutive model, elasticity modulus, dilatancy angle, cohesion, and internal friction angle; a little influence: excavation mode, cyclic footage, tensile strength, and Poisson’s ratio; trifling influence: parameter uniformity and density.A variety of factors can have a significant effect on the simulation results, and the stress and displacement show different patterns with the changes of the influencing factors, but in most cases, the trend of displacement and stress is the opposite. In addition, even neglected factors (e.g., mesh density, model size, etc.) can have a significant impact on the simulation results. Therefore, when researching through numerical simulation, it is necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.Through searching and analyzing the literature, we found that FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” or “tunnel.” A brief introduction to the software is given, and the suggested steps to carry out the hydrostatic simulation are given.The simulation results show that there is a significant difference in the influence of different parameters on the simulation results. The ones with greater influence are model size, zone amount, mesh gradient coefficient, roadway area, roadway shape, lateral stress coefficient, constitutive model, elasticity modulus, dilatancy angle, cohesion, and internal friction angle; a little influence: excavation mode, cyclic footage, tensile strength, and Poisson’s ratio; trifling influence: parameter uniformity and density.A variety of factors can have a significant effect on the simulation results, and the stress and displacement show different patterns with the changes of the influencing factors, but in most cases, the trend of displacement and stress is the opposite. In addition, even neglected factors (e.g., mesh density, model size, etc.) can have a significant impact on the simulation results. Therefore, when researching through numerical simulation, it is necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy restrictions.The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.This work was financially supported by the Key Project of Education Department of Hunan Province (22A0293), the General Project of Education Department of Hunan Province (22C0235), and the Postgraduate Scientific Research Innovation Project of Hunan Province (QL20220213).","PeriodicalId":18147,"journal":{"name":"Lithosphere","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Effect of Multiple Factors for the Roadway Excavation Process Stability in FLAC3D\",\"authors\":\"Li Danli, Dai Bing, Zhang Lei\",\"doi\":\"10.2113/2024/lithosphere_2023_219\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Appropriate simulation set parameters are the precondition to obtain accurate results; while the simulation results are affected by multiple factors, it is thus crucial to investigate the sensibility of different factors. This paper first analyses the application situation of numerical simulation software in the field of geotechnical engineering and finds that Fast Lagrangian analysis of continua in three dimensions (FLAC3D) has been widely used on roadways or tunnels. Then, taking the roadway excavation process as the engineering background, FLAC3D was used to create 171 schemes of different simulation parameters and analyze the influence of different factors on the simulation results. The findings show that there is a considerable difference in the degree of effect of different parameters on the simulation results. Most of the factors have a remarkable effect on the numerical simulation results (displacement and stress), and only some factors (parameter uniformity and density) have almost no effect on the results. Meanwhile, the trend of displacement and stress is opposite in most cases. In addition, some neglected factors can also have a considerable effect on the simulation results, such as the zone amount; therefore, it is necessary to avoid the variation of nonstudy factors as possible when carrying out the numerical simulation. This study may significantly assist concerned engineers and technicians in developing a more organized and thorough grasp of the impacts of various parameters on simulation outcomes.The challenges of mining underground mineral resources have grown increasingly difficult and dangerous due to the increasing depth of mining. Numerous researchers have conducted studies to address these challenges that limit the safe and effective production of mines, from the appearance [1, 2] to the essence [3, 4], from the Macro [5, 6] to the Microscopic [7, 8] to the Micro [9, 10] structures, and from the single physical field [11, 12] to multiple physical coupling field [13, 14], and there have been many outcomes. Nevertheless, the complex and variable environment of underground roadways makes it difficult for traditional theoretical analyses [15, 16] to resolve a specific complex engineering problem, and it is laborious and time-consuming to conduct scaled physical simulation tests [17, 18], and it is difficult to reproduce overly complex scenarios, and the accuracy of the obtained results cannot be guaranteed. As the understanding of the properties of geotechnical materials grows and computers continue to develop, computational mechanics [19] is in a flourishing stage. Considering the mutual coupling relationship between various fields, computational mechanics, an emerging interdisciplinary discipline, has significant advantages in processing practice engineering problems. Numerical simulation code based on computational mechanics can simulate approximate object comprehensions for almost any complex operating conditions. At present, the common numerical simulation methods are Finite Element Method [20] (FEM), Finite Difference Method [21] (FDM), Discrete Element Method [22], Boundary Element Method [23], and so on. Among them, due to its precision and speed, the Fast Lagrangian analysis of continua in three dimensions (FLAC3D) [24], a representative of the FDM, has emerged as one of the most popular numerical simulation software.Researchers and technicians have conducted a large number of simulation studies on roadway/tunnel excavation using FLAC3D. Unlu et al. [25] used FLAC3D to determine the variation rule of the radial boundary displacement along the longitudinal direction of a circular tunnel located in the initial stress field, and based on the deformation behavior of linear elastic materials, the expression for the radial displacement of the tunnel excavation surface was obtained by nonlinear curve fitting. Xiao et al. [26] based on the internal stress field distribution law of coal rock in the process of mine roadway excavation obtained by FLAC3D, combined with the force-electricity coupling relationship equation between the electromagnetic radiation intensity generated in the process of compression and deformation and rupture of the coal rock and the internal stress of the coal rock, and researched the change rule of the electromagnetic emission (EME) signals generated in the process of roadway excavation. Meng et al. [27, 28] used FLAC3D to simulate the rheological characteristics of a deep high-stress soft rock tunnel, analyzed the rheological deformation law of the top plate, bottom plate, and two gangs of the surrounding rock of the soft rock tunnel under the action of high stress, and obtained the depth of burial of the tunnel-time creep curve, lateral pressure coefficient-time creep curve, elasticity modulus-time creep curve, and hysteresis coefficient-time creep curve. Suo et al. [29] applied FLAC3D to analyze the plastic damage of the tunnel when the inner, overlapping, and outer staggered arrangement of the working face of the coal seam tunnel under the very close coal seam group, and the plastic damage of the tunnel, the vertical stress of the top plate, and the sinking displacement of the top plate. Niu et al. [30] established a strength attenuation model for the ruptured perimeter rock of a deep tunnel and implanted the model into FLAC3D to verify the reasonableness of the established model. Pongpanya et al. [31] used FLAC3D to study the damage behavior of the roadway at different depths of overburden and found that factors such as the depth of excavation, the bearing capacity of the support system, and the depth of overburden are closely related to the plastic zone of the roadway. Zuo et al. [32] used FLAC3D to obtain the distribution law of roof stress and displacement under anchor support and equal-strength beam support and found that the use of the concept of equal-strength beam support can significantly optimize the distribution of stress in the roadway so that the local stress in the roof plate shows a uniform state, and the deformation of the surrounding rock is effectively controlled, which verifies the feasibility of the equal-strength beam support technology. Xue et al. [33] proposed a comprehensive mining roadway over-support program using automatic support and anchor combination unit based on FLAC, described the structure and working principle of the support robot, and proposed a method for determining the working resistance of the over-support bracket based on the over-support bracket peripheral rock mechanics coupling model. Dibavar et al. [34] focused on the effect of longitudinal and transverse spacing on the stability of tunnels with “umbrella arch” support and proposed to keep the longitudinal and transverse spacing more than 2.5 times the diameter of the tunnel. Wang et al. [35] compiled a command flow for energy dissipation to realize the secondary development of FLAC3D strain softening constitutive model, which extends the energy calculation module of FLAC3D. Mahmoudi et al. [36] used FLAC3D to model tunnels adjacent to caverns and investigated the effect of location, size, distance, shape, and arrangement of the caverns on the displacements, bending moments, and axial forces in the tunnel lining. Wu