Acta GeotechnicaPub Date : 2025-06-04DOI: 10.1007/s11440-025-02631-w
Chenchen Qiu, Yujun Cui, Giulia Bossi, Xueyu Geng
{"title":"A physics-informed method for dynamic warning of debris flows in remote areas","authors":"Chenchen Qiu, Yujun Cui, Giulia Bossi, Xueyu Geng","doi":"10.1007/s11440-025-02631-w","DOIUrl":"10.1007/s11440-025-02631-w","url":null,"abstract":"<div><p>A reliable precipitation estimation in mountainous areas plays a critical role in issuing timely warnings for debris flows. However, the scarcity of rainfall gauge stations and the coarse resolution of satellite products pose challenges in developing an effective warning model. To generate precipitation with fine resolution, we need to assess some descriptors of the spatial variability of precipitation called the regional environmental variables (REVs). Physical equations were therefore designed to decide REVs, such as the normalised difference vegetation index (NDVI), normalised difference water index (NDWI), modified soil-adjust vegetation index (MSAVI2), the difference of land surface temperature between daytime and night-time (<span>(Delta text{LST})</span>), and the surface soil moisture (SSM). Then, a deep learning model was developed to establish the relationship between REVs and Global Precipitation Measurement (GPM) daily product, enabling the downscaling of GPM to daily precipitation at a spatial resolution of 1 km. The rain gauge observations were used to calibrate the downscaled results using the geographical differential analysis (GDA) method relying on data from a transition zone between the Tibetan Plateau and Sichuan Basin, China, spanning the year of 2010. After that, event rainfall–duration (<i>E</i>-<i>D</i>) equations were developed using the calibrated rainfall data and then utilised the relationships to improve debris-flow susceptibility to propose a debris-flow warning model in the Luding earthquake-affected area. The results show that: (1) REVs based on a physical equation can effectively reproduce the spatial distribution of precipitation; (2) the calibrated GPM exhibits a substantial improvement, with an average 48.6% reduction in mean absolute error (MAE), a 51.5% decrease in root mean square error (RMSE), and a remarkable 63.9% reduction in mean bias (MB) when compared to original GPM; (3) the newly developed warning model exhibits a better performance than susceptibility map in forecasting debris-flow occurrence. Overall, this model can provide accurate regional-scale alerts for debris flows by overcoming the limitations of susceptibility maps, which are inherently static products.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 7","pages":"3329 - 3348"},"PeriodicalIF":5.7,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11440-025-02631-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-06-03DOI: 10.1007/s11440-025-02653-4
Xu-Wei Wang, Ye-Shuang Xu, Ge Gao
{"title":"Experimental investigation of the critical water head and failure mechanisms leading to uprush hazards in foundation pits","authors":"Xu-Wei Wang, Ye-Shuang Xu, Ge Gao","doi":"10.1007/s11440-025-02653-4","DOIUrl":"10.1007/s11440-025-02653-4","url":null,"abstract":"<div><p>Uprush hazards represent a significant risk in foundation pit engineering, and understanding the failure mechanisms is critical for mitigating environmental impacts. Laboratory tests were conducted to investigate the failure mechanisms of uprush hazards, with a focus on the development process of surface cracks in clay. These tests examined the variations in the thickness of the clay layer underlying the excavation surface (<i>T</i>) and the ratio of the length to the width of the foundation pit (<i>R</i>). The results indicate that the anti-uprush capacity of the pit improves, and surface cracks are more likely to form as <i>T</i> increases. The water head for surface cracks appearance (<i>H</i><sub>C</sub>) increases as <i>T</i> increases and same as the critical water head for uprush hazards occurrence (<i>H</i><sub>U</sub>). The maximum vertical deformation of the clay at the central point inside the pit during the test process (<i>D</i><sub>m1</sub>) is constrained by comprehensive effect of the shorter and longer walls of pit, and all peak values of <i>D</i><sub>m1</sub> were observed in tests where <i>R</i> equaled to 2 among all test types. Pit with this shape is advantageous for preventing uprush hazards, as it allows early