Residual Volumetric Strain Research Articles

Post-liquefaction deformation mechanisms of stone column-improved liquefiable sloping ground under cyclic loadings

Liquefaction-induced large deformations in sloping ground caused heavy damage to buildings and infrastructures during earthquakes, and its evaluation and mitigation challenge. In this study, a series of soil element tests using hollow cylinder apparatus (HCA) were conducted to investigate the relationship between residual volumetric strain and residual shear strain of medium dense to dense saturated sand with moderate initial static shear stress. The soil element tests indicate that the developments of residual volumetric strain and residual shear strain are dominated by the Post-liquefaction Deformation Potential (PLDP) of soil, which is well correlated to the maximum cyclic shear strain developed during cyclic loading. Then, the applicability of PLDP to characterize the post-liquefaction deformation response in gently sloping ground was investigated by centrifuge model tests without and with stone column improvement. The model tests of medium dense and dense sand slopes proved the applicability of PLDP preliminarily. The mitigation mechanisms against settlement and lateral spreading in gentle slopes by densification and drainage effects induced by stone columns were also observed and discussed. The present study provides the conceptual term of PLDP for evaluating post-liquefaction deformations of natural and stone column-improved gently sloping grounds, which helps to develop mitigation techniques for liquefiable sloping ground subjected to earthquake loadings.

Evolution of bulk compressibility and permeability of granite due to thermal cracking

Granite samples were subjected to heating at different temperatures and rapid water cooling. Hydrostatic compression tests were performed on the thermally treated samples. The initial tangent bulk modulus was measured. The critical value of hydrostatic stress for closing thermally induced micro-cracks was identified and the residual volumetric strain after unloading was determined. Gas permeability of granite samples was also determined under different levels of hydrostatic stress. It is found that the density of thermally induced micro-cracks can be correlated with the residual volumetric strain, both increasing when the pre-treatment temperature is higher. There is a significant increase of gas permeability up to several orders of magnitude as a consequence of micro-cracks induced by the heating and water-cooling process.

Determination of internal residual strain induced by cryogenic thermal cycling in partially-crystalized Fe-based metallic glasses

The intrinsic heterogeneities of the metallic glasses can be activated through cryogenic thermal cycling, making irreversible structural changes after the treatment and inducing rejuvenation to the materials. Although the energy rise after cryogenic thermal cycling can be easily determined from calorimetry, the energy change made by the heterogeneities is unknown because of the difficulty in witnessing these heterogeneities. In this paper, we investigated the changes of a typical heterogeneity: the Fe3Si crystallite, embedded in two partially-crystallized Fe-based metallic glasses, and subsequently deduced its influence on the neighbouring glassy matrix. It was found that even in the initial, partially-crystallized alloys, the Fe3Si nanocrystals were under residual expansion. Furthermore, both expansion and contraction can be detected after cryogenic thermal cycling depending on the applied number of cycles. The maximum residual volumetric strain preserved after CTC is in the order of 0.1%. Moreover, the stored energy of both crystals and glasses are calculated and the total energy rise is determined at the order of 5–50 mJ/g. The study of partially-crystallized alloys not only provides a useful model of heterogeneous materials but also reflects the structural change of the glassy phases, making this method attractive in understanding the effects of thermo-mechanical processing on heterogeneities.

Fatigue and damage properties of frozen silty sand samples subjected to cyclic triaxial loading

Cyclic triaxial tests were conducted to explore the influences of dynamic axial loading on the dynamic features and fatigue of frozen silty sand, using an MTS-810 apparatus from Material Testing Systems (MTS). The temperature was −15 °C, and the cyclic axial loads with different amplitudes at 1.0 Hz were applied under confining pressures of 0.6, 1.4, and 6.0 MPa. The cyclic triaxial test results demonstrate that the residual axial strain of the frozen silty sand samples increases gradually during the initial cycles and then increases with increasing number of cycles at a constant speed until failure. The residual volumetric strain contracts during the initial loading cycles and then dilates until failure. Both the residual strain method and the residual volumetric strain method proposed here can be used to describe the degradation process in frozen silty sand samples subjected to cyclic loading. The dynamic axial stiffness of a frozen sample decreases rapidly in the initial cycles and then approaches a stable value with increasing cycle number. The initial damage increases when the stress ratio increases; the larger the stress ratio, the smaller the number of cycles at failure.