et al. [37] used FLAC3D software to conduct stability analysis of five different section-shape tunnel models under the conditions of no support and different base-angle support angles and carried out simulation verification under the actual working conditions of the Sanshandao gold mine.In conclusion, although FLAC3D has been widely applied, most of the literature focuses on the use of the software to solve a specific problem but seldom focuses on the proper use of the tool itself. For beginners, how to set up various parameters in the simulation (not only geotechnical parameters) to obtain accurate and reliable simulation results has always been a problem for them. Therefore, in this paper, we designed 171 simulation scenarios based on the engineering background of roadway excavation (FLAC3D-based) and comprehensively and systematically explored the influence of twelve factors on the numerical simulation results, which can provide a careful reference for many FLAC3D users to design and adjust the parameters.FLAC3D was created by Cundall et al. and is widely applied in geotechnical and mining engineering analysis and design at present [24]. It is a 3D numerical analysis code that was developed based on continuous medium theory and explicit FDM. FLAC3D is especially well suited for dealing with FEM difficult-to-solve complex geotechnical subjects, typically such as complex multiconditions, large deformation, nonlinear material behavior, occurrence, and development of destabilization damage [38]. Therefore, FLAC3D is a well-suited numerical simulation software for underground subterranean works.The numerical simulation section of the China Geotechnical Forum (aka YanTuBBS) was surveyed, and the more active sections (those with more than 1000 posts) were statistically analyzed (Figure 1). FLAC is the most active section of them all (over 40% of the total). The literature search engines Google Scholar (GS), Web of Science (WOS), China National Knowledge Infrastructure (CNKI), and WanFang Academic Search System (WFASS) were used for keyword retrieval. Where WOS, an English literature search engine, only used the keywords “roadway” and “tunnel,” whereas CNKI and WFASS, Chinese literature search engines, only used the keywords “巷道” and “隧道” (i.e., “roadway” and “tunnel” in Chinese). GS is a literature search engine with mixed, and the outcomes are derived by applying logical operators like “AND/OR” to the search terms. Due to the different operating principles of each search engine, GS obtained the highest number of documents, while WOS obtained the least (Figure 2). The Large general numerical simulation software such as ANSYS, ABAQUS, MIDAS, and so on retrieves the papers in GS totaling more than 200,000. FLAC3D (about 34,500) is larger than FLAC2D (about 5950), so it can be seen that the 3D version is currently being used more frequently than its 2D counterpart in FLAC. Figure 3 demonstrates how FLAC is widely utilized in the field of “roadway” or “tunnel.”In summary, FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” and “tunnel” Therefore, it is of great engineering significance and theoretical value to study the influence of various factors (in FLAC3D) on the stability of the tunneling process and to provide guidance and help for the beginners of many simulation software.FLAC3D is a finite difference numerical program, which mathematically uses the fast Lagrangian method. Among them, the FDM is a method for finding numerical solutions to definite problems of partial differential equations and systems of equations [39, 40]. The basic idea of FDM is to discretize the problem’s defining domain into a mesh (zone) and then, at the gridpoints, replace the differential quotient in the definite problem with the difference quotient according to the appropriate numerical discretization formulas, thus discretizing the problem into a different format, which in turn leads to a numerical solution. This method is widely used because it is easy to implement on computers [41]. The fast Lagrangian method [42] is a stepwise solution based on explicit differencing to obtain all the equations of motion and constitutive equations of the model, whose constitutive equations are derived from the basic stress-strain definitions and Hooke’s law, while the equations of equilibrium of motion are directly applied to the Cauchy equations of motion (which are derived from Newton’s law of motion). Its computational model is generally composed of several different shapes of three-dimensional units, that is, the dissected spatial unit mesh area, and each unit is further divided into tetrahedra consisting of four nodes in the computation, and the stress-strain of the tetrahedra is only transferred to the other tetrahedra through the four nodes, which is then transferred to other units. When a load is applied to a node, the load acting at that point only affects several surrounding nodes (neighboring nodes) for a tiny period. Using the equations of motion, the relative displacements between the units can be calculated based on the change in velocity and time of the unit nodes, which in turn leads to the unit strains, and then using the constitutive model of the unit, the unit stresses can be calculated. In the process of calculating the strain, the Gaussian integral theory is utilized to simplify the three-dimensional problem by transforming it into a two-dimensional problem. In the equation of motion, the viscosity of the geotechnical body is also fully considered, which is regarded as damping attached to the equation.The “roadway” and “tunnel” (the follow-up is all called: roadway) excavation simulation can be broken down into the following phases, as indicated in Figure 4, depending on the “FLAC3D user help manual” and the author’s practical experience with the software. The simulation process of statics is roughly divided in the “FLAC3D user help manual” into fourteen phases. The “Project Planning and Setup” section contains another seven steps, and the “Tips and Advice” section also gives thirteen tips and advice. Without going into the details of each section, readers can refer to the “FLAC3D help” section of FLAC3D for more specific information.The models are generated by the built-in command flow of FLAC3D, and some special section-shaped roadway models are generated by Rhino. To study the influence of different factors on the stability of the roadway excavation process, a certain initial model and its initial parameters are used as the baseline group (control group). To avoid the interference of irrelevant factors, the following assumptions are made for the model of the benchmark group: (1) the phenomenon of rock mass layering is not considered; (2) rock mass defects, such as fracture zones, joints, and fissures, are ignored, and the model is a homogeneous geological body; and (3) the geostress is applied perpendicularly on the surface of the model. The bottom, left, right, front, and rear faces of the model were fixed, and a compressive stress of 30 MPa was uniformly applied to all the faces except the bottom, and the displacement and plastic zones were zeroed after the model converged. Subsequently, according to the content of the study, to carry out the corresponding excavation simulation, the maximum unbalanced force in the model is 1 × 10 − 5 (the default convergence conditions of the software) to stop the calculation (part of the simulation program under the model cannot be converged, the calculation of 5000 steps).A total of twelve primary types and 171 groups of simulation test scenarios were created based on the baseline group by changing various factors. Due to the large number of scenarios, this section does not provide a detailed description of each set of scenario parameters. The parameters of the baseline group model and the specific simulation scenarios are shown in Table 1, and the scenario parameters that are not specifically described are the baseline group model parameters for variable control in this study. In addition, the displacement and stress results of the analysis section are the maximum value in the model (or in different directions). The analysis of the results is carried out in terms of displacement and stress.The model size is the overall size (length, width, and height) of the numerical model created, and its value mainly relates to the influence of boundary effects. Figure 5 shows the simulation results in fourteen schemes of model size (with seven model sizes in two conditions of considering gravity and did not consider). The roadway could not converge when the model size is 10 × 10 × 10 m due to the roadway outline being too near to the model boundary. The displacement of the roadway tends to gradually decrease with the increase in model size. On the contrary, the stress in the model tends to gradually increase as the model size increases. Additionally, when gravity is considered, the displacement and stress in the model are slightly higher than gravity, which is not considered.In FLAC3D, the model is mainly composed of zones and gridpoints, and the more zones there are, the more time is needed for computation. Figure 6 exhibits the simulation results in four schemes of zone amount. The displacement and stress in the model tend to gradually increase with the increase in zone amount. It should be noted that the vertical stress is higher than the horizontal stress in terms of the magnitude of the increase.A common strategy used in simulations is to encrypt the mesh (zone) attached to the important region to improve computational accuracy. Here, the mesh gradient coefficient is the degree to which the mesh is gradually encrypted from the model boundary to the roadway outline. Figure 7 expresses the simulation results in seven schemes of mesh gradient coefficient. The displacement of the roadway tends to increase as the mesh gradient coefficient increases. The stress in the model is to