循环荷载下南京片状细砂的动应力——应变关系

以片状颗粒成分为主的片状结构砂与常用的圆形颗粒标准石英砂相比,在物理力学特性上有显著的差异。循环荷载作用下,饱和砂土振动孔压上升会导致土体刚度发生软化,当振动孔压累积达到一定水平时,会产生液化现象,从而引起土体结构发生破坏。采用英国WFI动三轴仪,研究了南京片状细砂在循环荷载作用下,静偏应力水平、循环应力比水平和循环次数对其动应力一应变关系的影响,考虑每一次循环过程中动应力—应变关系滞回曲线的卸载及再加载割线动剪切模量Gsec和最大割线模量Gmax的变化特性,建立了动剪模量软化的经验公式;静偏应力水平对动剪模量软化有显著影响,随着循环次数的增加,动应力—应变滞回圈逐渐向应变累积方向滑移和向应变轴方向倾斜,且彼此分离;考虑循环软化特性,采用修正的Masing准则,描述了循环荷载下南京片状细砂的动应力—应变关系。     

Settlements under consecutive series of cyclic loading

In this study, consolidation settlements of soft clay caused by cyclic loading and the affecting factors such as number of cycles and stress level were experimentally investigated. A group of samples prepared in slurry consolidometer in the laboratory were tested using cyclic simple shear testing device. Normally consolidated samples were subjected to five consecutive series of cyclic loading and drainage for 60 min were applied between each cyclic loading stages. Cyclic tests were performed with stress controlled two-way sinusoidal wave loading with different stress levels and number of cycles. Frequency of cyclic loading was constant as 0.1 Hz. As a result of this study, it can be concluded that soft clays subjected to undrained cyclic loading and drainage cycles exhibit more resistance against subsequent cyclic shear stresses. The consolidation settlements, pore pressures and shear strains decrease after each stage of cyclic loading.     

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.     

Undrained behaviour of two silica sands and practical implications for modelling SSI in liquefiable soils

The aim of the present study is twofold. Firstly, the paper investigates the undrained cyclic and post-cyclic behaviour of two silica sands by means of multi-stage cyclic triaxial tests. Secondly, based on the post-cyclic response observed in the element test, the authors formulate a simplified stress–strain relationship that can be conveniently used for the construction of p–y curves for liquefiable soils. The multi-stage loading condition consists of an initial cyclic loading applied to cause liquefaction, followed by undrained monotonic loading that aimed to investigate the post-cyclic response of the liquefied sample. It was found that due to the tendency of the liquefied soil to dilate upon undrained shearing, the post-liquefaction strain–stress response was characterised by a distinct strain–hardening behaviour. The latter is idealized by means of a bi-linear stress–strain model, which can be conveniently formulated in terms of three parameters, i.e.: (i) take-off shear strain, γ_to, i.e. shear strain required to mobilize 1 kPa of shear strength; (b) initial secant shear modulus, G₁, defined as 1/γ_to; (c) post-liquefied shear modulus at large strain, G₂ (γ⪢γ_to). Based on the experimental results, it is concluded that these parameters are strongly influenced by the initial relative density of the sample, whereby γ_to decreases with increasing relative density. Differently both shear moduli (G₁ and G₂) increases with increasing relative density. Lastly, the construction of new p–y curves for liquefiable soils based on the idealized bi-linear model is described.     

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.     

Shear modulus degradation model for cohesive soils

One of the key issues in cyclic behaviour of soft clays is gradual degradation of shear modulus. In most of the cyclic soil models such degrdation of shear modulus of soil with the progression of loading cycle was incorporated, addition to the standard non-linear backbone curves. Such cyclic degradation was usually represented by a parameter, degradation index, which is a function of loading cycles and cyclic shear strain amplitude. However it is well understood from the past experimental studies that the degradation index depends on various other factors as well. The present paper aims to develop a simple empirical model involving degradation index as a function of number of loading cycles, plasticity index, cyclic shear strain, overconsolidation ratio, loading frequency based on the experimental results. It is then fitted with the hyperbolic hysteretic model to estimate the modulus degradation for different cycles. Finally the damping ratio is calculated based on Masing rule with correction factors and validated through experimental results.     

波浪荷载作用下软黏土软化模型研究

波浪荷载能引起海床土体的主应力轴连续旋转。不同于地震、交通等循环荷载,在周期性波浪荷载作用的土体应力路径方式下,软黏土的软化效用更为明显。本文分别对天然和扰动的海床土体在波浪荷载作用下的应力响应进行模拟,并分析应力路径的特点;为描述软化后的应力-应变关系,将软化效用和累积塑性应变的参数引入到能够反应土体动力非线性的Hardin-Drnevich模型中,建立修正模型,使之能够反应软黏土体软化与塑性应变累计特性;通过与模拟波浪荷载下土体应力特征的循环耦合试验结果进行对比分析,验证该修正模型的可靠性。     

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.     

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.     

Pore water pressure increment model for saturated Nanjing fine sand subject to cyclic loading

Three groups of dynamic triaxial tests were performed for saturated Nanjing fine sand subjected to uniform cyclic loading. The tested curves of the excess pore water pressure (EPWP) ratio variation with the ratio of the number of cycles are provided. The concept of the EPWP increment ratio is introduced and two new concepts of the effective dynamic shear stress ratio and the log decrement of effective stress are defined. It is found that the development of the EPWP increment ratio can be divided into three stages: descending, stable and ascending. Furthermore, at the stable and ascending stages, a satisfactory linear relationship is obtained between the accumulative EPWP increment ratio and natural logarithm of the effective dynamic shear stress ratio. Accordingly, the EPWP increment ratio at the number of cycles N has been deduced that is proportional to the log decrement of effective stress at the cycle number N-1, but is independent of the cyclic stress amplitude. Based on the analysis, a new EPWP increment model for saturated Nanjing fine sand is developed from tested data fitting, which provides a better prediction of the curves of EPWP generation, the number of cycles required for initial liquefaction and the liquefaction resistance.     