Particle breakage of artificially crushable materials subject to drained cyclic triaxial loading

Upon cyclic loading, particle breakage of constituent granular materials occurs when the resulting local stresses exceed their strength, which has a significant influence on the deformation of the embankment, foundation and pavement structures. In this study, the artificially crushable materials were tested to investigate the particle breakage properties of these structures when subjected to drained cyclic triaxial loading. Twelve sets of samples were tested at the confining pressures of 100, 125, 150 and 175kPa and a frequency of 1.0Hz using a GCTS triaxial system. The cyclic test results indicate that at the same confining pressure, the residual volumetric strain increases with decreasing maximal deviatoric stress qmax at a given ratio of the number of cycles (N) to the number of cycles of failure (Nf). The cumulative crushing ratio Rcc decreases with increasing qmax, leading to a reduction in Nf. The internal frictional angle decreases with increasing Rcc, and Rcc increases with increasing Nf. Furthermore, the confining pressure, maximal cyclic deviatoric stress and N have significant influences on the degree of particle breakage, which leads to volumetric contraction during the cyclic loading process. Finally, the resilient modulus at failure increases linearly with increasing Rcc.

Effects of relative density and accumulated shear strain on post-liquefaction residual deformation

Abstract. The damage caused by liquefaction, which occurs following an earthquake, is usually because of settlement and lateral spreading. Generally, the evaluation of liquefaction has been centered on settlement, that is, residual volumetric strain. However, in actual soil, residual shear and residual volumetric deformations occur simultaneously after an earthquake. Therefore, the simultaneous evaluation of the two phenomena and the clarification of their relationship are likely to evaluate post-liquefaction soil behaviors more accurately. Hence, a quantitative evaluation of post-liquefaction damage will also be possible. In this study, the effects of relative density and accumulated shear strain on post-liquefaction residual deformations were reviewed through a series of lateral constrained-control hollow cylindrical torsion tests under undrained conditions. In order to identify the relationship between residual shear and residual volumetric strains, this study proposed a new test method that integrates monotonic loading after cyclic loading, and K0-drain after cyclic loading – in other words, the combination of cyclic loading, monotonic loading, and the K0 drain. In addition, a control that maintained the lateral constrained condition across all the processes of consolidation, cyclic loading, monotonic loading, and drainage was used to reproduce the anisotropy of in situ ground. This lateral constrain control was performed by controlling the axial strain, based on the assumption that under undrained conditions, axial and lateral strains occur simultaneously, and unless axial strain occurs, lateral strain does not occur. The test results confirmed that the recovery of effective stresses, which occur during monotonic loading and drainage after cyclic loading, respectively, result from mutually different structural restoration characteristics. In addition, in the ranges of 40–60% relative density and 50–100% accumulated shear strain, relative density was found to have greater effects than the number of cycles (accumulated shear strain).

Effects of cyclic dynamic loading on the mechanical properties of intact rock samples under confining pressure conditions

A series of laboratory tests were performed to assess the effects of confining pressure on the mechanical properties and fatigue damage evolution of sandstone samples subjected to cyclic loading. Six levels of confining pressure (2.0, 10.0, 20.0, 30.0, 40.0 and 50.0MPa) were applied during axial cyclic loading at a 1.0Hz frequency using a MTS-815 Rock and Concrete Test System. Results from the cyclic dynamic loading tests indicated that the level of confining pressure had a significant influence on the cyclic dynamic deformation and fatigue damage evolution of the sandstone samples tested. With increasing confining pressure, the axial strain at failure increased, as did the residual volumetric strain at the initiation of dilatancy. The residual axial strains of sandstone samples obtained at a confining stress state can be described as three deformational stages, namely, the initial phase, uniform velocity phase and accelerated phase. Both the residual strain method and the axial secant modulus method proposed here could be used to describe the initial fatigue damage and degradation process of sandstone samples subjected to fatigue loading under a confining stress state; however, the latter also considers the influence of stress level on fatigue damage evolution when fatigue loads are applied. At a constant confining pressure, the shear fracture plane can form under static and cyclic dynamic loading conditions, and the higher the confining pressure, the wider the shear fracture planes become under cyclic dynamic loadings.