decrease and then level off as the mesh gradient coefficient increases; the vertical stress is a little higher than the horizontal stress.Metallic materials have a uniform distribution of physical and mechanical parameters, whereas rock mass is a nonhomogeneous material. However, the usual simulation treats the rock mass as a homogeneous material and assigns it to uniform parameters. Here, the Gaussian distribution command was utilized to assign nonuniform values to the rock mass material. Figure 8 demonstrates the simulation results in five schemes of Gaussian distribution rate. As the Gaussian distribution rate increases (within 10%), the displacement and stress in the model remain essentially unchanged.There are two main ways to excavate a roadway in FLAC3D: one way is to use the “null” command to “excavate” the roadway, which is a kind of sudden change; the other way is to use the “relax excavate” command, which gradually reduces the physical–mechanical parameters in the region, which is a kind of slow change, which can avoid the interference of inertia effect on the result due to sudden change to a certain extent. In practical engineering, tunnel excavation is a “slow” process, but the “null” command is commonly used for simulation. Figure 9 displays the simulation results in two schemes of excavation mode. When “relax excavate” is used, the displacement in the model can be reduced by about 4.5%, and the stress can be increased by about 7.5% compared with “null.” The excavation mode has a slight effect on the simulation results.The cross-sectional area of the roadway is one of the direct factors concerning the stability of excavation. Therefore, many studies on the stability of the roadway directly focus on the roadway span and height (area) as the key considerations. Figure 10 manifests the simulation results in seven schemes of roadway area (rectangle). As the area of the roadway increases, the displacement in the roadway continues to grow in an approximately linear fashion. The stress is decreasing, the rate of stress decreases is also decreasing. In addition, the values of vertical and horizontal stresses converge as the area of the roadway increases.The shape of the roadway is a key factor affecting the state of geostress redistribution after excavation. Here, based on engineering experience, the study was carried out with typical six shapes of roadway sections. In addition, the model built in this section was generated by Rhino software (which also utilized the griddle plug-in to optimize the mesh), and the zone amount and so on were inevitably disturbed, so it was difficult to keep consistent with the baseline group. For this reason, the model size (changed to 50 × 50 × 5.5 m) and the cyclic footage (changed to 5.5 m) were also changed to speed up the simulation process. Figure 11 indicates the simulation results in six schemes of roadway shape. For the displacements, overall, the displacements of the sidewall of the roadway are generally larger than the other positions, while the horizontal displacements are generally slightly larger than the vertical displacements, in addition to the overall displacements: rectangle > trapezoid > straight wall semicircular arch > horseshoe > three-center arch > round. When the stress law is opposite to it, the stress of the roadway shape schemes with large displacement is relatively small.The cyclic footage is the length of the roadway or tunnel that is excavated at one time during the boring process. Figure 12 shows the simulation results for eight cyclic feed scenarios (four of the cyclic footage lengths under two stopping calculation conditions, the maximum imbalance force reaches 1 × 10−5, or a total of 2000 steps are calculated). The displacements in the model are generally greater when the maximum unbalanced force is used as the convergence condition than when the computational step is used as the convergence condition. This is because the model needs to be calculated after each excavation until equilibrium, so the cumulative steps for the convergence condition of maximum unbalanced force are significantly higher than 2000. Hence, the displacement values are larger for the scheme with maximum unbalanced force as the convergence condition. It should be noted that the stress values in the model are very little affected by this factor. In addition, the effect of cyclic footage on the simulation results is “fluctuating, not simply increasing or decreasing, suggesting that there may be an optimal value for cyclic footage within the simulation range. At the same time, the effect of cyclic footage on the results is relatively slight.The in situ stresses are natural stresses present in the earth’s crust that have not been disturbed by engineering, whose values are influenced by many factors (one of the main ones being the depth of burial) and are at the heart of underground engineering hazards, such as rockburst, collapse, and so on, which are also known as stress-induced hazards. Figure 13 illustrates the simulation results for twelve in situ stress values. The displacement of the roadway increases as the in situ stress increases (as the in situ stress increases, the increase in the rate of displacement is also growing), and the stress in the model also increases. A gentler phase exists at about 30 MPa and before a significant and sustained increase begins at about 40 MPa. In addition, as the in situ stresses exceed 40 MPa, the vertical stresses also begin to be significantly greater than the horizontal stresses.The formation of the in situ stress field is influenced by a variety of factors, such as self-gravity stress, tectonic stress, and residual stress, and presents an extremely complex state. Therefore, the values of horizontal and vertical stresses are often different. The lateral stress coefficient is defined as the ratio of horizontal stress to vertical stress. Figure 14 shows the simulation results for eight lateral stress coefficients. The overall displacement of the roadway roughly increases with the growth of the lateral stress coefficient. In particular, when the lateral stress coefficient is small, the displacement of the sidewall of the roadway is larger than that at the floor, and with the increase of the lateral stress coefficient ( >1.0), the displacement at the floor begins to be larger than that at the sidewall, the horizontal stress begins to be larger than that at the vertical stress, and the vertical stress and the maximum shear stress tend to be gradually stabilized.A constitutive model, also known as the mechanical constitutive equation of a material, or the stress-strain model of a material, is a mathematical expression that describes the mechanical properties of a material (stress-strain-strength-time relationship). Currently, the M-C and H-B constitutive models are the most commonly used regarding the simulation of engineering scales (geotechnical). To be able to compare the influence of these constitutive models on the simulation results to a certain extent, we have chosen to analyze only the constitutive models with some of the same parameters (Elastic/E, Mohr–Coulomb/M-C, and Mohr–Coulomb strain softening/MSC). Figure 15 shows the simulation results for three constitutive models. It can be seen that the effect of the constitutive model on the simulation results is prominent. Especially for the MSC constitutive model (using the softening coefficients commonly used in the FLAC3D case), the values of the channel displacements are significantly higher than those of other constitutive models, even though the parameters before softening are consistent with those of the M-C constitutive model.The physical–mechanical parameters of a geotechnical body (hereafter referred to as geotechnical parameters) are one of the most crucial factors to be considered in engineering design. In numerical simulation, different constitutive models require different geotechnical parameters, and different constitutive models can be selected according to different engineering characteristics and engineering requirements. The M-C constitutive model is one of the most commonly applied constitutive models for geotechnical bodies. The required parameters are elasticity modulus, tensile strength, dilatancy angle, cohesion, internal friction angle, and Poisson’s ratio in addition to the density of the surrounding rock is also necessary. Figure 16 displays the simulation results for a total of seven influencing factors and ninety-four sets of simulation scenarios.For the stress, some factors have essentially no effect on it, such as density, elasticity modulus, tensile strength, and dilatancy angle. The stress has increased gently and slowly with the Poisson’s ratio growth; additionally, the stress fluctuates but has a total rising trend with the cohesion and internal friction angle enlarging. For the displacement, the density also has essentially no effect on it. The growth of most factors (elasticity modulus, tensile strength, cohesion, and internal friction angle) causes the displacement to show a pattern of decreasing and then leveling off. In addition, an increase in dilatancy angle leads to an increase in displacement, while a growth in Poisson’s ratio causes the displacement to fluctuate within a small range.Numerical simulation has become an indispensable means to solve complex engineering problems, and reasonable setting parameters are the key to guaranteeing the reliability of numerical simulation results. In this paper, we take the tunnel excavation as the engineering background and FLAC3D as the research object to explore the effect of various factors on the simulation results. Although some studies have analyzed the influence of different factors on roadway excavation, for example, Peng et al. [43] studied the influence of the ground stress and the roadway area on the damage zone of the roadway excavation. Zhong-Cheng et al. [44] investigated