warning in the process of surface crack development. Two distinct failure modes were identified based on the degree of deformation and the distribution of cracks. Failure Mode-1, characterized by non-fully developed deformation of the clay, represents a localized seepage failure without cracks, culminating in uprush or inrush hazards. In contrast, failure Mode-2 is a general failure accompanied by fully developed deformation and prominent cracks. Mode-2 was further subdivided into Mode-2a, in which surface cracks were concentrated near the central position, and Mode-2b, in which cracks were distributed along the wall sides. These findings provide potential failure modes of uprush hazards for actual engineering under complex conditions, accompanied with qualitive laws between <i>H</i><sub>C</sub>, <i>H</i><sub>U</sub> and <i>R</i>, which is beneficial for preventing the occurrence of uprush hazards.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 9","pages":"4651 - 4669"},"PeriodicalIF":5.7,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Deep learning-based calibration of resistance factors for pile groups with load tests","authors":"Yuting Zhang, Jinsong Huang, Jiawei Xie, Shui-Hua Jiang, Cheng Zeng","doi":"10.1007/s11440-025-02634-7","DOIUrl":"10.1007/s11440-025-02634-7","url":null,"abstract":"<div><p>Resistance factors for pile groups are typically derived using empirical methods that do not directly account for system redundancy and overlook the correlation between individual piles, which are inherently influenced by the spatial variability of soils. While rigorous three-dimensional (3D) random finite difference (RFD) or random finite element (RFE) analyses could potentially address these issues, they are constrained by significant computational demands. Therefore, this paper proposes a deep learning-based approach for calibrating resistance factors for pile groups with individual pile load tests. Specifically, a surrogate model based on a convolutional neural network (CNN) is proposed, which is trained and validated using the database generated by RFD analyses. The trained model is further used to derive pile resistances in spatially variable soils. Finally, the resistance factors are calibrated by counting and conditional probability based on the outcomes of load test results. The proposed approach is demonstrated using a pile group example. Results show that the proposed approach effectively captures the impacts of load test results and their corresponding locations, as well as the spatial variability of soil properties, on resistance factors.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 9","pages":"4355 - 4367"},"PeriodicalIF":5.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11440-025-02634-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-06-02DOI: 10.1007/s11440-025-02640-9
Shao-Heng He, Zhen-Yu Yin, Zhi Ding, Rui-Dong Li
{"title":"Novel observations for the impact of particle morphology on shear modulus of granular materials","authors":"Shao-Heng He, Zhen-Yu Yin, Zhi Ding, Rui-Dong Li","doi":"10.1007/s11440-025-02640-9","DOIUrl":"10.1007/s11440-025-02640-9","url":null,"abstract":"<div><p>The influence of particle shape on the shear modulus at very small strain (<i>G</i><sub>max</sub>) of granular materials remains poorly understood and correlated. Using both micro-CT and bender element tests, this study aims to further systematically investigate this influence by comparing six granular materials with distinct particle shapes. The study included materials with angular and rounded particles, as well as relatively spherical and moderately angular particles, with particle morphological factors assessed using micro-CT. A series of bender element tests was conducted on these materials under various relative densities (<i>D</i><sub>r</sub>) and mean effective stresses (<i>p</i>′). Additionally, computed tomography (CT) technique was employed to interpret the role of particle shape on <i>G</i><sub>max</sub> from a microstructural perspective. The test results reveal that under the same relative density condition, as the irregularity of particle shape increases, the <i>G</i><sub>max</sub> of the materials first increases and then decreases. Angular materials exhibit the lowest <i>G</i><sub>max</sub> values, primarily due to their larger void ratio, while the mediumly angular materials display the highest <i>G</i><sub>max</sub> values compared