Research PaperSeismic analysis of stone column improved liquefiable ground using a plasticity model for coarse-grained soil
Introduction
Soil liquefaction and its associated large post-liquefaction deformation is a major source of damage during earthquakes (e.g. (Seed, 1979, Hamada, 1992, Seed et al., 2001, Yasuda et al., 2012). Installation of stone columns or gravel drains (SCs) is often an effective liquefaction mitigation technique (e.g. (Seed and Booker, 1977, Hausler, 2002, Adalier and Elgamal, 2004) to reduce the risk and consequences of soil liquefaction. SC installation can densify surrounding soils, increase overall ground stiffness, and improve drainage conditions (Doan and Fatahi, 2020), and has benefits of high time and cost efficiency. However, even coarse gravelly soils and dense sands with poor drainage conditions can also be potentially vulnerable to cyclic pore pressure generation and liquefaction during intense earthquake shaking (e.g. (Seed et al., 2001, Hatanaka et al., 1997, Cao et al., 2011). These evidence suggest that the seismic performance of coarse-grained soil (CGS), including both gravel and sand, and SCs improved liquefiable grounds should be carefully considered.
Extensive investigations on liquefaction mitigation using SCs have been conducted via case history analysis (Yasuda et al., 2012, Hausler, 2002), laboratory tests (e.g. (Brennan, 2004, Adalier et al., 2003, Badanagki and Dashti, 2018), and numerical simulations (e.g. (Elgamal et al., 2009, Asgari et al., 2013, Rayamajhi et al., 2016, Li et al., 2018). Centrifuge model tests by Brennan (Brennan, 2004), Adalier et al (Adalier et al., 2003), and Badanagki et al (Badanagki and Dashti, 2018) investigated various aspects of the drainage, stiffening, and densification effects of SC improved liquefiable ground. The results of these tests have provided the excellent basis validation of numerical simulations, allowing for further in depth analysis.
For numerical simulation of SC improved liquefiable sandy ground (e.g. (Elgamal et al., 2009, Asgari et al., 2013, Rayamajhi et al., 2016, Li et al., 2018, Bouckovalas and Papadimitriou, 2012, Kumari et al., 2018), sand has been modelled using various constitutive models, including: multi-yield-surface plasticity models (Yang et al., 2003, Elgamal et al., 2003); bounding surface plasticity models (Dafalias and Manzari, 2004, Andrianopoulos et al., 2010), and UBC sand models (Puebla et al., 1997). However, these models for sand (Yang et al., 2003, Elgamal et al., 2003, Dafalias and Manzari, 2004, Andrianopoulos et al., 2010, Puebla et al., 1997) either are not able to reflect the accumulation of shear strain at liquefaction during each load cycle after initial liquefaction (Dafalias and Manzari, 2004, Andrianopoulos et al., 2010, Puebla et al., 1997), or model the accumulation of shear strain at liquefaction through introducing an artificial shear accumulation when the effective stress path crossed the phase transformation line (Yang et al., 2003, Elgamal et al., 2003). For the simulation of coarse-grained SCs, linear elastic model (Bouckovalas and Papadimitriou, 2012), Mohr-Coulomb elastic-perfectly plastic model (Noui et al., 2019), the Ramberg-Osgood nonlinear model (Papadimitriou et al., 1548), or the same model as that used for sand (e.g. (Kumari et al., 2018, Elgamal et al., 2009, Asgari et al., 2013, Rayamajhi et al., 2016, Li et al., 2018) have been adopted. Such approaches often do not reflect the building-up of excess pore pressure in SCs (e.g. (Bouckovalas and Papadimitriou, 2012, Noui et al., 2019, Papadimitriou et al., 1548) or over-simplify the dynamic features of gravels (e. g. (Kumari et al., 2018, Elgamal et al., 2009, Asgari et al., 2013, Rayamajhi et al., 2016, Li et al., 2018), including the nonlinear shear strength of gravels (e.g. (Charles and Watts, 1980, Indraratna and Salim, 2002, Indraratna et al., 1998). Padadimitriou et al (Papadimitriou et al., 1548) and Li et al (Li et al., 2018) simulated the centrifuge model tests by Brennan (Brennan, 2004) and Badanagki et al (Badanagki and Dashti, 2018) with two-dimensional (2D) plane strain analysis, in which SCs were simulated by equivalent drain walls. However, the shear strain and stress responses of liquefiable ground improved by SCs showed evidently three-dimensional (3D) variations under seismic shakings (Elgamal et al., 2009); (Rayamajhi et al., 2016)).