the influence of different geotechnical parameters on roadway deformation and damage by carrying out orthogonal numerical simulation experiments and concluded that the influence of various factors on roadway deformation is in the following order of significance: cohesion > tensile strength > elasticity modulus > internal friction angle > Poisson’s ratio. In addition, there have been studies on the grid size effect [45-47], but they have not been extended to the engineering scale of the roadway excavation. Most of these studies focus on the effect of one or more factors, which may not provide readers with more comprehensive and intuitive help. To the best of our knowledge, nothing like this paper has been reported. Therefore, the results of this paper may provide researchers or engineers with more comprehensive guidance and reference for numerical simulation.The factors discussed in this paper are not only limited to geotechnical and construction parameters but also involve some modeling parameters (Figure 17). The results of this study show that the impacts of roadway excavation on rock mass are not only affected by “direct” parameters such as geotechnical and construction parameters but also by modeling parameters such as model size and zone amount. Even the effects of these modeling factors are as strong as those of geotechnical and construction parameters, but they are often “neglected.” For example, when the model size was increased from 20 × 20 × 20 m to 70 × 70 × 70 m, the displacement in the model decreased by 21%, and the stress increased by 38%, while all other parameters were kept constant (Figure 5). When the number of meshes was increased by about three times (from 320,000 to 972,000 considering the self-gravity), the displacement in the model increased by 31%, and the horizontal stress increased by 55% (Figure 6). When the mesh gradient coefficient was increased from 0.8 to 1.4, the displacement in the model doubled by about six times, and the horizontal and vertical stresses were reduced by 50% and 58%, respectively (Figure 7). The effect of such a change on the results is significant. Therefore, when using numerical simulation to study a particular problem, parameter calibration should be performed first, and once all parameters are calibrated, no further changes should be made to parameters other than those of the study objective, or this may lead to significant deviations in the results.The purpose of conducting numerical simulations is mostly to get regular conclusions (of course, there are some studies to get specific values, at which time it is necessary to try to guarantee that each simulation parameter is consistent with the actual parameter), so some parameters can be simplified appropriately. For example, in reality, the geotechnical body is a nonhomogeneous material, and its parameters cannot be as homogeneous as in common numerical models [48], but assuming its parameters as homogeneous, which has almost no effect on the simulation results (Figure 8). Similarly, the excavation of the roadway can be performed by using commands such as “assign null” and “relax excavation.” Theoretically, “relax excavation” is more in line with the actual excavation process, but “assign null” is more commonly used, and the results show that the effect of these two methods on the results is extremely slight, so the excavation pattern may not interfere with the results more significantly (Figure 9).In addition, the roadway area (Figure 10), roadway shape (Figure 11), in situ stress (Figure 13), and lateral stress coefficient (Figure 14) all have a more significant effect on the displacements and stresses of the model. The type of constitutive model, on the other hand, determines the various parameters required for the simulation and has an extremely significant effect on the results (Figure 15). At the same time, different geotechnical parameters based on the M-C constitutive model have different effects on the tunneling process and may even lead to a certain arching of the stress (horizontal) distribution characteristics (Figure 18), but this phenomenon has not been reported to the best of our knowledge, perhaps because the cohesion of the rock mass in practical engineering is difficult to reach 10 MPa.A variety of factors can have a significant impact on the simulation results, and the stress and displacement with the change of the influencing factors show different patterns, but in most cases, the change rule of displacement and stress is opposite (Figures 5,7,9-11,15,16(e), (f) and (g), and in a small number of cases, the change rule of displacement and stress is consistent (Figures 6, 13, 14 and 16(d)), and there are a few cases in which stress is not affected, only displacement changes (Figure 16(b) and (c)). This phenomenon still needs to be further analyzed.In this paper, a large number of simulation experiments are carried out to visualize the influence of different factors on the simulation results, which may be able to provide a reference for the parameter design and adjustment in numerical simulation research. Generally speaking, the simulation results are affected by many factors; even the zone amount and model size, which are often neglected, will have a great influence on the simulation results. Therefore, when the research is carried out through numerical simulation, it is very necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and at the same time, it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.In addition, the design of the schemes in the study is based on the author’s experience, and to further reflect the influence of the parameters on the results, the designed parameter values may exceed the limits that can be observed in practical engineering. Moreover, due to the rich variety of factors studied in the article, an in-depth and detailed analysis of each set of simulation results is difficult to be carried out; thus, the paper only briefly discusses the pattern of the results.Aiming at the challenges in the numerical simulation process, a brief survey and analysis of simulation software in the field of geotechnical engineering were carried out first, followed by designing more than 100 sets of research scenarios based on FLAC3D to analyze the influence of various factors on the stability of the roadway excavation with the roadway excavation as the engineering background. The main conclusions are as follows:Through searching and analyzing the literature, we found that FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” or “tunnel.” A brief introduction to the software is given, and the suggested steps to carry out the hydrostatic simulation are given.The simulation results show that there is a significant difference in the influence of different parameters on the simulation results. The ones with greater influence are model size, zone amount, mesh gradient coefficient, roadway area, roadway shape, lateral stress coefficient, constitutive model, elasticity modulus, dilatancy angle, cohesion, and internal friction angle; a little influence: excavation mode, cyclic footage, tensile strength, and Poisson’s ratio; trifling influence: parameter uniformity and density.A variety of factors can have a significant effect on the simulation results, and the stress and displacement show different patterns with the changes of the influencing factors, but in most cases, the trend of displacement and stress is the opposite. In addition, even neglected factors (e.g., mesh density, model size, etc.) can have a significant impact on the simulation results. Therefore, when researching through numerical simulation, it is necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.Through searching and analyzing the literature, we found that FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” or “tunnel.” A brief introduction to the software is given, and the suggested steps to carry out the hydrostatic simulation are given.The simulation results show that there is a significant difference in the influence of different parameters on the simulation results. The ones with greater influence are model size, zone amount, mesh gradient coefficient, roadway area, roadway shape, lateral stress coefficient, constitutive model, elasticity modulus, dilatancy angle, cohesion, and internal friction angle; a little influence: excavation mode, cyclic footage, tensile strength, and Poisson’s ratio; trifling influence: parameter uniformity and density.A variety of factors can have a significant effect on the simulation results, and the stress and displacement show different patterns with the changes of the influencing factors, but in most cases, the trend of displacement and stress is the opposite. In addition, even neglected factors (e.g., mesh density, model size, etc.) can have a significant impact on the simulation results. Therefore, when researching through numerical simulation, it is necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy restrictions.The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.This work was financially supported by the Key Project of Education Department of Hunan Province (22A0293), the General Project of Education Department of Hunan Province (22C0235), and the Postgraduate Scientific Research Innovation Project of Hunan Province (QL20220213).\",\"PeriodicalId\":18147,\"journal\":{\"name\":\"Lithosphere\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lithosphere\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://doi.org/10.2113/2024/lithosphere_2023_219\",\"RegionNum\":4,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"GEOCHEMISTRY & GEOPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lithosphere","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.2113/2024/lithosphere_2023_219","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
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摘要