to rounded and angular materials. Additionally, it was observed that overall regularity (<i>OR</i>) can be used to describe the significant transitional <i>G</i><sub>max</sub> response of granular material in relation to the variations in particle morphology. As <i>OR</i> decreases, the sensitivity of <i>G</i><sub>max</sub> to <i>p</i>′ initially decreases and then increases, which was found to be related to the shape-dependent particle mean coordination number (<span>(overline{Z})</span>). Notably, in materials with an extremely low <span>(overline{Z})</span> value, <i>G</i><sub>max</sub> exhibits a significantly faster increase with <i>p</i>′. Consequently, based on test data from granular materials with a wide range of particle shapes and transitional <i>G</i><sub>max</sub> responses, practical equations for correlating the parameters of <i>G</i><sub>max</sub> prediction model with particle morphology were formulated and validated.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 9","pages":"4631 - 4650"},"PeriodicalIF":5.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11440-025-02640-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-06-02DOI: 10.1007/s11440-025-02662-3
Y. F. Zhou, W. Wu, J. J. Pan, Z. L. Cheng, Y. Z. Zuo
{"title":"Mechanical properties of rockfill under generalized stress conditions: true triaxial testing and constitutive modeling","authors":"Y. F. Zhou, W. Wu, J. J. Pan, Z. L. Cheng, Y. Z. Zuo","doi":"10.1007/s11440-025-02662-3","DOIUrl":"10.1007/s11440-025-02662-3","url":null,"abstract":"<div><p>Rockfill, a coarse granular material commonly used in dam construction, exhibits complex mechanical behavior under generalized stress conditions. This paper investigates the mechanical properties of rockfill through a series of stress-path tests conducted on a self-developed, large-scale true triaxial apparatus with cubical specimens of 60 × 30 × 30cm. Three test series are carried out by varying the mean effective stress, the deviator stress and the Lode’s angle, respectively. An elastoplastic constitutive model is presented to describe the behavior of rockfill. An improved dilatancy equation is introduced by considering the phase transformation stress ratio instead of the critical stress ratio.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 9","pages":"4453 - 4466"},"PeriodicalIF":5.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-06-02DOI: 10.1007/s11440-025-02658-z
Xuelai Wang, Chengshun Xu, Hesham M. El Naggar, Xiuli Du, Chunyi Cui
{"title":"Seismic response characteristics of standard and connection sections of subway station structures in liquefiable sites","authors":"Xuelai Wang, Chengshun Xu, Hesham M. El Naggar, Xiuli Du, Chunyi Cui","doi":"10.1007/s11440-025-02658-z","DOIUrl":"10.1007/s11440-025-02658-z","url":null,"abstract":"<div><p>In seismic regions, many underground structures are inevitably partially embedded in liquefiable sites, which may cause complex seismic response mechanisms due to the varying distribution of liquefiable soil layers. This study investigates dynamic interaction between underground structures and liquefiable soils employing three-dimensional nonlinear finite element models. The seismic response of both standard and connection sections of the subway station–tunnel of underground structures in liquefiable sites is evaluated to reveal the seismic response patterns of the soil–structure system under different liquefiable soil distribution forms. The results revealed that compared to homogeneous liquefiable sites, liquefiable interlayer sites can cause greater seismic damage to underground structures, potentially leading to failure along the entire length of the subway station. Therefore, the post-earthquake failure modes of the structure and site should be comprehensively considered based on the site layers distribution characteristics.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 9","pages":"4861 - 4886"},"PeriodicalIF":5.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-05-30DOI: 10.1007/s11440-025-02630-x
Kangze Yuan, Wankui Ni, Gabriele Della Vecchia, Xiangfei Lü, Haiman Wang, Yongpeng Nie
