Numerical analysis of concrete piles driving in saturated dense and loose sand deposits

Abstract

Many approaches and techniques are used to evaluate pile axial capacity ranging from static methods to dynamic methods, which are based on either the results of pile driving or numerical simulations, which require reliable constitutive models representing the real soil behaviour and the interaction between the pile and soil. In this paper, using PLAXIS software and different constitutive soil models including MohrCoulomb, Hardening Soil and Hypoplastic with Intergranular Strain models, the behaviour of concrete piles driven into saturated dense and loose sand deposits under a hammer blow is evaluated. The main objective of this study is to assess the influence of different factors including frequency of loading and Hypoplastic soil model parameters on the recorded velocity and pile head displacement. In addition, the concept of one-dimensional wave propagation induced by pile driving is discussed. It is indicated that using the Intergranular Strain concept, defined in Hypoplastic soil model, small strain behaviour of soil around the pile during driving can directly be captured. The results of this study reveals that considering the Hypoplastic model, incorporating the Intergranular Strain concept, can accumulate much less strains than the corresponding predictions excluding the Intergranular Strain, and hence predict the pile performance during driving more realistically. predicted through various soil models have been evaluated and compared. It should be noted that, the small strain behaviour of soil around the pile, which is observed during pile driving, has been assessed using an advanced soil model as a part of this study. 2 NUMERICAL MODEL CHARACTERISTICS In this study, the axisymmetric finite element model was used in numerical simulation. Concrete pile as a volume pile element with a diameter of 0.4 m and a total length of 10 m was modelled numerically. A linear elastic model with an elastic modulus of 300 GPa, a Poissons ratio of 0.2 and a unit weight of 25 kN/m was assigned to the pile cluster. Whereas, elastic perfectly plastic Mohr-Coulomb (MC), Hardening Soil (HS) and Hypoplastic (HP) with Intergranular Strain (IGS) soil models were assigned to the soil cluster. In addition, viscous boundaries were used in the numerical model to simulate the geometric damping and the far-field boundaries. The hammer impact was simulated as a harmonic signal with an amplitude of 5 MPa, a phase of zero degree and a frequency of 50 Hz similar to what was reported in PLAXIS (2017). In numerical simulations, loose and dense Baskarp sands were used as the soil deposit. As explained by Elmi Anaraki (2008), Baskarp sand is a uniform sand with a total unit weight of 20 kN/m, an initial void ratio of 0.83 and 0.65 representing the loose and dense conditions, respectively. The soil properties assigned for Hardening Soil and Hypoplastic soil models were selected based on Dung (2009) and Elmi Anaraki (2008) studies, while the equivalent MohrCoulomb soil model properties were obtained from Aghayarzadeh et al. (2018), who correlated the results of a drained triaxial test using the soil test facility defined in PLAXIS software. The soil properties corresponding to each soil model and interface parameters used in numerical simulation are summarised in Tables 1 to 4. It should be noted that in order to simulate the interaction between the pile and soil, appropriate interface elements were considered. In all soil models, the interface strength and deformation parameters were assumed to be correlated to the surrounding soil parameters without consideration of any reduction factor for the sake of simplicity. In other words, for Mohr-Coulomb and Hardening Soil models the interface strength reduction factor (Rint) was assumed to be equal to one and for the Hypoplastic model, according to PLAXIS (2017), the interface parameters defined in Table 4 were considered. According to ASTM D 4945 (2010), the strain gauge and the accelerometer during the dynamic load testing should be mounted at least 1.5D (D is diameter of pile) below the pile head. In this study, force and velocity traces were recorded at 2D distance below the pile head. An illustration of the finite element model used in analysis is shown in Figure 1a. As shown in Figure 1b, half sine load with a dynamic time interval of 0.01 s (i.e. 50 Hz as mentioned earlier) was applied on the pile head to simulate