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.     

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.     

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.     

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.     

Modelling exterior unreinforced beam‐column joints in seismic analysis of non‐ductile RC frames

The seismic response of non‐ductile reinforced concrete (RC) buildings can be affected by the behaviour of beam‐column joints involved in the failure mechanism, especially in typical existing buildings. Conventional modelling approaches consider only beam and column flexibility, although joints can provide a significant contribution also to the overall frame deformability. In this study, the attention is focused on exterior joints without transverse reinforcement, and a possible approach to their modelling in nonlinear seismic analysis of RC frames is proposed. First, experimental tests performed by the authors are briefly presented, and their results are discussed. Second, these tests, together with other tests with similar features from literature, are employed to calibrate the joint panel deformability contribution in order to reproduce numerically the experimental joint shear stress–strain behaviour under cyclic loading. After a validation phase of this proposal, a numerical investigation of the influence of joints on the seismic behaviour of a case study RC frame – designed for gravity loads only – is performed. The preliminary failure mode classification of the joints within the analysed frame is carried out. Structural models that (i) explicitly include nonlinear behaviour of beam‐column joints exhibiting shear or anchorage failure or (ii) model joints as elements with infinite strength and stiffness are built and their seismic performance are assessed and compared. A probabilistic assessment based on nonlinear dynamic simulations is performed by means of a scaling approach to evaluate the seismic response at different damage states accounting for uncertainties in ground‐motion records. Copyright © 2016 John Wiley & Sons, Ltd.     

Modelling of material non-linearities in steel structures subjected to transient dynamic loading

This paper is concerned with the modelling of the behaviour of steel under cyclic and dynamic loading conditions. After a general discussion regarding the requirements for accurate and efficient modelling in dynamics, two models are described and implemented. The bilinear stress-strain constitutive relationship with kinematic hardening is widely used in many computer codes, hence is used for ‘control’ purposes. The multisurface plasticity model is said to exhibit the important qualities of strain hardening, softening and relaxation to a mean stress. This model is described in detail and notes on model parameter evaluation are given. A number of validation examples are presented, due to the complexity of implementation of the multisurface formulation. This is followed by comparisons between the bilinear response predictions and those of the multisurface model for cyclic and dynamic tests on beam-columns. It is concluded that in the absence of material test data under cyclic loading, the bilinear model provides acceptably accurate response predictions. However, the multisurface model provides a significantly closer fit to experimental results, due to its ability to model a yield plateau and a non-linear strain-hardening regime as well as cyclic degradation. It can also be used for new types of steel where no distinct yield point is observed.     

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...     

Fiber-based hysteretic model for simulating strength and stiffness deterioration of steel hollow structural section columns under cyclic loading

An efficient component model has been developed that captures strength and stiffness deterioration of steel hollow structural section (HSS) columns. The proposed model consists of two fiber-based segments at a member's ends along with an elastic segment in between. The fibers exhibit nonlinear uniaxial stress–strain behavior, which is explicitly defined by uniaxial monotonic tensile and cyclic round coupon tests. The postbuckling behavior of an HSS column is traced through a proposed uniaxial effective stress–strain constitutive formulation, which includes a softening branch in compression and an energy-based deterioration rule to trace the influence of cyclic deterioration in the inelastic cyclic straining. These may be inferred by uniaxial stub-column tests. The component model captures the coupling between the column axial force and flexural demands. Consistent model parameters for a number of steel materials used in the steel construction in North America and Japan are proposed along with the associated model calibration process. The efficiency of the proposed model in predicting the hysteretic behavior of HSS columns is demonstrated by comparisons with physical steel column tests subjected to various loading histories, including representative ones of ratcheting prior to earthquake-induced collapse. The proposed model is implemented in an open-source finite element software for nonlinear response history analysis of frame structures. The effectiveness of the proposed model in simulating dynamic instability of steel frame buildings is demonstrated through nonlinear response simulations of a four-story steel frame building, which was tested at full-scale through collapse. Limitations as well as suggestions for future work are discussed.     

Seismic performance of precast shear wall-slab connection under cyclic loading: experimental test vs. numerical analysis

The structural behaviour of precast shear wall-diaphragm connection was compared with the monolithic connection under seismic loading. The monolithic connection was made by using U-bars connecting shear wall and slab, and the precast connection was made by using dowel bars in two steps. Firstly, U-shaped dowel bars from the precast shear wall lower panel and precast slab were connected by the longitudinal reinforcement, and screed concreting was done above the precast slab. Secondly, the shear wall upper panel was connected using the dowel bar protruding from the shear wall lower panel. The gap between the dowel bars and the duct was filled with non-shrink grout. The specimens were subjected to reverse cyclic loading at the ends of the slab. This study also aimed to develop a 3-D numerical model using ABAQUS software. The non-linear properties of concrete were defined by using the concrete damaged plasticity(CDP) model to analyse the response of the structure. The precast dowel connection between the shear wall and slab showed superior performance concerning ductility, strength, stiffness and energy dissipation. The developed finite element model exactly predicted the behaviour of connections as similar to that of experimental testing in the laboratory. The average difference between the results from finite element analysis and experimental testing was less than 20%. The results point to the conclusion that the shear resistance is provided by the dowel bars and the stiffness of the precast specimen is due to the diaphragm action of the precast slab. The damage parameter and the interaction between structural members play a crucial role in the modelling of precast connections.