Strain accumulation in sand due to cyclic loading: Drained cyclic tests with triaxial extension

This paper presents results of numerous drained cyclic tests with triaxial extension. The influence of the strain amplitude, the average stress and the number of load cycles on the accumulation rate was studied. A simple cyclic flow rule was observed. Most findings confirm a previous study with cyclic triaxial compression tests. The test results serve as the basis of an explicit accumulation model.     

Undrained deformation behavior of saturated soft clay under long-term cyclic loading

Subgrade soils of traffic infrastructures are subjected to large numbers of load applications at a stress level below their shear strength. It is therefore of great practical relevance to study the deformation behavior of soft clay under long-term cyclic loading. In this study, a series of monotonic triaxial tests and long-term cyclic (50,000 cycles) triaxial tests have been carried out to investigate the undrained deformation behavior of undisturbed soft clay from Wenzhou, China. The stress–strain hysteretic loop, resilient modulus and permanent strain of the tested samples were found significantly dependent on CSR and confining pressure. With an increase of CSR and confining pressure, the resilient modulus decreases more significantly with increasing number of cycles and the accumulation rate of permanent strain increases. Furthermore, the shape of the stress–strain hysteretic loop almost remains unchanged and the resilient modulus tends to a steady value after a large number of cycles. Based on the experimental results, two equations are established for the prediction of long-term resilient modulus and permanent strain. Finally, a new critical value of 0.65 is suggested for CSR. When CSR>0.65, the resilient modulus for large number of cycles is reduced to a so called “asymptotic stiffness” and the accumulation rate of permanent strain significantly increases.     

Strain accumulation in sand due to cyclic loading: drained triaxial tests

Our aim is the prediction of the accumulation of strain and/or stress under cyclic loading with many (thousands to millions) cycles and relatively small amplitudes. A high-cycle constitutive model is used for this purpose. Its formulas are based on numerous cyclic tests. This paper describes drained tests with triaxial compression and uniaxial stress cycles. The influence of the strain amplitude, the average stress, the density, the cyclic preloading history and the grain size distribution on the direction and the intensity of strain accumulation is discussed.     

Correlation of cyclic preloading with the liquefaction resistance

The compactivity of sand due to cyclic loading with a high number (N>10³) of small cycles (ε^ampl≤10⁻³) cannot be described by void ratio and stress alone. It depends strongly on the soil fabric usually described as ‘cyclic preloading’. The cyclic preloading cannot be measured directly in situ but correlates well with the liquefaction resistance. This paper demonstrates this correlation on the basis of laboratory tests. Practical applications can be derived from this work.     

Influence of a cyclic and dynamic loading history on dynamic properties of dry sand, part I: cyclic and dynamic torsional prestraining

Initial fabric of a soil induced by its cyclic strain history is an important parameter together with the void ratio, state of stress and amplitude in respect to further accumulation of deformations under drained cyclic loading. It is of importance for the further deformation prediction to determine the initial fabric of the grain skeleton or the cyclic loading history of the soil. An attempt is made within this paper to correlate small strain stiffness of non-cohesive soil with its cyclic loading history. The results of performed cyclic and dynamic torsional tests show that small strain shear modulus is only moderately affected by cyclic prestraining even if high amplitudes are applied. A signature of prestraining history is observed in the tests since the sand memorizes its prestraining amplitude and the number of applied cycles.     

Effects of cyclic confining pressure on the deformation characteristics of natural soft clay

To investigate the coupling effects of cyclic deviator stress and cyclic confining pressure on the deformation behavior of natural soft clay under partially-drained conditions, a series of one-way cyclic triaxial tests with and without cyclic confining pressure were carried out. Test results show that, at the same amplitude of cyclic deviator stress, the increase of cyclic confining pressure amplitude will accelerate the accumulation of both permanent volumetric and axial strain significantly. The comparison between test results for different amplitudes of cyclic confining pressure shows that tests with a cyclic confining pressure corresponding to a stress path of η^ampl=p^ampl/q^ampl=1 lead to a 1.4 times larger permanent volumetric strain and a 1.2 times larger permanent axial strain compared to the conventional cyclic triaxial tests with constant confining pressure (η^ampl=1/3). In case of η^ampl=2 the permanent strains are found to be even 2.0 or 1.5 times larger compared to the standard tests. Finally, an empirical formula is proposed for the prediction of permanent axial deformations of natural soft clays under partially-drained conditions, considering the effects of cyclic confining pressure.     

