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.     

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 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.     

Nonlinear elastic behavior of fiber-reinforced soil under cyclic loading

Experimental investigations and modeling of nonlinear elasticity of fiber-reinforced soil under cyclic loading at small strain are conducted in this paper. The investigations include three aspects. First, cyclic shear tests are conducted using conventional triaxial apparatus. Twenty-seven specimens with three different fiber contents are employed to conduct triaxial cyclic shear tests under different confining pressure and loading repetition. Effects of geofiber, confining pressure and loading repetition on elastic shear modulus of reinforced soil are studied and analyzed. Second, a hyperbolic function is introduced to describe the nonlinear stress–strain skeletal curve under cyclic loading. Nonlinear elastic modulus is expressed as a function of shear strain and two variables A and B that are related to the initial tangential modulus and ultimate cyclic loading stress, respectively. In the present paper, variables A and B both are further assumed to be functions of geofiber content, confining pressure and loading repetition. Finally, eight constitutive coefficients of the nonlinear elastic model are calibrated using stress–strain curves from cyclic triaxial shear tests. The calibration of parameters is conducted using the technique of the linear regression for multiple variables. Impacts and effects of geofiber, confining pressure and loading repetitions on soil nonlinear elastic behavior are discussed.     

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.     

Numerical modeling of centrifuge cyclic lateral pile load experiments

To gain insight into the inelastic behavior of piles, the response of a vertical pile embedded in dry sand and subjected to cyclic lateral loading was studied experimentally in centrifuge tests conducted in Laboratoire Central des Ponts et Chaussées. Three types of cyclic loading were applied, two asymmetric and one symmetric with respect to the unloaded pile. An approximately square-root variation of soil stiffness with depth was obtained from indirect in-flight density measurements, laboratory tests on re...     

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.     

Liquefaction potential and strain dependent dynamic properties of Kasai River sand

The availability of efficient numerical techniques and high speed computation facilities for carrying out the nonlinear dynamic analysis of soil-structure interaction problems and the analysis of ground response due to earthquake loading increase the demand for proper estimation of dynamic properties of soil at small strain as well as at large strain levels. Accurate evaluation of strain dependent dynamic properties of soil such as shear modulus and damping characteristics along with the liquefaction potential are the most important criteria for the assessments of geotechnical problems involving dynamic loading. In this paper the results of resonant column tests and undrained cyclic triaxial tests are presented for Kasai River sand. A new correlation for dynamic shear damping (D_s) and maximum dynamic shear modulus (G_max) are proposed for the sand at small strain. The proposed relationships and the observed experimental data match quite well. The proposed relationships are also compared with the published relationships for other sands. The liquefaction potential of the sand is estimated at different relative densities and the damping characteristics at large strain level is also reported. An attempt has been made to correlate the G_max with the cyclic strength of the soil and also with the deviator stress (at 1% strain) from static triaxial tests.     

A modified parallel IWAN model for cyclic hardening behavior of sand

A modified parallel IWAN model, which includes a cyclic hardening function, is proposed and verified. The proposed model consists of elasto-perfect plastic and isotropic hardening elements. The model is able to predict cyclic hardening behavior through the adjustment of the internal slip stresses of its elements beyond the cyclic threshold, and satisfies Bauschinger's effect and the Masing rule with its own behavior characteristics. The cyclic hardening function is developed based on the irrecoverable plastic strain (accumulated shear strain) of dry sand during shearing, which is assumed to be a summation of shear strain beyond the cyclic threshold. Symmetric-limit cyclic loading and irregular loading tests were performed to determine model parameters and to verify the behavior of the proposed model. Finally, a one-dimensional site response analysis program (KODSAP) is developed by using the proposed model. The effects of cyclic hardening behavior on site response are evaluated using KODSAP.     

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.     

Investigation of a cyclic laterally loaded model pile group

In certain regions of the world, designing deep foundations to withstand seismic loading is a reality. Seismic loading of structures and foundations reaches its most critical state as a cyclic lateral force. The response of soils and foundations to repetitive lateral forces is highly complex, relegating most design methods to be based upon overly conservative rules-of-thumb. The primary objective of this research was to analyze the mechanics of seismic loading on pile groups in clay soils. To achieve this a model testing facility was constructed to house a fully instrumented 1×5 model pile group that was subjected to cyclic lateral loading. An empirically based method for pile group design is suggested based upon the results generated from model pile group testing.     

