A strain-based procedure to estimate strength softening in saturated clays during earthquakes

doi:10.1016/j.soildyn.2014.07.003

Soil Dynamics and Earthquake Engineering

Volume 66, November 2014, Pages 191-198

https://doi.org/10.1016/j.soildyn.2014.07.003 Get rights and content

Highlights

•
We propose a simplified procedure for evaluating cyclic softening of clays during earthquakes.
•
A key aspect of the proposed procedure is adoption of a strain‐based approach.
•
The procedure has two main steps: (1) demand; and (2) consequence.
•
The procedure can estimate post cyclic strength and implements it into pseudo static analysis.
•
The capability of the procedure is demonstrated with three case histories.

Abstract

Cyclic softening and strength loss of saturated clays during earthquakes is often an important consideration in engineering problems such as slope stability, dam/levee safety, and foundation bearing capacity. This study proposes a simplified procedure for evaluating cyclic softening (amount of strength loss) that may be expected in saturated clays during earthquakes and illustrates how to implement it in engineering analysis. The procedure has two main steps: (1) estimation of an equivalent cyclic shear strain amplitude and associated number of cycles induced in the soil mass by an earthquake; and (2) estimation of softening and strength loss in the soil mass. A key aspect of the proposed procedure is adoption of a strain-based approach to estimate cyclic softening as opposed to the widely used stress-based approach of liquefaction assessments. A threshold strain concept originating from the strain-based approach is first discussed and the development of a procedure is presented subsequently. The proposed procedure provides reasonable, first-order estimates of cyclic softening consistent with the other developed procedures. In addition, the capability of the procedure is demonstrated with two case histories identified as involving cyclic softening of clays.

Introduction

Cyclic softening of clays is commonly understood as the reduction in soil stiffness and strength due to repeated cyclic loading, as shown in Fig. 1 and discussed in [1]. Experiments by Idriss et al. [2] showed that the initial stiffness and the ordinates of the backbone curve of soft clay are reduced after several cycles. Vucetic and Dobry [3] studied the effect of the overconsolidation ratio (OCR) on the cyclic shear modulus degradation of clay. They found that higher OCR of soil is, less degradation is observed. Matasovic and Vucetic [4] further discussed the coupling of cyclic softening of clay and pore-water pressure generation. With the use of a threshold strain concept, they proposed a model to predict softening behavior based on cyclic shear strain amplitude. More recently, Soroush and Soltani-Jigheh [5] compared pre-cyclic and post-cyclic behavior of mixed clayey soils. The tests results suggest that the post-cyclic undrained shear strength and secant deformation modulus of the specimens are comparatively reduced. The reduction level depends on the granular material content, cyclic shear strain level, and to some degree, the effective confining pressure.

Recent case histories have revealed evidence of cyclic softening of clays during earthquakes. The 1999, Chi-Chi, Taiwan Earthquake caused extensive ground failure and structural damage in Wufeng, Taiwan. Some of the most interesting cases of damage involved ground failure in areas underlain by low plasticity clayey soils [6]. During the 1999 Kocaeli earthquake, in situ deformation measurements at the Carrefour Shopping Center showed significant vertical strains in elastic silt (ML)/lean clay (CL) and fat clay (CH) strata. Martin et al. [7] concluded that the ML/CL layer had exhibited “liquefaction type behavior” while “a definitive explanation for significant earthquake-induced settlements in a high-plasticity clay stratum (CH) in Lot C has not yet been found.” Tsai and Hashash [8] used a novel inverse analysis framework, SelfSim, to extracting the in-situ soil behavior under seismic loading through vertical array recordings in Lotung and La Cienega. The underlying soils exhibit degradation behavior, in which sandy soil is more significant than clayey soil.

Recently, Boulanger and Idriss [9] developed a procedure for evaluating the potential for cyclic softening in clay-like fine-grained soils during earthquakes. Their procedure uses a stress-based approach comparable to that used in semi-empirical liquefaction procedures (e.g. [10]). The procedure is to assess the factor of safety (possibility of onset of significant strains or strength loss) in saturated silts and clays during earthquakes. Mejia et al. [11] applied a procedure similar to the Boulanger and Idriss procedure to estimate post-cyclic strengths of clay-like fine-grained soils and applied it to dam safety evaluation.

This paper, however, proposes a different approach, which uses cyclic shear strain (i.e. strain- based procedure) to evaluate cyclic softening of clayey soils. In addition, unlike [9] to evaluate the onset of soil failure due to cyclic softening, the proposed procedure can directly estimate post cyclic strength and implements it into pseudo static analysis. A threshold strain concept originating from the strain-based approach is first discussed in the paper and the development of a procedure is presented subsequently. Then, the application of proposed procedure is demonstrated by three case studies. It was first compared with another more complex analysis procedure [11] by analyzing the same design case. After that, the procedure is applied to case histories involving strength loss of clayey soils during 1999 Chi-Chi Earthquake and the 1999 Kocaeli earthquake.