Influence of a cyclic and dynamic loading history on dynamic properties of dry sand, part II: cyclic axial preloading

Initial fabric of a soil induced by its cyclic strain history is an important parameter among others like void ratio, state of stress and amplitude concerning the further accumulation of deformations under cyclic loading. It is of high importance to determine methods in order to estimate the initial fabric of the grain skeleton or the cyclic loading history of the soil. An attempt is made in this paper to correlate small strain stiffness of non-cohesive soil with its cyclic loading history. For this purpose several cyclic triaxial tests with specimens subjected to cyclic axial loading were performed and changes of small strain soil properties due to this cyclic loading were studied. All these tests showed only moderate changes of small strain stiffnesses independently of the different boundary conditions. Thus, a correlation between fabric or strain history and small strain stiffnesses seems not to be possible.     

Influence of cyclic loading history on small strain shear modulus of saturated clays

Small strain shear modulus G_max is an essential parameter in soil dynamics, and it is usually estimated based on the Hardin and Richart equation. However, many previous researches on sands have indicated that the Hardin and Richart equation does not consider the influences of cyclic loading history on G_max. In this paper, effects of cyclic loading history on G_max of saturated clays under undrained conditions are studied using a combination device of piezoelectric-ceramic bender element system and cyclic triaxial apparatus. The dynamic pre-loading includes both relatively high amplitudes of cyclic stresses and cyclic strains. G_max without cyclic loading history is also investigated for the comparison purpose. Test results show that, at the same effective stress, both cyclic strain history and cyclic stress history will induce reduction of G_max compared to the corresponding G_max values with non-cyclic loading effects. In strain-controlled tests, the reduction of G_max is slight and relatively stable; while in stress-controlled tests, the reduction of G_max increases suddenly and remarkably when the effective stresses degrade to a certain degree. The comparison between double amplitude axial strain and residual excess pore water pressure behaviors show that the remarkable reduction of G_max can demonstrate the cyclic failure of saturated clays.     

Influence of colloidal silica grout on liquefaction potential and cyclic undrained behavior of loose sand

Cyclic triaxial tests were performed to investigate the influence of colloidal silica grout on the deformation properties of saturated loose sand. Distinctly different deformation properties were observed between grouted and ungrouted samples. Untreated samples developed very little axial strain prior to the onset of liquefaction. However, once liquefaction was triggered, large strains occurred rapidly and the samples collapsed within a few additional loading cycles. In contrast, grouted sand samples experienced very little strain during cyclic loading. Additionally, the strain accumulated uniformly throughout loading rather than rapidly prior to collapse and the samples never collapsed. Cyclic triaxial tests were done on samples stabilized with colloidal silica at concentrations of 5, 10, 15, and 20%. In general, samples stabilized with higher concentrations of colloidal silica experienced very little strain during cyclic loading. Sands stabilized with lower concentrations tolerated cyclic loading well, but experienced slightly more strain. Thus, treatment with colloidal silica grout significantly increased the deformation resistance of loose sand to cyclic loading.     

Mechanical hysteresis in rocks at low strain amplitudes and seismic frequencies

A sensitive capacitance displacement transducer has been used to record hysteresis loops in the stress-strain diagrams of laboratory samples of granite, basalt, sandstone and concrete subjected to cyclic axial strains with amplitudes of order 10^?5 and periods of 10–300 sec. The ends of the loops are always cusped, whether the load cycle is sinusoidal or not, and at low strain amplitudes the loop shape becomes symmetrical and appears to be independent of amplitude. Thermal relaxation influences the observed loop shapes, so that the strain cycles represent a compromise between adiabatic and isothermal compressions. However, this does not affect the conclusion that stress-strain loops are always cusped. This observation does not appear to be consistent with linear theories of damping of acoustic and seismic waves, which indicate elliptical loops.     