the hammer load. Table 1. Baskarp sand properties for Hypoplastic soil model with Intergranular Strain (after Dung 2009) Parameters Hypoplastic model with intergranular strain φc (degree) 30 hs (MPa) 4000 n 0.42 ed0 0.548 ec0 0.929 ei0 1.08 α 0.12 β 0.96 mT 2 mR 5 Rmax 0.0001 βr 1 χ 2 Table 2. Baskarp sand properties for Hardening Soil model (after Dung 2009) Parameters Dense Loose E50 ref (MPa) 40.5 31 Eoed ref (MPa) 50 33 Eur ref (MPa) 121.5 93 φ (degrees) 37 31.3 ψ (degrees) 9 2 m 0.5 0.5 νur 0.2 0.2 p (kPa) 100 100 Table 3. Baskarp sand properties for Mohr-Coulomb soil model including both tangent and secant soil modulus (after Aghayarzadeh et al. 2018) Parameters Dense Loose Ei (MPa) 60 45 E50 (MPa) 33 24.75 υ 0.35 0.25 φ (degree) 37 31.3 ψ (degree) 9 2 The first version of the Hypoplastic constitutive law was proposed by Kolymbas (1985), describing the stress-strain behaviour of granular materials in a rate form. The Hypoplastic model can successfully predict the soil behaviour in the medium to large strain ranges. However, in the small strain range and upon cyclic loading it cannot predict the high quasielastic soil stiffness accurately. To overcome this problem, an extension of the Hypoplastic equation by considering an additional state variable, termed ̋Intergranular Strain (IGS) ̋, was proposed by Niemunis & Herle (1997) to determine the direction of the previous loading. In fact, the Intergranular Strain concept enables to model small-strain-stiffness effects in Hypoplasticity and therefore adopted in this study. Table 4. Interface parameters for Hypoplastic soil model used in numerical modelling (after Aghayarzadeh et al. 2018) Parameters Dense Loose Eoed ref (MPa) 50 33 cref ′ (kPa) 0.1 0.1 φ (degree) 37 31.3 ψ (degree) 9 2 UD-Power 0 0 UD-P (kPa) 100 100 3 PILE DRIVING SIMULATION As explained by Masouleh & Fakharian (2008), one of the important advantages of pile driving and pile load testing simulation in finite element and finite difference software is that the radiation or geometric damping is automatically considered in numerical modelling. In fact, the travelling compressive or tensile wave along the pile shaft causes a relative displacement between pile and soil, which results in generation of shear wave in the adjacent soil that can propagate radially. For evaluating the radiation damping effect, in this study shear stress variations with time at a depth of 4 m and at different distances from the pile axis (i.e. 1, 3, 6 and 9 m) in both dense sand and loose sand were recorded (Figure 2). Figure 2 represents a rapid reduction of shear stress wave amplitude with distance from the pile skin, such that near the vertical boundaries, it is practically zero for both dense and loose sand. This finding not only confirms the soil inertia or radiation damping effect in finite element modelling, but also proves that the viscous boundary has been regarded far enough to prevent the wave reflection in the model. During the pile load testing and pile driving, the pile head displacement is one of the most important factors that should be taken into account. In this paper the pile head displacement of concrete pile driven into the saturated dense and loose sand using three constitutive soil models are obtained and compared to each other, as illustrated in Figure 3. Referring to Figure 3, it is evident that driving a pile into dense sand induces less displacement compared to loose sand. All employed constitutive soil models including Mohr-Coulomb, Hardening Soil and Hypoplastic with Intergranular Strain (IGS) delivered reasonably a similar trend. It is worth mentioning that in the study conducted by Aghayarzadeh et al. (2018) related to simulation of the static load testing, E50 (the secant modulus) was used in MohrCoulomb model and it showed a reasonable correlation with other soil models, hence in this study MohrCoulomb model was used embracing this elastic modulus. However, it can be seen that using Hypoplastic soil model without activating the Intergranular Strain generates an increase in the observed displacement of pile head with time. Since the stress wave induced by the hammer impact dissipates, then it is not expected that the displacement to increase significantly. It is evident that HP model with IGS activation yields much less strain compared to the case when the IGS is not applied. This is mainly attributed to the fact that IGS concept simulates the small strain behaviour which is dominant during the pile driving.