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Effects of residual effective stress and particle size distribution on reconsolidation characteristics of granular materials after undrained cyclic shear: a 3D DEM study
Abstract
Ground reconsolidation following strong earthquakes can severely damage buildings and infrastructure. However, the nonlinear void ratio–effective stress relationship during reconsolidation remains poorly characterized owing to limitations of laboratory testing. The discrete element method is utilized to examine reconsolidation characteristics in K0-consolidated granular materials. The results demonstrate that the residual effective stress is the core indicator of the volumetric strain during reconsolidation. Particular focus is given to the post-liquefaction reconsolidation process, which can be divided into two stages: liquefied portion and subsequent solidified portion. The former stage accounts for a substantial proportion of total volumetric strain. For specimens with identical average size, particle size distribution has a major influence on volumetric strain in the liquefied portion while a negligible impact in the solidified portion. This study also finds a higher proportion of floaters in the polydisperse (PD) versus monodisperse (MD) specimen. Furthermore, pore uniformities in both specimens increase during undrained cyclic shear. During the reconsolidation process, pore uniformity rises in the MD specimen while the PD specimen exhibits variable changes.
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In the study of liquefaction behavior associated with seismic loading conditions, it is often assumed that liquefaction occurs owing to the upward propagation of shear waves, despite evidence that liquefaction damage may result from or be aggravated by horizontally propagating surface waves. In this study, a series of numerical tests, based on the three-dimensional discrete element method, is performed to examine the liquefaction behavior of granular materials under Love-wave strain conditions. The response of granular packings under horizontally polarized shear- (SH-) and Love-wave strain conditions is discussed at both macro- and microscales. The simulation results indicate that, at the macroscale, the effective stress reduction ratio increases more rapidly under Love-wave strain conditions than under SH-wave strain conditions. Based on the concept of energy, the granular materials under Love-wave strain conditions can be considered more vulnerable to liquefaction than those under SH-wave strain conditions. Microscale analysis indicates the spatial rotation of the dominant direction of backbone force-chains under Love-wave strain conditions. In addition, focus here is placed on the coordination number, which represents the average contact number per particle. The difference in the degradation speed of the skeleton structure of the granular packings between the SH- and Love-wave strain conditions may not appear until the coordination number has decreased to a critical value of around 4. After the coordination number has approached approximately 3, the granular packings become unstable and soon liquefy. The minimum mean effective stress is discussed herein.
きれいな砂の液状化後に発生する再圧密体積ひずみと非排水繰返しせん断履歴の関係を, 体積ひずみ速度を制御した再圧密試験により評価した. 繰返しせん断履歴は中空ねじりせん断試験機を用いたハイブリッドオンライン実験手法に基づく不規則波とした. その結果, 繰返しせん断中の履歴指標は従来, 高い相関があるといわれている最大せん断ひずみよりもむしろ累加せん断ひずみが再圧密時体積ひずみと相関が高いことがわかった. さらに, 再圧密体積ひずみは, 相対密度が小さいほど, 累加せん断ひずみが大きくなるほど大きくなることがわかった. これらの実験結果を基に, 履歴指標, 相対密度の影響を考慮することが可能な再圧密時の体積収縮特性を表現するモデルを提案した.
In liquefaction analyses, liquefaction is conventionally assumed to originate from the vertical propagation of shear waves. However, some field and theoretical evidence has demonstrated that the risk of liquefaction may be induced or increased by surface waves. In this study, the liquefaction characteristics of K0-consolidated granular materials under Rayleigh-wave strain conditions, ideal deformation conditions under the assumption of constant volume, were investigated by the three-dimensional discrete element method (3D DEM). The results indicate that Rayleigh-wave strain conditions combine pure and simple shear modes. As the ratio of the shear strain amplitude to the normal strain amplitude (RSN) increases from 1 to +∞, granular materials tend to have a slower liquefaction rate and higher liquefaction resistance; however, the difference in the undrained responses is negligible when the RSN is less than 1. The distribution of the magnitude and orientation of the contact forces also varies with the RSN, while it is similar when the RSN is less than 1. The degradation of the skeleton structure and the evolution of the structural anisotropy accelerate the liquefaction of granular materials. Moreover, in situations with the same accumulated equivalent strain per cycle, the Rayleigh-wave strain condition with a low RSN value will make granular materials more vulnerable to liquefaction compared with Love- and SH-wave strain conditions.
Based on experimental observations and cause analysis of formation, an intrinsic relationship was revealed between the large post-liquefaction shear deformation of saturated sand under undrained cyclic loading and three types of volumetric strain components (i.e., a reversible component due to dilatancy, an irreversible component due to dilatancy and a component due to change in mean effective stress). It was found that the development of the large post-liquefaction shear deformation is governed by coupling variation of the three volumetric strain components and is accompanied with three physical states of soil particles (i.e., the frictional contact state, the critical contact state and the suspension state) that appear alternately. The above new knowledge provides a rational explanation why unstable flow slides and large reconsolidation deformation may take place after the initial liquefaction and also a rational approach to the establishment of an elasto-plastic constitutive model used to describe the large post-liquefaction deformation.