{"title":"A microstructural insight on a lime-stabilized loess: experimental evidences and pore size distribution modeling","authors":"Kangze Yuan, Wankui Ni, Gabriele Della Vecchia, Xiangfei Lü, Haiman Wang, Yongpeng Nie","doi":"10.1007/s11440-025-02630-x","DOIUrl":"10.1007/s11440-025-02630-x","url":null,"abstract":"<div><p>Lime stabilization is a traditional method for improving foundation soils, and it also has potential applications for embankments and earth structures. In this study, several experimental techniques, including scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and nuclear magnetic resonance (NMR), were used to provide a clear picture of the microstructural evolution of a lime-stabilized loess (LSL) from China. SEM micrographs were used not only to qualitatively highlight the dual porosity nature of the material, but also to provide quantitative information using Image-Pro Plus (IPP) 6.0 software. As the lime content increases, the pore area ratio decreases, the shape of the macropores and mesopores flattens, and the pore angle distribution becomes more uniform. The FTIR results show that the functional group strength of the LSL samples first increases and then decreases with increase in lime content, while the pore volume continues to decrease. A non-monotonic evolution of the strength with the lime content is then expected, as also confirmed by unconfined compression tests performed at different lime contents and curing times: at low lime contents, the reduction of the pore volume and the increase in the functional group strength imply an increase in the strength; at high lime contents, the competing effects of the reduction of the pore volume and the increase in the functional group strength lead to an overall decrease in the strength with the lime content. Then, as an intermediate step toward further quantitative predictions of the hydromechanical behavior of LSL, a pore size distribution model inspired by the proposal of Della Vecchia et al. (Int J Numer Anal Meth Geomech 39:702–723, 2015) was developed and used to reproduce NMR experimental data. The pore size distribution model proved to be able to reproduce the cumulative porosity curves for the whole range of lime content and curing time studied, with only four parameters kept constant for all the simulations. The predictive capabilities of the model were also confirmed by simulating experimental data from recent literature.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 7","pages":"3249 - 3267"},"PeriodicalIF":5.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-05-27DOI: 10.1007/s11440-025-02633-8
A. Ads, J. Dinotte, M. Omidvar, S. Bless, M. Iskander
{"title":"Influence of high-strain rate on the shear strength of normally consolidated kaolin clay","authors":"A. Ads, J. Dinotte, M. Omidvar, S. Bless, M. Iskander","doi":"10.1007/s11440-025-02633-8","DOIUrl":"10.1007/s11440-025-02633-8","url":null,"abstract":"<div><p>Stress–strain results from high-strain rate consolidated-undrained (CU) triaxial compression tests on partially saturated kaolin clay are presented. The work addresses the scarcity of high-strain rate data for cohesive soils and provides updated strain rate coefficients for kaolin clay. It covers strain rates from quasi-static (0.01%/s) to dynamic (800%/s) regimes. Kaolin clay specimens were prepared wet of optimum using static compaction at a constant water content of 32 ± 1% and a degree of saturation of 96 ± 2%. The specimens were then loaded into triaxial cells and consolidated under pressures ranging from 70 to 550 kPa for 24 h prior to testing. Tests were conducted using a modified hydraulic frame, and a methodology for correcting compression data to account for inertial effects observed during high-rate testing was adopted. The data revealed significant strengthening of clays with increased strain rates, especially at low confining pressures. Lightly confined clays (<i>σ</i><sub>3</sub> = 70 kPa) experienced a 165% strength increase, while highly confined clays (<i>σ</i><sub>3</sub> = 550 kPa) showed a 52% increase. Analysis using secant moduli revealed increased stiffening with loading rate. Posttest examination of specimens revealed a decrease of shear localization with increasing strain rate, indicating that a transition in failure mode contributes to the increased strengthening and stiffening of clays at high rates. The stress–strain data were used to calibrate the semilogarithmic and power law strain hardening models, yielding <i>λ</i> and <i>β</i> values that decreased linearly with increasing confining pressure. Equations relating <i>λ</i> and <i>β</i> to confining pressure were developed for practical applications, applicable to normally consolidated clays under confining pressures up to approximately 5 atmospheres.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 8","pages":"4183 - 4197"},"PeriodicalIF":5.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-05-27DOI: 10.1007/s11440-025-02642-7