大型通用数值模拟软件,如 ANSYS、ABAQUS、MIDAS 等,在 GS 中检索到的论文总数超过 20 万篇。其中,FLAC3D(约 34500 篇)多于 FLAC2D(约 5950 篇),由此可见,目前 FLAC 中三维版本的使用频率高于二维版本。图 3 展示了 FLAC 在 "路基 "或 "隧道 "领域的广泛应用情况。"综上所述,FLAC3D 在岩土工程领域,尤其是在 "路基 "和 "隧道 "领域得到了广泛的应用,因此,研究(FLAC3D 中)各种因素对隧道掘进过程稳定性的影响具有重要的工程意义和理论价值,也为众多仿真软件的初学者提供了指导和帮助。"FLAC3D 是一种有限差分数值程序,在数学上采用快速拉格朗日法。其中,FDM 是一种求偏微分方程和方程系统定值问题数值解的方法[39, 40]。FDM 的基本思想是将问题的定义域离散成网格(区),然后在网格点上,根据适当的数值离散化公式,用差商代替定值问题中的微分商,从而将问题离散成不同的格式,进而得到数值解。这种方法易于在计算机上实现,因此被广泛使用[41]。快速拉格朗日法[42]是一种基于显式差分的分步求解方法,可以得到模型的所有运动方程和构成方程,其构成方程由基本的应力应变定义和胡克定律导出,而运动平衡方程则直接应用于考希运动方程(由牛顿运动定律导出)。其计算模型一般由多个不同形状的三维单元组成,即剖分的空间单元网格区域,每个单元在计算中又被划分为由四个节点组成的四面体,四面体的应力应变只通过四个节点传递给其他四面体,再由其他四面体传递给其他单元。当对一个节点施加载荷时,作用于该点的载荷只会在极短的时间内影响周围的几个节点(相邻节点)。利用运动方程,可以根据单元节点的速度和时间变化计算出单元之间的相对位移,进而得出单元应变,然后利用单元的构成模型计算出单元应力。在计算应变的过程中,利用高斯积分理论将三维问题转化为二维问题,从而简化了三维问题。在运动方程中,还充分考虑了岩土体的粘滞性,将其视为附加在方程中的阻尼。"巷道 "和 "隧道"(后续均称为:巷道)的开挖模拟,根据《FLAC3D 用户帮助手册》和笔者对软件的实践经验,可分为以下几个阶段,如图 4 所示。在 "FLAC3D 用户帮助手册 "中,静力学模拟过程大致分为十四个阶段。项目规划和设置 "部分包含另外七个步骤,"提示和建议 "部分也给出了十三条提示和建议。模型由 FLAC3D 的内置命令流生成,部分特殊断面巷道模型由 Rhino 生成。为研究不同因素对巷道掘进过程稳定性的影响,采用某一初始模型及其初始参数作为基线组(对照组)。为避免无关因素的干扰,对基准组模型做了如下假设:(1) 不考虑岩体分层现象;(2) 忽略岩体缺陷,如断裂带、节理、裂隙等,模型为均质地质体;(3) 在模型表面垂直施加地应力。固定模型的底面、左面、右面、正面和背面,在除底面以外的所有面上均匀施加 30 MPa 的压应力,模型收敛后位移和塑性区归零。随后,根据研究内容,进行相应的开挖模拟,在模型最大不平衡力为 1×10 - 5(软件默认收敛条件)时停止计算(部分模拟程序下模型无法收敛,计算步数为 5000 步)。 特别是 MSC 构成模型(采用 FLAC3D 案例中常用的软化系数),尽管软化前的参数与 M-C 构成模型的参数一致,但通道位移值明显高于其他构成模型。岩土体的物理力学参数(以下简称岩土参数)是工程设计中需要考虑的最关键因素之一。在数值模拟中,不同的构成模型需要不同的岩土参数,可根据不同的工程特点和工程要求选择不同的构成模型。M-C 构成模型是岩土体最常用的构成模型之一。所需的参数包括弹性模量、抗拉强度、膨胀角、内聚力、内摩擦角和泊松比,此外还需要围岩的密度。图 16 显示了共七个影响因素和九十四组模拟方案的模拟结果。对于应力,有些因素基本没有影响,如密度、弹性模量、抗拉强度和膨胀角。应力随着泊松比的增大而缓慢上升;此外,应力随着内聚力和内摩擦角的增大而波动,但总体呈上升趋势。对于位移,密度也基本上没有影响。大多数因素(弹性模量、抗拉强度、内聚力和内摩擦角)的增长都会导致位移呈现先减小后趋于平稳的模式。数值模拟已成为解决复杂工程问题不可或缺的手段,而合理的参数设置是保证数值模拟结果可靠性的关键。本文以隧道开挖为工程背景,以 FLAC3D 为研究对象,探讨各种因素对仿真结果的影响。虽然有一些研究分析了不同因素对巷道开挖的影响,如彭晓明等[43]研究了地应力和巷道面积对巷道开挖破坏区的影响。Zhong-Cheng 等人[44]通过正交数值模拟实验研究了不同岩土参数对路基变形和破坏的影响,认为各种因素对路基变形的影响程度依次为:内聚力 > 抗拉强度 > 弹性模量 > 内摩擦角 > 泊松比。此外,也有关于网格尺寸效应的研究 [45-47],但尚未扩展到路基开挖的工程规模。这些研究大多侧重于一个或多个因素的影响,可能无法为读者提供更全面、更直观的帮助。据我们所知,还没有类似本文的报道。因此,本文的研究结果可以为研究人员或工程师的数值模拟提供更全面的指导和参考。本文讨论的因素不仅限于岩土工程和建筑参数,还涉及一些建模参数(图 17)。研究结果表明,巷道开挖对岩体的影响不仅受岩土工程参数和施工参数等 "直接 "参数的影响,还受模型尺寸和分区量等建模参数的影响。即使这些建模因素的影响与岩土工程和施工参数的影响一样大,但它们往往被 "忽略"。例如,当模型尺寸从 20 × 20 × 20 m 增加到 70 × 70 × 70 m 时,在其他参数保持不变的情况下,模型中的位移减少了 21%,应力增加了 38%(图 5)。当网格数增加约三倍时(考虑到自重力,从 32 万增加到 97.2 万),模型的位移增加了 31%,水平应力增加了 55%(图 6)。当网格梯度系数从 0.8 增加到 1.4 时,模型的位移增加了约六倍,水平应力和垂直应力分别减少了 50%和 58%(图 7)。这种变化对结果的影响是显著的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Effect of Multiple Factors for the Roadway Excavation Process Stability in FLAC3D
Appropriate simulation set parameters are the precondition to obtain accurate results; while the simulation results are affected by multiple factors, it is thus crucial to investigate the sensibility of different factors. This paper first analyses the application situation of numerical simulation software in the field of geotechnical engineering and finds that Fast Lagrangian analysis of continua in three dimensions (FLAC3D) has been widely used on roadways or tunnels. Then, taking the roadway excavation process as the engineering background, FLAC3D was used to create 171 schemes of different simulation parameters and analyze the influence of different factors on the simulation results. The findings show that there is a considerable difference in the degree of effect of different parameters on the simulation results. Most of the factors have a remarkable effect on the numerical simulation results (displacement and stress), and only some factors (parameter uniformity and density) have almost no effect on the results. Meanwhile, the trend of displacement and stress is opposite in most cases. In addition, some neglected factors can also have a considerable effect on the simulation results, such as the zone amount; therefore, it is necessary to avoid the variation of nonstudy factors as possible when carrying out the numerical simulation. This study may significantly assist concerned engineers and technicians in developing a more organized and thorough grasp of the impacts of various parameters on simulation outcomes.The challenges of mining underground mineral resources have grown increasingly difficult and dangerous due to the increasing depth of mining. Numerous researchers have conducted studies to address these challenges that limit the safe and effective production of mines, from the appearance [1, 2] to the essence [3, 4], from the Macro [5, 6] to the Microscopic [7, 8] to the Micro [9, 10] structures, and from the single physical field [11, 12] to multiple physical coupling field [13, 14], and there have been many outcomes. Nevertheless, the complex and variable environment of underground roadways makes it difficult for traditional theoretical analyses [15, 16] to resolve a specific complex engineering problem, and it is laborious and time-consuming to conduct scaled physical simulation tests [17, 18], and it is difficult to reproduce overly complex scenarios, and the accuracy of the obtained results cannot be guaranteed. As the understanding of the properties of geotechnical materials grows and computers continue to develop, computational mechanics [19] is in a flourishing stage. Considering the mutual coupling relationship between various fields, computational mechanics, an emerging interdisciplinary discipline, has significant advantages in processing practice engineering problems. Numerical simulation code based on computational mechanics can simulate approximate object comprehensions for almost any complex operating conditions. At present, the common numerical simulation methods are Finite Element Method [20] (FEM), Finite Difference Method [21] (FDM), Discrete Element Method [22], Boundary Element Method [23], and so on. Among them, due to its precision and speed, the Fast Lagrangian analysis of continua in three dimensions (FLAC3D) [24], a representative of the FDM, has emerged as one of the most popular numerical simulation software.Researchers and technicians have conducted a large number of simulation studies on roadway/tunnel excavation using FLAC3D. Unlu et al. [25] used FLAC3D to determine the variation rule of the radial boundary displacement along the longitudinal direction of a circular tunnel located in the initial stress field, and based on the deformation behavior of linear elastic materials, the expression for the radial displacement of the tunnel excavation surface was obtained by nonlinear curve fitting. Xiao et al. [26] based on the internal stress field distribution law of coal rock in the process of mine roadway excavation obtained by FLAC3D, combined with the force-electricity coupling relationship equation between the electromagnetic radiation intensity generated in the process of compression and deformation and rupture of the coal rock and the internal stress of the coal rock, and researched the change rule of the electromagnetic emission (EME) signals generated in the process of roadway excavation. Meng et al. [27, 28] used FLAC3D to simulate the rheological characteristics of a deep high-stress soft rock tunnel, analyzed the rheological deformation law of the top plate, bottom plate, and two gangs of the surrounding rock of the soft rock tunnel under the action of high stress, and obtained the depth of burial of the tunnel-time creep curve, lateral pressure coefficient-time creep curve, elasticity modulus-time creep curve, and hysteresis coefficient-time creep curve. Suo et al. [29] applied FLAC3D to analyze the plastic damage of the tunnel when the inner, overlapping, and outer staggered arrangement of the working face of the coal seam tunnel under the very close coal seam group, and the plastic damage of the tunnel, the vertical stress of the top plate, and the sinking displacement of the top plate. Niu et al. [30] established a strength attenuation model for the ruptured perimeter rock of a deep tunnel and implanted the model into FLAC3D to verify the reasonableness of the established model. Pongpanya et al. [31] used FLAC3D to study the damage behavior of the roadway at different depths of overburden and found that factors such as the depth of excavation, the bearing capacity of the support system, and the depth of overburden are closely related to the plastic zone of the roadway. Zuo et al. [32] used FLAC3D to obtain the distribution law of roof stress and displacement under anchor support and equal-strength beam support and found that the use of the concept of equal-strength beam support can significantly optimize the distribution of stress in the roadway so that the local stress in the roof plate shows a uniform state, and the deformation of the surrounding rock is effectively controlled, which verifies the feasibility of the equal-strength beam support technology. Xue et al. [33] proposed a comprehensive mining roadway over-support program using automatic support and anchor combination unit based on FLAC, described the structure and working principle of the support robot, and proposed a method for determining the working resistance of the over-support bracket based on the over-support bracket peripheral rock mechanics coupling model. Dibavar et al. [34] focused on the effect of longitudinal and transverse spacing on the stability of tunnels with “umbrella arch” support and proposed to keep the longitudinal and transverse spacing more than 2.5 times the diameter of the tunnel. Wang et al. [35] compiled a command flow for energy dissipation to realize the secondary development of FLAC3D strain softening constitutive model, which extends the energy calculation module of FLAC3D. Mahmoudi et al. [36] used FLAC3D to model tunnels adjacent to caverns and investigated the effect of location, size, distance, shape, and arrangement of the caverns on the displacements, bending moments, and axial forces in the tunnel lining. Wu et al. [37] used FLAC3D software to conduct stability analysis of five different section-shape tunnel models