The cyclic behaviour of soils and effects of geotechnical factors in microzonation

Geotechnical site conditions that can be very different due to changes in thickness and properties of soil layers, depth of bedrock and water table are among the main factors controlling earthquake characteristics on the ground surface. Soil layers subjected to cyclic stresses may lead to degradation of stress–strain and shear strength properties. The laboratory tests were conducted to evaluate the changes in the stress–strain and shear strength characteristics in terms of threshold cyclic shear stresses and cyclic yield stress. The effects of local site conditions are assessed based on geotechnical site conditions and earthquake source characteristics.     

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.     

静动应力作用下大连饱和黏土的剪切特性研究

针对人工制备的大连饱和黏土,在静应力与循环应力联合作用下进行了多组循环剪切试验,着重探讨了初始静力大小及加载速率对循环剪切变形特性的影响.试验表明静应力与循环应力作用下饱和黏土具有循环蠕变特性,总应变由初始静应变和循环蠕变两部分组成,其中循环蠕变主要受循环应力幅值、初始静应力大小及其加载速率的影响,循环蠕变的逐次增加量...     

Consolidation of inelastic clays under rectangular cyclic loading

This paper presents a semi-analytical solution for one dimensional consolidation problem of inelastic clays under cyclic loading considering the effect of the change of the consolidation coefficient of the soil layer. Due to change of the consolidation coefficient, and time-dependant loading, Terzaghi's theory would not be applicable in cyclic conditions. In this research, a method based on the time variable exchange along with the superimposing rule is employed to overcome these shortcomings. Changes in the consolidation coefficient are applied in the solution by modifying the loading and unloading durations introducing a Virtual Time. Based on the superimposing rule a set of continuous static loads in specified times are used instead of the cyclic load in the transformed time space. Each full cycle of loading is replaced by a pair of static loads with different signs. Based on the Terzaghi's theory the pore-water pressure distribution and the degree of consolidation are calculated for each static load and the results are superimposed. A set of laboratory consolidation tests under cyclic load and numerical analysis are performed in order to verify the presented method. The numerical solution and laboratory tests results showed the accuracy of the presented method.     

Pre-shear effect on liquefaction resistance of a Fujian sand

Pre-shear history has been shown to be a critical factor in the liquefaction resistance of sand. By contrast to prior experimental studies in which triaxial shear tests were used to examine the effects of pre-shear on the liquefaction resistance of sand, hollow cylinder torsional shear tests were used in this study to avoid the influence of the inherent anisotropy that is inevitably produced during the sample preparation process because of gravitational deposition. A series of cyclic undrained shear tests were performed on sand samples that had experienced medium to large pre-shear loading. The test results showed that the liquefaction resistance of sand can be greatly reduced by its pre-shear history, and a pre-shear strain within the range from 0.1% to 5% can cause sand to be more prone to liquefaction. During the cyclic shear tests, the samples that had experienced pre-shear loading exhibited different behaviors when cyclic shear loading started in different directions, i.e., the clockwise direction and the counterclockwise direction. If the cyclic loading started in the identical direction as the pre-shear loading, then the mean effective stress of the sand was almost unchanged during the first half of the loading cycle; if the cyclic loading started in the direction opposite to that of the pre-shear loading, then the mean effective stress decreased significantly during the first half of the loading cycle. However, this anisotropic behavior was only remarkable during the first loading cycle. From the second cycle onward, the speeds of the decrease in the mean effective stresses in the two types of shear tests became similar.     

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.     

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.     

Impact and cyclic shaking on loose sand properties in laminar box using gap sensors

This paper focuses on using high-frequency GAP-SENSORs (GSs), accelerometers, and load cells in a laminar shear box (LSB) filled with loose Toyoura sand to understand the effects of impact loads and cyclic shaking at 1-G on soil properties. The shear wave velocity at small strain (V_s) was calculated directly from first arrival reference using displacement time-history of two GSs under impact loading. Moreover, from first peak using the reduced deformation amplitude technique, damping ratio was calculated. In addition, shaking table tests were performed under harmonic loading with amplitude of acceleration inside the model ground varying from 0.02 g to 1 g. The frequencies of excitation varied from 1 Hz to 10 Hz. GSs and inside accelerometers were used to directly measure the outside lateral deformation and shear stress at different elevations of LSB, respectively. Results show that the shear modulus (G) and the damping ratio (D) behavior of model sand are generally consistent with the behavior presented by similar tests using only accelerometers. In addition, damping ratio increases as frequency loading increases. Characteristic changes in two shear stress components in shaking loading conditions were also investigated using high precision inside load cells.