Cyclic shear response of channel-fill Fraser River Delta silt

The cyclic shear response of a channel-fill, low-plastic silt was investigated using constant-volume direct simple shear testing. Silt specimens, initially consolidated to stress levels at or above the preconsolidation stress, displayed cyclic-mobility-type strain development during cyclic loading without static shear stress bias. Liquefaction in the form of strain softening accompanied by loss of shear strength did not manifest regardless of the applied cyclic stress ratio, or the level of induced excess pore water pressure, suggesting that the silt is unlikely to experience flow failure under cyclic loading. The cyclic shear resistance of the silt increased with increasing overconsolidation ratio (OCR) for OCR>1.3. The silt specimens that experienced high equivalent excess cyclic pore water pressure ratios (r_u>80%) resulted in considerable volumetric strains (2.5%–5%) during post-cyclic reconsolidation implying potentially significant changes to the particle fabric under cyclic loading.     

循环荷载下液化对土层水平往返变形的影响

采用多工况振动台实验研究液化对土层水平往返变形的影响.以干砂实验为参照,分析孔压增长与土层加速度和土层往返变形之间的关系.结果表明:液化将引起土表加速度显著降低,减小惯性力传递,但同时会引起土层往返剪应变明显增大.对往返变形而言,液化土层往返剪应变就可达到1%～5%的大变形状态,且液化土层往返剪应变沿深度呈下大上小分布.土层中孔压比0.4～0.8是往返变形出现放大的敏感段,在孔压比0.8左右而不是在1.0达到最大.作为其结果,土层液化将对刚性上部结构振动起减震作用,但同时增大的往返剪应变也易导致基础和地下结构破坏,特别是对液化层与下部非液化层交界处的构件更敏感.     

Crustal strain observation for nine years with a laser strainmeter in Kobe, Japan

We carried out precise crustal strain observation using a laser strainmeter system at the Rokko-Takao station in Kobe, Japan from 1989 to 1997. The long-term strain record is characterized by remarkable annual changes of the order of 2–3×10⁻⁶ and linear strain accumulation of −4.4×10⁻⁷/year (in contraction). The annual strain changes are inversely proportional to temperature changes that precede the strain changes by about 1 month. The apparent annual strain changes were mainly caused by refractive-index changes in the light path due to the ambient temperature changes. After eliminating the annual temperature effect, linear strain accumulation is corrected to be −6.3−6.7×10⁻⁷/year. Residual strains show the oscillating behavior, in which the oscillating cycle seems to become shorter and shorter as time goes by. During the period, a destructive earthquake of M=7.2 occurred near the Kobe City on 17 January 1995. We investigated the oscillating behavior in secular variations of ground-strains by introducing the deterministic approach of earthquake prediction to search for the “critical point” of the occurrence of an earthquake in the extended power law equation. However, we could not obtain a unique solution to determine eight unknown parameters including the “critical point”. This may be mainly due to lack of data for 4 months from August to November in 1994 by the failure of the laser source before the occurrence of earthquake on 17 January 1995. After removing environmental effects and tidal components, we carefully re-examined strain changes in 7 days and 1 day before the occurrence of the earthquake, but we could not detect anomalous strain changes exceeding 1×10⁻⁸ before the earthquake.     

The stiffness degradation and damping ratio evolution of Taipei Silty Clay under cyclic straining

The non-linear behavior of Taipei Silty Clay under cyclic strain loading was investigated through a series of undrained cyclic strain-controlled tests. The Ramberg–Osgood equation was used with our proposed stiffness degradation model to calculate degraded secant moduli. The proposed degradation model is simple in that it has only one more component than Idriss's model, the modulus ratio for the first cycle, which reflects the effects of the previous cyclic strain history and the current level of the cyclic strain amplitude, and can be used to describe softening and hardening behavior under irregular cyclic straining. It was found that the Ramberg–Osgood equation successfully predicts the damping ratio for small to medium strains. However, it overestimates the damping ratio for larger strains, so we suggest it can be corrected with a damping ratio index. In addition, the proposed equation for describing the evolution of the damping ratio provides the means to assess the variation for Taipei Silty Clay in the measured damping ratio with both the number of cycles and the strain amplitude.     