The results of consolidation tests under K0 condition and cyclic triaxial tests on Fujian sand at a given relative density are introduced, and the mechanism of the liquefaction-induced volumetric strain is revealed, which is composed of the re-sedimentation and the re-consolidation processes. The re-sedimentation is closely related to the cyclic shear strain history, especially that after liquefaction, and the more the accumulated shear strain ratio is, the more the re-sedimentation volumetric is. Besides, the re-consolidation behavior is significantly affected by the previous consolidation history and cyclic stress history, and the post-liquefaction reconsolidation will follow the trend of the previous normal consolidation curve, and the compression index is larger than that of the normal consolidation curve under the same conditions. A post-liquefaction volumetric strain model accounting for both the consolidation and cyclic shear strain histories is proposed, which treats the re-sedimentation as part of the re-consolidation by introducing the concept of assumed initial stress, and the estimation methods for re-compression index and the assumed initial stress are recommended accordingly. Then dynamic centrifuge model tests are performed, and the consolidation settlement and liquefaction responses are monitored, whereupon the mechanisms of liquefaction-induced volumetric strain are observed at the model scale, and the proposed model for post-liquefaction settlement estimation is preliminarily validated.
This study presents a simplified method for estimating earthquake-induced settlements of saturated sand deposits based on previously available studies and undrained cyclic loading tests followed by drained reconsolidation under non-zero or zero lateral strains for various sands. It has been shown that: (1) the volume change of different sands over a wide density range can be uniquely related to 'relative compression' as defined by Δe/(ei-emin); (2) the total volumetric strain of saturated sand is not obviously influenced by a swelling history following undrained cyclic loading; and (3) the volumetric strain after undrained cyclic loading is not significantly affected by the boundary constraint of non-zero or zero lateral strains. It has been found that the relationship between the logarithm of the relative compression after complete or incomplete liquefaction and the logarithm of the maximum shear strain induced during preceding undrained cyclic loading is approximately linear over a range of maximum shear strain from 0.01% to 10% and of relative densities from 20% to 90% for five sands under non-zero or zero lateral strain conditions. The results predicted by the proposed method compare favorably with experimental observations of shaking table tests on saturated sand in a laminar container. The proposed method may therefore be used as a first approximation for estimating earthquake-induced settlements of saturated sand deposits.
Volume change measurements following cyclic loading triaxial tests on saturated sands provided data for estimating the settlement induced in a layer of saturated sand subjected to an earthquake. Expected settlements for well-designed fills where liquefaction will not occur are less than 0. 5%. If liquefaction develops the reconsolidation settlement may be 1% to 4%. Field data from several case history examples agree with these general predictions.
By employing a dozen of irregular time histories of motions obtained during the recent major earthquakes, two series of simple shear tests, one in uni-directional and the other in multi-directional loading conditions, were carried out on saturated loose, medium dense and dense samples of Fuji river sand. Following the undrained application of irregular loads, the generated pore water pressures were made to dissipate and the volumetric strains measured. The amount of reconsolidation volumetric strains thus determined is regarded as representing the settlement characteristics of sand which takes place in-situ deposits following the liquefaction during earthquakes. The test results indicated that the magnitude of maximum shear strain induced during the irregular loading is uniquely correlated with the volumetric strains during the reconsolidation.
Simplified methods of analysis are proposed for estimating probable settlements in either saturated or unsaturated sand deposits subjected to earthquake shaking. It is suggested that the primary factors controlling induced settlement are the cyclic stress ratio and maximum shear strain induced in saturated sands by the earthquake shaking and the cyclic strains induced in dry or partially saturated sands, together with the SPT N-value of the sand and the magnitude of the earthquake. Charts are presented for estimating settlements using these parameters, and the results are shown to compare favorably with settlements observed at six sites for which good data on settlements have been observed.
By examining a bulk of laboratory test data on sands obtained by using a simple shear apparatus, a family of curves was established in which the volumetric strain resulting from dissipation of pore water pressures is correlated with the density of sand and conventionally used factor of safety against liquefaction. Thus, given the factor of safety and the density in each layer of a sand deposit at a given site, the volumetric strain can be calculated and by integrating the volume changes throughout the depth, it becomes possible to estimate the amount of settlements on the ground surface produced by shaking during earthquakes. The outcome of the data arrangements as above was put in a framework of methodology to estimate the liquefaction-induced settlements of the ground. The proposed methodology was used to estimate the settlements at several sites devastated by liquefaction during the 1964 Niigata earthquake. The estimated values of the settlements were examined in the light of known performances of the sand deposits at respective site. It was shown that the proposed methodology may be used for predicting liquefaction-induced settlements with a level of accuracy suitable for many engineering purposes.
The distinct element method is a numerical model capable of describing the mechanical behavior of assemblies of discs and spheres. The method is based on the use of an explicit numerical scheme in which the interaction of the particles monitored contact by contact and the motion of the particles modelled particle by particle. The main features of the distinct element method are described. The method is validated by comparing force vector plots obtained from the computer program BALL with the corresponding plots obtained from a photoelastic analysis.
Voro++ is a free software library for the computation of three dimensional Voronoi cells. It is primarily designed for applications in physics and materials science, where the Voronoi tessellation can be a useful tool in the analysis of densely-packed particle systems, such as granular materials or glasses. The software comprises of several C++ classes that can be modified and incorporated into other programs. A command-line utility is also provided that can use most features of the code. Voro++ makes use of a direct cell-by-cell construction, which is particularly suited to handling special boundary conditions and walls. It employs algorithms which are tolerant for numerical precision errors, and it has been successfully employed on very large particle systems.
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