Yingbin Liu, Shaoming Liao, Yaowen Yang, Junzuo He
{"title":"Analytical study on multiple-mode deformation behaviors of tunnels subjected to asymmetric loading in composite strata","authors":"Yingbin Liu, Shaoming Liao, Yaowen Yang, Junzuo He","doi":"10.1007/s11440-025-02642-7","DOIUrl":"10.1007/s11440-025-02642-7","url":null,"abstract":"<div><p>Underground tunnels subjected to asymmetric load or ground conditions are susceptible to experiencing uneven longitudinal bending, shearing, and torsional deformations, which further induce cross sectional flattening and warping. The intrinsic damages caused by multiple deformation modes are critical for tunnel health and safety but have long been neglected in practice. In the paper, a three-dimensional analytical model for soil–tunnel interactions was proposed with multiple-mode deformations incorporated, where the tunnel is assumed as a thin-walled pipe resting on an elastic foundation with five deformation modes: bending, shearing, torsion, warping, and flattening. Besides, a three-dimensional variable soil spring model was adopted, accounting for the strata discontinuities in longitudinal and transverse directions. A finite element solution for the proposed model was derived under arbitrary external loads using the principle of minimum potential energy. The validity of the proposed model was substantiated through three case studies. Based on the model, the coupling relationship of tunnel structure in transverse and longitudinal directions was revealed. Furthermore, parametric analysis was conducted to reveal the impact of tunnel width-to-thickness ratio, soil resistance coefficient, and composite strata on tunnel behaviors. These results significantly contribute to a deeper understanding of the intricate behaviors of tunnels, offering potential advancements for improved tunnel design methodologies.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 7","pages":"3223 - 3248"},"PeriodicalIF":5.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acta GeotechnicaPub Date : 2025-05-26DOI: 10.1007/s11440-025-02626-7
Tao Dong, Weiming Gong, Guoliang Dai, Wenbo Zhu, Hongguang Lin, Tao Hu, Liyang Zhu, Meiru Jin
{"title":"Investigation of the O-cell test conversion coefficient in extremely soft rock conditions based on energy conversion","authors":"Tao Dong, Weiming Gong, Guoliang Dai, Wenbo Zhu, Hongguang Lin, Tao Hu, Liyang Zhu, Meiru Jin","doi":"10.1007/s11440-025-02626-7","DOIUrl":"10.1007/s11440-025-02626-7","url":null,"abstract":"<div><p>The O-cell test is a widely used method for assessing pile bearing capacity, with the accuracy of its conclusions significantly influenced by the conversion coefficient, <i>γ</i>. However, the determination of <i>γ</i> in rock geological conditions, particularly in extremely soft rock, remains underexplored. This study, based on the Xuanji high-speed railway project, conducts static load tests on pile foundations using both the O-cell test method and the anchor pile method on test piles of the identical dimensions. These tests were designed to evaluate the bearing capacity of piles in extremely soft rock conditions. A power function fitting model for pile side friction resistance at varying depths is proposed, revealing that the measured and fitted values are approximately 50%–67% higher than the recommended friction resistance values in geological prospecting. Using the energy method, a calculation model for <i>γ</i> under extremely soft rock conditions is developed. Results indicate that <i>γ</i> decreases gradually and converges to 0.6 as the load increases, with the measured and theoretical average value of <i>γ</i> being approximately 0.79 and 0.76, respectively. Verification with data from other projects demonstrates that the model is also applicable to conventional geological conditions, such as rock, sand, and clay. Ultimately, considering construction safety, a <i>γ</i> value of 0.9 is recommended for extremely soft rock geological conditions.</p></div>","PeriodicalId":49308,"journal":{"name":"Acta Geotechnica","volume":"20 9","pages":"4841 - 4860"},"PeriodicalIF":5.7,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}