Plasticity model for sand under small and large cyclic strains: a multiaxial formulation

This paper presents the multiaxial formulation of a plasticity model for sand under cyclic shearing. The model adopts a kinematic hardening circular cone as the yield surface and three non-circular conical surfaces corresponding to the deviatoric stress ratios at phase transformation, peak strength and critical state. The shape of the non-circular surfaces is formulated in accordance with the experimentally established failure criteria, while their size is related to the value of the state parameter ψ. To simulate cyclic response under small and large shear strain amplitudes without a change in model parameters, it was found necessary to introduce: (a) a non-linear hysteretic (Ramberg–Osgood type) formulation for the strain rate of elastic states and (b) an empirical index of the effect of fabric evolution during shearing which scales the plastic modulus. This index is estimated in terms of a macroscopic second-order fabric tensor, which develops as a function of the plastic volumetric strain increment and the loading direction in the deviatoric plane. Comparison of simulations to pertinent data from 27 resonant column, cyclic triaxial and cyclic direct simple shear tests provide a measure for the overall accuracy of the model.     

Factors affecting shear modulus degradation of cement treated clay

Cement stabilization is often used to improve the bearing capacity and compressibility of soft clays. The present paper aims to investigate the shear modulus degradation of cement treated clay during cyclic loading. A series of cyclic triaxial test was conducted on artificially cement treated marine clay to study the factors affecting the shear modulus degradation. The parameters considered for the study are cement content (2.5–7.5%), curing days (7–28), cyclic shear strain amplitude (0.3–1%), number of loading cycles (1–100) and loading frequency (0.1–0.5 Hz). As in the case of natural clays, cement treated clays exhibit stiffness degradation which depends on mix ratio, curing days and loading conditions. The results show that the shear modulus degradation decreases with increase in the shear strain amplitude, cement content and curing days. It is also noted that irrespective of the mix ratio and curing conditions, the degradation decreases with increase in loading frequency. An empirical relationship is proposed to predict the shear modulus degradation based on Idriss׳s degradation model. The performance of the proposed empirical model is validated with the present experimental results.     

Evaluation of shear strength of rock joints subjected to cyclic loading

Variation of the shear strength of rock joints due to cyclic loadings is studied in the present paper. Identical joint surfaces were prepared using a developed moulding method with special mortar and shear tests were performed on these samples under both static and cyclic loading conditions. Different levels of shear displacement were applied on the samples to study joint behaviour before and during considerable relative shear displacement. It was found that the shear strength of joints is related to rate of displacement (shearing velocity), number of loading cycles and stress amplitude. Finally, based on the experimental results, mathematical models were developed for evaluation of shear strength in cyclic loading conditions.     

循环荷载下饱和岩石的滞后和衰减

通过对饱和砂岩和大理岩的循环荷载实验,分析了饱和岩石在循环荷载下的应力-应变滞后回线、瞬时杨氏模量、泊松比的“X”形变化曲线,以及杨氏模量随应变振幅的增加而减少等滞后现象,并分析了施加外力的应变振幅对衰减的影响,认为岩石在循环荷载作用下的衰减与应变振幅成正比,提出的衰减b值反映了岩石在循环荷载作用下衰减的程度. 岩石的衰减和滞后存在密切的关系,通过饱和岩石的宏观行为,探讨了饱和岩石在循环荷载下的滞后和衰减现象的微观机理,认为孔隙流体流动在岩石的滞后和衰减中起着重要作用,岩石内部的颗粒接触粘合和黏滑摩擦可能是孔隙岩石在循环荷载作用下产生滞后和衰减的原因.     

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 175 kPa and a frequency of 1.0 Hz 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 q_max at a given ratio of the number of cycles (N) to the number of cycles of failure (N_f). The cumulative crushing ratio R_cc decreases with increasing q_max, leading to a reduction in N_f. The internal frictional angle decreases with increasing R_cc, and R_cc increases with increasing N_f. 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 R_cc.