under the conditions of no support and different base-angle support angles and carried out simulation verification under the actual working conditions of the Sanshandao gold mine.In conclusion, although FLAC3D has been widely applied, most of the literature focuses on the use of the software to solve a specific problem but seldom focuses on the proper use of the tool itself. For beginners, how to set up various parameters in the simulation (not only geotechnical parameters) to obtain accurate and reliable simulation results has always been a problem for them. Therefore, in this paper, we designed 171 simulation scenarios based on the engineering background of roadway excavation (FLAC3D-based) and comprehensively and systematically explored the influence of twelve factors on the numerical simulation results, which can provide a careful reference for many FLAC3D users to design and adjust the parameters.FLAC3D was created by Cundall et al. and is widely applied in geotechnical and mining engineering analysis and design at present [24]. It is a 3D numerical analysis code that was developed based on continuous medium theory and explicit FDM. FLAC3D is especially well suited for dealing with FEM difficult-to-solve complex geotechnical subjects, typically such as complex multiconditions, large deformation, nonlinear material behavior, occurrence, and development of destabilization damage [38]. Therefore, FLAC3D is a well-suited numerical simulation software for underground subterranean works.The numerical simulation section of the China Geotechnical Forum (aka YanTuBBS) was surveyed, and the more active sections (those with more than 1000 posts) were statistically analyzed (Figure 1). FLAC is the most active section of them all (over 40% of the total). The literature search engines Google Scholar (GS), Web of Science (WOS), China National Knowledge Infrastructure (CNKI), and WanFang Academic Search System (WFASS) were used for keyword retrieval. Where WOS, an English literature search engine, only used the keywords “roadway” and “tunnel,” whereas CNKI and WFASS, Chinese literature search engines, only used the keywords “巷道” and “隧道” (i.e., “roadway” and “tunnel” in Chinese). GS is a literature search engine with mixed, and the outcomes are derived by applying logical operators like “AND/OR” to the search terms. Due to the different operating principles of each search engine, GS obtained the highest number of documents, while WOS obtained the least (Figure 2). The Large general numerical simulation software such as ANSYS, ABAQUS, MIDAS, and so on retrieves the papers in GS totaling more than 200,000. FLAC3D (about 34,500) is larger than FLAC2D (about 5950), so it can be seen that the 3D version is currently being used more frequently than its 2D counterpart in FLAC. Figure 3 demonstrates how FLAC is widely utilized in the field of “roadway” or “tunnel.”In summary, FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” and “tunnel” Therefore, it is of great engineering significance and theoretical value to study the influence of various factors (in FLAC3D) on the stability of the tunneling process and to provide guidance and help for the beginners of many simulation software.FLAC3D is a finite difference numerical program, which mathematically uses the fast Lagrangian method. Among them, the FDM is a method for finding numerical solutions to definite problems of partial differential equations and systems of equations [39, 40]. The basic idea of FDM is to discretize the problem’s defining domain into a mesh (zone) and then, at the gridpoints, replace the differential quotient in the definite problem with the difference quotient according to the appropriate numerical discretization formulas, thus discretizing the problem into a different format, which in turn leads to a numerical solution. This method is widely used because it is easy to implement on computers [41]. The fast Lagrangian method [42] is a stepwise solution based on explicit differencing to obtain all the equations of motion and constitutive equations of the model, whose constitutive equations are derived from the basic stress-strain definitions and Hooke’s law, while the equations of equilibrium of motion are directly applied to the Cauchy equations of motion (which are derived from Newton’s law of motion). Its computational model is generally composed of several different shapes of three-dimensional units, that is, the dissected spatial unit mesh area, and each unit is further divided into tetrahedra consisting of four nodes in the computation, and the stress-strain of the tetrahedra is only transferred to the other tetrahedra through the four nodes, which is then transferred to other units. When a load is applied to a node, the load acting at that point only affects several surrounding nodes (neighboring nodes) for a tiny period. Using the equations of motion, the relative displacements between the units can be calculated based on the change in velocity and time of the unit nodes, which in turn leads to the unit strains, and then using the constitutive model of the unit, the unit stresses can be calculated. In the process of calculating the strain, the Gaussian integral theory is utilized to simplify the three-dimensional problem by transforming it into a two-dimensional problem. In the equation of motion, the viscosity of the geotechnical body is also fully considered, which is regarded as damping attached to the equation.The “roadway” and “tunnel” (the follow-up is all called: roadway) excavation simulation can be broken down into the following phases, as indicated in Figure 4, depending on the “FLAC3D user help manual” and the author’s practical experience with the software. The simulation process of statics is roughly divided in the “FLAC3D user help manual” into fourteen phases. The “Project Planning and Setup” section contains another seven steps, and the “Tips and Advice” section also gives thirteen tips and advice. Without going into the details of each section, readers can refer to the “FLAC3D help” section of FLAC3D for more specific information.The models are generated by the built-in command flow of FLAC3D, and some special section-shaped roadway models are generated by Rhino. To study the influence of different factors on the stability of the roadway excavation process, a certain initial model and its initial parameters are used as the baseline group (control group). To avoid the interference of irrelevant factors, the following assumptions are made for the model of the benchmark group: (1) the phenomenon of rock mass layering is not considered; (2) rock mass defects, such as fracture zones, joints, and fissures, are ignored, and the model is a homogeneous geological body; and (3) the geostress is applied perpendicularly on the surface of the model. The bottom, left, right, front, and rear faces of the model were fixed, and a compressive stress of 30 MPa was uniformly applied to all the faces except the bottom, and the displacement and plastic zones were zeroed after the model converged. Subsequently, according to the content of the study, to carry out the corresponding excavation simulation, the maximum unbalanced force in the model is 1 × 10 − 5 (the default convergence conditions of the software) to stop the calculation (part of the simulation program under the model cannot be converged, the calculation of 5000 steps).A total of twelve primary types and 171 groups of simulation test scenarios were created based on the baseline group by changing various factors. Due to the large number of scenarios, this section does not provide a detailed description of each set of scenario parameters. The parameters of the baseline group model and the specific simulation scenarios are shown in Table 1, and the scenario parameters that are not specifically described are the baseline group model parameters for variable control in this study. In addition, the displacement and stress results of the analysis section are the maximum value in the model (or in different directions). The analysis of the results is carried out in terms of displacement and stress.The model size is the overall size (length, width, and height) of the numerical model created, and its value mainly relates to the influence of boundary effects. Figure 5 shows the simulation results in fourteen schemes of model size (with seven model sizes in two conditions of considering gravity and did not consider). The roadway could not converge when the model size is 10 × 10 × 10 m due to the roadway outline being too near to the model boundary. The displacement of the roadway tends to gradually decrease with the increase in model size. On the contrary, the stress in the model tends to gradually increase as the model size increases. Additionally, when gravity is considered, the displacement and stress in the model are slightly higher than gravity, which is not considered.In FLAC3D, the model is mainly composed of zones and gridpoints, and the more zones there are, the more time is needed for computation. Figure 6 exhibits the simulation results in four schemes of zone amount. The displacement and stress in the model tend to gradually increase with the increase in zone amount. It should be noted that the vertical stress is higher than the horizontal stress in terms of the magnitude of the increase.A common strategy used in simulations is to encrypt the mesh (zone) attached to the important region to improve computational accuracy. Here, the mesh gradient coefficient is the degree to which the mesh is gradually encrypted from the model boundary to the roadway outline. Figure 7 expresses the simulation results in seven schemes of mesh gradient coefficient. The displacement of the roadway tends to increase as the mesh gradient coefficient increases. The stress in the model is to decrease and then level off as the mesh gradient coefficient increases; the vertical stress is a little higher than