At the core of high-fidelity seismic analysis of SC improved liquefiable ground is the demand for a 3D cyclic constitutive model for both sand and gravel. For appropriate simulation of liquefiable soil, the constitutive model for sand should be able to appropriately describe its dilatancy and the generation of shear strain after initial liquefaction (Wang et al., 2017). Zhang and Wang (Zhang and Wang, 2012) and Wang et al (Wang et al., 2014) proposed plasticity models for large post-liquefaction shear deformation of sand based on extensive test observations, which adopts a unique formulation for dilatancy. These models (Zhang and Wang, 2012, Wang et al., 2014) not only provide good description of the overall cyclic contraction towards liquefaction state under undrained cyclic loading, but also appropriately captures the shear strain generation and accumulation at liquefaction state. The models have been validated via a series of monotonic/cyclic drained/undrained laboratory tests and centrifuge model tests on various types of sands (e.g. (Wang et al., 2017, Chen et al., 2018). To extend the application of Wang et al.’s (Wang et al., 2014) model to SC improved liquefiable ground, some mechanical features of gravel must be incorporated (Seed et al., 2001, Choi, 2004). Most notably, the shear strength of gravel is often significantly higher than that of sands, and exhibits distinct nonlinearity with respect to confining stress (e.g. (Mello and VFB, 1977, Charles and Watts, 1980, Indraratna and Salim, 2002, Indraratna et al., 1998). The dilatancy together with the particle breakage affects the nonlinear strength characteristics and stress–strain relation of coarse-grained soil, including gravel and sand. The particle breakage of gravels can be significant compared with that of sand with a similar set of minerals and particle shape, causing the peak friction angle of gravels to exhibit distinct nonlinearity with respect to confining stress (Indraratna and Salim, 2002). In the revision, Fig. 1 shows the nonlinear strength features of Latite basalt (Indrarana et al., 1998), exhibiting significant decrease in peak friction angle with increasing confining stress (Indraratna et al., 1998).
The current work aims to conduct 3D seismic analysis of SC improved liquefiable ground, through development of a model with description for both sand and gravel, modified based on Wang et al. (Wang et al., 2014). The modified model improves the formulation for strength with new strength formulations in the π-plane and the meridian plane in 3D stress space, and is implemented in FLAC3D (Itasca. Fast, 2012), which is presented in Section 2. The model and implementation program is calibrated based on element tests for both gravel and sand in Section 3. In Section 4, seismic analysis of SC improved liquefiable grounds is conducted, first by simulating a centrifuge shaking table test and then by investigating the influence of soil density, permeability, and strength nonlinearity on seismic response.
Section snippets
Constitutive equations
The current study improves on the plasticity model of Wang et al (Wang et al., 2014) to achieve unified description of coarse-grained soil including both sand and gravel. Therefore, this section focuses on the modifications made to the original model and just provide a brief description of the previous model.
The formulation of the original model is outlined in Table 1.
A very brief description of some key model features is provided here, detailed formulation should be referred to in Wang et al. (
Model parameters
The proposed modified model has a total of 17 parameters. Details on the calibrated procedure for 13 of the parameters, which are shared by the modified and original models, have been well documented in Wang et al (Wang et al., 2014) and Zhang and Wang (Zhang and Wang, 2012). Some parameters used in the original model, including the elastic modulus modulus (G0, κ) (Zhang and Wang, 2012, Richart et al., 1970), plastic modulus (h) (Wang et al., 1990) and critical state parameters (λc; e0, ξ) (Li
Centrifuge test simulation
The performance of the proposed model in reproducing the seismic response of SC improved liquefiable ground is evaluated in this section. A model test conducted by Brennan (Brennan, 2004) (AJB-8a in their original paper) to investigate liquefaction mitigation through gravel drains is first simulated. The centrifuge model was conducted in a laminar box at 50g centrifugal acceleration. All data presented hereon are in prototype scale.
The test arrangement and instrumentation are shown in Fig. 13
Conclusions
Seismic analysis of stone column (SC) improved liquefiable ground is conducted in this study, using a three-dimensional plasticity model for coarse-grained soil including both sand and gravel.
The model is developed based on a model proposed by Wang et al (Wang et al., 2014) for large post-liquefaction deformation of sand, with improvements on the formulation for strength representation in the π-plane and the meridian plane in 3D stress space. The new formulations provide more accurate
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to thank the National Natural Science Foundation of China (No. 51879141 and No. 51708332) and Tsinghua University Initiative Scientific Research Program (2019Z08QCX01) for funding this work.
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