Section snippets

Threshold strain and strain-based approach to cyclic loading problems

The cyclic threshold shear strain, γ_t, is a key characteristic of the behavior of soils subjected to cyclic loading [12]. According to the definition by Hsu and Vucetic [13], the threshold shear strain amplitude γ_t separates the domains of cyclic pore-water pressure development (or permanent volume change under drained conditions) and practically no development at all. At a cyclic shear strain amplitude, γ_c, larger than γ_t, the residual excess pore-water pressure, Δu, or the volumetric strain, ε

Cyclic softening models for clay

Matasovic and Vucetic [16], [17] proposed a modified hyperbolic model to describe the stress (τ)–strain (γ) behavior (with coupled pore water generation), modulus degradation, and strength softening of clays based on the following equation: $τ = \frac{δ_{c} G_{\max} γ}{1 + β {((δ_{c} G_{\max} / δ_{τ} τ_{\max}) γ)}^{s}}$ where G_max is small strain shear modulus, τ_max is shear strength, δ_c is the modulus degradation index function and δ_τ is the stress softening index function as indicated in Fig. 1. Both indexes are coupled with the excess pore

Equivalent cyclic shear strain amplitude

An equivalent (effective) amplitude of cyclic shear strain is first approximated by Tokimatsu and Seed [18] to estimate the seismic compression of unsaturated cohesionless soils. The original Tokimatsu and Seed analysis procedure is based on a simplified representation of the distribution of shear stress with depth in a one-dimensional soil column as proposed by Seed and Idriss [10]. At depth z, the effective cyclic stress, τ_eff, can be approximated as $τ_{eff} = 0.65 \frac{a_{\max}}{g} σ_{0} r_{d}$ where a_max is the maximum

Equivalent number of uniform strain cycles (N_c)

A large number of studies converted random cycles into equivalent number of uniform strain cycles N_c by using concepts in fatigue studies. Seed et al. [24] first calculated N_c for evaluating liquefaction potential based on the damage accumulation concepts. Using a strong motion data set from tectonically active regions, Liu et al. [25] developed empirical regression equations to evaluate the equivalent number of uniform stress cycles of earthquake shaking as a function of magnitude (M_w),

Recommended analysis procedure

The procedure to estimate strength softening has two general steps: Step 1 Demand: estimation of the shear strain amplitude and the equivalent number of uniform strain cycles within the soil mass from the peak acceleration at the ground surface or other seismological and site parameters; Step 2 Consequence: estimation of strength softening of the soil based on the effective shear strain amplitude, and the equivalent number of uniform strain cycles. Details on the two steps are described in the

Comparison to case histories

In this section, we apply the above analysis procedure to estimate strength softening at three sites during past earthquakes and compare the predicted consequences due to softening with observed ground failure.

Conclusions

In this paper, we present an analysis procedure to estimate cyclic softening of saturated clays under seismic loading. Unlike common liquefaction potential analysis procedures that use a stress-based approach, the procedure uses a strain-based approach to estimate cyclic softening and associated strength loss. The procedure has two main components: (1) demand: estimation of the shear strain amplitude and the equivalent number of uniform strain cycles within the soil mass induced by an

Acknowledgments

This study was initialized by the first author during his employment with URS Corporation and completed at National Chung Hsing University with the funding from the National Science Council under Award Number NSC102-2625-M-005-004. The authors gratefully acknowledge this support.

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Mejia et al. (2009) applied a procedure similar to the Boulanger and Idriss procedure to estimate the post-cyclic strength of clay-like fine-grained soils and applied it to dam safety evaluation. Tsai et al. (2014) proposed a strain-based procedure to evaluate the level of cyclic softening of clayey soils and implemented the procedure in pseudo static analysis for slope stability and bearing capacity assessment. Case histories have provided evidence of cyclic softening of clays during earthquakes.
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View full text

A strain-based procedure to estimate strength softening in saturated clays during earthquakes

Highlights

Abstract

Introduction

Section snippets

Threshold strain and strain-based approach to cyclic loading problems

Cyclic softening models for clay

Equivalent cyclic shear strain amplitude

Equivalent number of uniform strain cycles (Nc)

Recommended analysis procedure

Comparison to case histories

Conclusions

Acknowledgments

Soil behavior in earthquake geotechniques

Nonlinear behavior of soft clays during cyclic loading

J Geotechn Eng Div

Degradation of marine clays under cyclic loading

J Geotech Eng

Generlized cyclic-degradation-pore- pressure generation model for clays

J Geotech Geoenviron Eng

Pre- and post-cyclic behavior of mixed clayey soils

Can Geotech J

Cyclic softening of low-plasticity clay and its effect on seismic foundation performance

J Geotech Geoenviron Eng

High-modulus columns for liquefaction mitigation

J Geotech Geoenviron Eng

Learning of dynamic soil behavior from downhole arrays

J Geotech Geoenviron Eng

Evaluation of cyclic softening in silts and clays

J Geotech Geoenviron Eng

Simplified procedure for evaluating soil liquefaction potential

J Soil Mech Found Div, ASCE

Cyclic threshold shear strains in soil

J Geotech Eng

Threshold shear strain for cyclic pore-water pressure in cohesive soils

J Geotech Geoenviron Eng

Geotechnical earthquake engineering

Equivalent number of uniform strain cycles (N_c)