the horizontal stress.Metallic materials have a uniform distribution of physical and mechanical parameters, whereas rock mass is a nonhomogeneous material. However, the usual simulation treats the rock mass as a homogeneous material and assigns it to uniform parameters. Here, the Gaussian distribution command was utilized to assign nonuniform values to the rock mass material. Figure 8 demonstrates the simulation results in five schemes of Gaussian distribution rate. As the Gaussian distribution rate increases (within 10%), the displacement and stress in the model remain essentially unchanged.There are two main ways to excavate a roadway in FLAC3D: one way is to use the “null” command to “excavate” the roadway, which is a kind of sudden change; the other way is to use the “relax excavate” command, which gradually reduces the physical–mechanical parameters in the region, which is a kind of slow change, which can avoid the interference of inertia effect on the result due to sudden change to a certain extent. In practical engineering, tunnel excavation is a “slow” process, but the “null” command is commonly used for simulation. Figure 9 displays the simulation results in two schemes of excavation mode. When “relax excavate” is used, the displacement in the model can be reduced by about 4.5%, and the stress can be increased by about 7.5% compared with “null.” The excavation mode has a slight effect on the simulation results.The cross-sectional area of the roadway is one of the direct factors concerning the stability of excavation. Therefore, many studies on the stability of the roadway directly focus on the roadway span and height (area) as the key considerations. Figure 10 manifests the simulation results in seven schemes of roadway area (rectangle). As the area of the roadway increases, the displacement in the roadway continues to grow in an approximately linear fashion. The stress is decreasing, the rate of stress decreases is also decreasing. In addition, the values of vertical and horizontal stresses converge as the area of the roadway increases.The shape of the roadway is a key factor affecting the state of geostress redistribution after excavation. Here, based on engineering experience, the study was carried out with typical six shapes of roadway sections. In addition, the model built in this section was generated by Rhino software (which also utilized the griddle plug-in to optimize the mesh), and the zone amount and so on were inevitably disturbed, so it was difficult to keep consistent with the baseline group. For this reason, the model size (changed to 50 × 50 × 5.5 m) and the cyclic footage (changed to 5.5 m) were also changed to speed up the simulation process. Figure 11 indicates the simulation results in six schemes of roadway shape. For the displacements, overall, the displacements of the sidewall of the roadway are generally larger than the other positions, while the horizontal displacements are generally slightly larger than the vertical displacements, in addition to the overall displacements: rectangle > trapezoid > straight wall semicircular arch > horseshoe > three-center arch > round. When the stress law is opposite to it, the stress of the roadway shape schemes with large displacement is relatively small.The cyclic footage is the length of the roadway or tunnel that is excavated at one time during the boring process. Figure 12 shows the simulation results for eight cyclic feed scenarios (four of the cyclic footage lengths under two stopping calculation conditions, the maximum imbalance force reaches 1 × 10−5, or a total of 2000 steps are calculated). The displacements in the model are generally greater when the maximum unbalanced force is used as the convergence condition than when the computational step is used as the convergence condition. This is because the model needs to be calculated after each excavation until equilibrium, so the cumulative steps for the convergence condition of maximum unbalanced force are significantly higher than 2000. Hence, the displacement values are larger for the scheme with maximum unbalanced force as the convergence condition. It should be noted that the stress values in the model are very little affected by this factor. In addition, the effect of cyclic footage on the simulation results is “fluctuating, not simply increasing or decreasing, suggesting that there may be an optimal value for cyclic footage within the simulation range. At the same time, the effect of cyclic footage on the results is relatively slight.The in situ stresses are natural stresses present in the earth’s crust that have not been disturbed by engineering, whose values are influenced by many factors (one of the main ones being the depth of burial) and are at the heart of underground engineering hazards, such as rockburst, collapse, and so on, which are also known as stress-induced hazards. Figure 13 illustrates the simulation results for twelve in situ stress values. The displacement of the roadway increases as the in situ stress increases (as the in situ stress increases, the increase in the rate of displacement is also growing), and the stress in the model also increases. A gentler phase exists at about 30 MPa and before a significant and sustained increase begins at about 40 MPa. In addition, as the in situ stresses exceed 40 MPa, the vertical stresses also begin to be significantly greater than the horizontal stresses.The formation of the in situ stress field is influenced by a variety of factors, such as self-gravity stress, tectonic stress, and residual stress, and presents an extremely complex state. Therefore, the values of horizontal and vertical stresses are often different. The lateral stress coefficient is defined as the ratio of horizontal stress to vertical stress. Figure 14 shows the simulation results for eight lateral stress coefficients. The overall displacement of the roadway roughly increases with the growth of the lateral stress coefficient. In particular, when the lateral stress coefficient is small, the displacement of the sidewall of the roadway is larger than that at the floor, and with the increase of the lateral stress coefficient ( >1.0), the displacement at the floor begins to be larger than that at the sidewall, the horizontal stress begins to be larger than that at the vertical stress, and the vertical stress and the maximum shear stress tend to be gradually stabilized.A constitutive model, also known as the mechanical constitutive equation of a material, or the stress-strain model of a material, is a mathematical expression that describes the mechanical properties of a material (stress-strain-strength-time relationship). Currently, the M-C and H-B constitutive models are the most commonly used regarding the simulation of engineering scales (geotechnical). To be able to compare the influence of these constitutive models on the simulation results to a certain extent, we have chosen to analyze only the constitutive models with some of the same parameters (Elastic/E, Mohr–Coulomb/M-C, and Mohr–Coulomb strain softening/MSC). Figure 15 shows the simulation results for three constitutive models. It can be seen that the effect of the constitutive model on the simulation results is prominent. Especially for the MSC constitutive model (using the softening coefficients commonly used in the FLAC3D case), the values of the channel displacements are significantly higher than those of other constitutive models, even though the parameters before softening are consistent with those of the M-C constitutive model.The physical–mechanical parameters of a geotechnical body (hereafter referred to as geotechnical parameters) are one of the most crucial factors to be considered in engineering design. In numerical simulation, different constitutive models require different geotechnical parameters, and different constitutive models can be selected according to different engineering characteristics and engineering requirements. The M-C constitutive model is one of the most commonly applied constitutive models for geotechnical bodies. The required parameters are elasticity modulus, tensile strength, dilatancy angle, cohesion, internal friction angle, and Poisson’s ratio in addition to the density of the surrounding rock is also necessary. Figure 16 displays the simulation results for a total of seven influencing factors and ninety-four sets of simulation scenarios.For the stress, some factors have essentially no effect on it, such as density, elasticity modulus, tensile strength, and dilatancy angle. The stress has increased gently and slowly with the Poisson’s ratio growth; additionally, the stress fluctuates but has a total rising trend with the cohesion and internal friction angle enlarging. For the displacement, the density also has essentially no effect on it. The growth of most factors (elasticity modulus, tensile strength, cohesion, and internal friction angle) causes the displacement to show a pattern of decreasing and then leveling off. In addition, an increase in dilatancy angle leads to an increase in displacement, while a growth in Poisson’s ratio causes the displacement to fluctuate within a small range.Numerical simulation has become an indispensable means to solve complex engineering problems, and reasonable setting parameters are the key to guaranteeing the reliability of numerical simulation results. In this paper, we take the tunnel excavation as the engineering background and FLAC3D as the research object to explore the effect of various factors on the simulation results. Although some studies have analyzed the influence of different factors on roadway excavation, for example, Peng et al. [43] studied the influence of the ground stress and the roadway area on the damage zone of the roadway excavation. Zhong-Cheng et al. [44] investigated the influence of different geotechnical parameters on roadway deformation and damage by carrying out orthogonal