Effects of Frequency on the Dynamic Properties of Intact Rock Samples Subjected to Cyclic Loading under Confining Pressure Conditions

A series of laboratory tests was performed to assess the effects of frequency on the dynamic properties of sandstone samples subjected to cyclic loading in the confining stress state. Three levels of confining pressure (2.0, 10.0, and 40.0 MPa) and three sets of frequencies (0.1, 1.0, and 3.0 Hz) were applied for the axial cyclic loading tests by the MTS-815 Rock and Concrete Test System. The results from the cyclic loading tests indicate that frequency has a strong influence on the dynamic deformation, the dynamic stiffness, and the failure mode at the same confining pressure. With an increase in the frequency, the axial strain and the number of cycles at failure increased at the same confining pressure, the residual volumetric strain increased when dilatancy occurred at the same confining pressure, and the number of cycles at failure increased. A new damage variable D was defined that describes the degradation process of sandstone samples upon dynamic cyclic loading. The larger the frequency, the wider the localized band. Sandstone samples subjected to dynamic cyclic loading responded with a significantly higher initial stiffness. The higher the initial stiffness, the greater the frequency.

Residual Deformation Behavior of Reinforced Rock-Fill Materials

Reinforcement technology is widely used in rock-fill dams in high seismic hazard zones. The evaluation of reinforcement on deformation and safety is concerned and it is one of the major study objectives in rock-fill engineering. The residual deformation behaviors of reinforced rock-fill materials were experimentally studies by use of a triaxial apparatus. The effects were analyzed of intervals of reinforcement layers, confining pressures and the conditions of cyclic loading on residual deformation. Results show that reinforcement improves the residual deformation behaviors of rock-fill materials. Both the residual shear strain and the residual volumetric strain are deduced. Based on the test results, the mechanism of the influence of reinforcement on residual deformation is proposed tentatively.

Evaluation of Seismic Settlement Potential of Saturated Sandy Ground Based On Concept of Relative Compression

ABSTRACT Mechanisms regarding the earthquake-induced settlements of saturated sandy deposits with level or nearly level ground surface are revealed based on new post-earthquake stress-strain constitutive analysis and experimental evidence. It was found that: 1) the residual volumetric strain of saturated sand evr induced by drained consolidation following cyclic undrained loading, depends on an irreversible dilatancy component evd.ir and a residual shear strain during the consolidation γr only; 2) change in evd.ir can universally be measured using an index “relative compression, Rc” for different sands over a wide range of density; and 3) a consistantly good correlation exists between Rc and maximum double amplitude shear strain induced by preceding cyclic undrained loading. From these theoretical and experimental findings, new analytical and empirical methods with a high degree of physical rationale were developed for predicting earthquake-induced maximum undrained shear strain and the resulting residual volumetric strains. As a consequence, the seismic ground surface settlement potential for level sandy deposits can be evaluated only by integrating the relative compression along ground depth. The proposed methods were confirmed to be effective by comparing the predictions with observations made during the 1995 Hyogoken-Nambu earthquake.

Residual Strains in Calcareous Sand due to Irregular Cyclic Loading

This paper describes a procedure for predicting the residual strains developed in calcareous sand under irregular cyclic triaxial loading conditions. The rates of accumulation of volumetric and shear strains are treated separately, with the volumetric strain response being used as the basis for characterizing the effects of cyclic loading. The residual volumetric strain developed as a result of repeated loading is related to the mean and the amplitude of the cyclic deviator stress. Thus, by using empirical correlations between the applied deviator stresses, the number of cycles, and the measured residual strains, the effect of cyclic loading under one set of cyclic loading conditions can be expressed in terms of an equivalent number of cycles under a different set of cyclic loading conditions. By using this equivalent number of cycles for the cyclic loading stresses, the residual strains developed as a result of further loading are then determined, so that the residual strains developed at any stage during irregular cyclic loading can be evaluated.

A quantitative model of dilatancy in dry rock and its application to westerly granite

A general model of dilatancy was developed based on the behavior of individual microcracks. Macroscopic effects were described by combining the effects of individual cracks using a statistical approach. The model was developed using distribution functions for crack size, crack strength, and local stress. Hysteresis in volumetric strain and stress‐strain data for partial unloading and reloading and general loading paths can be described. The model is best suited to describing rock which has been subjected to a number of loading cycles sufficient to remove the residual volumetric strain that is present in the initial cycles. This makes the rock more representative of the real earth and removes transient effects that obscure the dilatant effect. Volumetric strain data from triaxial experiments on Westerly granite were well described by the model for confining pressures from 0 to 4.11 kbar. Only one parameter was needed to describe the effect of changing the confining pressure, and this can be interpreted as an elastic effect on the crack volume. Some aspects of the crack behavior that were necessary to explain the data are incompatible with the usual sliding crack model of dilatancy. Combined with the lack of observable shear cracks, this casts serious doubts on the validity of the sliding crack model.