numerical simulation experiments and concluded that the influence of various factors on roadway deformation is in the following order of significance: cohesion > tensile strength > elasticity modulus > internal friction angle > Poisson’s ratio. In addition, there have been studies on the grid size effect [45-47], but they have not been extended to the engineering scale of the roadway excavation. Most of these studies focus on the effect of one or more factors, which may not provide readers with more comprehensive and intuitive help. To the best of our knowledge, nothing like this paper has been reported. Therefore, the results of this paper may provide researchers or engineers with more comprehensive guidance and reference for numerical simulation.The factors discussed in this paper are not only limited to geotechnical and construction parameters but also involve some modeling parameters (Figure 17). The results of this study show that the impacts of roadway excavation on rock mass are not only affected by “direct” parameters such as geotechnical and construction parameters but also by modeling parameters such as model size and zone amount. Even the effects of these modeling factors are as strong as those of geotechnical and construction parameters, but they are often “neglected.” For example, when the model size was increased from 20 × 20 × 20 m to 70 × 70 × 70 m, the displacement in the model decreased by 21%, and the stress increased by 38%, while all other parameters were kept constant (Figure 5). When the number of meshes was increased by about three times (from 320,000 to 972,000 considering the self-gravity), the displacement in the model increased by 31%, and the horizontal stress increased by 55% (Figure 6). When the mesh gradient coefficient was increased from 0.8 to 1.4, the displacement in the model doubled by about six times, and the horizontal and vertical stresses were reduced by 50% and 58%, respectively (Figure 7). The effect of such a change on the results is significant. Therefore, when using numerical simulation to study a particular problem, parameter calibration should be performed first, and once all parameters are calibrated, no further changes should be made to parameters other than those of the study objective, or this may lead to significant deviations in the results.The purpose of conducting numerical simulations is mostly to get regular conclusions (of course, there are some studies to get specific values, at which time it is necessary to try to guarantee that each simulation parameter is consistent with the actual parameter), so some parameters can be simplified appropriately. For example, in reality, the geotechnical body is a nonhomogeneous material, and its parameters cannot be as homogeneous as in common numerical models [48], but assuming its parameters as homogeneous, which has almost no effect on the simulation results (Figure 8). Similarly, the excavation of the roadway can be performed by using commands such as “assign null” and “relax excavation.” Theoretically, “relax excavation” is more in line with the actual excavation process, but “assign null” is more commonly used, and the results show that the effect of these two methods on the results is extremely slight, so the excavation pattern may not interfere with the results more significantly (Figure 9).In addition, the roadway area (Figure 10), roadway shape (Figure 11), in situ stress (Figure 13), and lateral stress coefficient (Figure 14) all have a more significant effect on the displacements and stresses of the model. The type of constitutive model, on the other hand, determines the various parameters required for the simulation and has an extremely significant effect on the results (Figure 15). At the same time, different geotechnical parameters based on the M-C constitutive model have different effects on the tunneling process and may even lead to a certain arching of the stress (horizontal) distribution characteristics (Figure 18), but this phenomenon has not been reported to the best of our knowledge, perhaps because the cohesion of the rock mass in practical engineering is difficult to reach 10 MPa.A variety of factors can have a significant impact on the simulation results, and the stress and displacement with the change of the influencing factors show different patterns, but in most cases, the change rule of displacement and stress is opposite (Figures 5,7,9-11,15,16(e), (f) and (g), and in a small number of cases, the change rule of displacement and stress is consistent (Figures 6, 13, 14 and 16(d)), and there are a few cases in which stress is not affected, only displacement changes (Figure 16(b) and (c)). This phenomenon still needs to be further analyzed.In this paper, a large number of simulation experiments are carried out to visualize the influence of different factors on the simulation results, which may be able to provide a reference for the parameter design and adjustment in numerical simulation research. Generally speaking, the simulation results are affected by many factors; even the zone amount and model size, which are often neglected, will have a great influence on the simulation results. Therefore, when the research is carried out through numerical simulation, it is very necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and at the same time, it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.In addition, the design of the schemes in the study is based on the author’s experience, and to further reflect the influence of the parameters on the results, the designed parameter values may exceed the limits that can be observed in practical engineering. Moreover, due to the rich variety of factors studied in the article, an in-depth and detailed analysis of each set of simulation results is difficult to be carried out; thus, the paper only briefly discusses the pattern of the results.Aiming at the challenges in the numerical simulation process, a brief survey and analysis of simulation software in the field of geotechnical engineering were carried out first, followed by designing more than 100 sets of research scenarios based on FLAC3D to analyze the influence of various factors on the stability of the roadway excavation with the roadway excavation as the engineering background. The main conclusions are as follows:Through searching and analyzing the literature, we found that FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” or “tunnel.” A brief introduction to the software is given, and the suggested steps to carry out the hydrostatic simulation are given.The simulation results show that there is a significant difference in the influence of different parameters on the simulation results. The ones with greater influence are model size, zone amount, mesh gradient coefficient, roadway area, roadway shape, lateral stress coefficient, constitutive model, elasticity modulus, dilatancy angle, cohesion, and internal friction angle; a little influence: excavation mode, cyclic footage, tensile strength, and Poisson’s ratio; trifling influence: parameter uniformity and density.A variety of factors can have a significant effect on the simulation results, and the stress and displacement show different patterns with the changes of the influencing factors, but in most cases, the trend of displacement and stress is the opposite. In addition, even neglected factors (e.g., mesh density, model size, etc.) can have a significant impact on the simulation results. Therefore, when researching through numerical simulation, it is necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.Through searching and analyzing the literature, we found that FLAC3D has been widely used in the field of geotechnical engineering, especially in the field of “roadway” or “tunnel.” A brief introduction to the software is given, and the suggested steps to carry out the hydrostatic simulation are given.The simulation results show that there is a significant difference in the influence of different parameters on the simulation results. The ones with greater influence are model size, zone amount, mesh gradient coefficient, roadway area, roadway shape, lateral stress coefficient, constitutive model, elasticity modulus, dilatancy angle, cohesion, and internal friction angle; a little influence: excavation mode, cyclic footage, tensile strength, and Poisson’s ratio; trifling influence: parameter uniformity and density.A variety of factors can have a significant effect on the simulation results, and the stress and displacement show different patterns with the changes of the influencing factors, but in most cases, the trend of displacement and stress is the opposite. In addition, even neglected factors (e.g., mesh density, model size, etc.) can have a significant impact on the simulation results. Therefore, when researching through numerical simulation, it is necessary to carry out a large number of pretests to calibrate the model parameters to obtain realistic simulation results, and it should be pointed out that the calibration is not only about the physical–mechanical parameters of the geotechnical body.The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy restrictions.The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.This work was financially supported by the Key Project of Education Department of Hunan Province (22A0293), the General Project of Education Department of Hunan Province (22C0235), and the Postgraduate Scientific Research Innovation Project of Hunan Province (QL20220213).
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来源期刊
Lithosphere
Lithosphere GEOCHEMISTRY & GEOPHYSICS-GEOLOGY
CiteScore
3.80
自引率
16.70%
发文量
284
审稿时长
>12 weeks
期刊介绍: The open access journal will have an expanded scope covering research in all areas of earth, planetary, and environmental sciences, providing a unique publishing choice for authors in the geoscience community.
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