Stiffness degradation of natural fine grained soils during cyclic loading

Cyclic behavior of natural fine grained soils under a broad range of strains were investigated considering the effects of plasticity index and changes in confining pressures based on cyclic triaxial tests. A total of 98 stress controlled cyclic triaxial tests were conducted on normally consolidated and slightly overconsolidated samples. The investigation was divided into two parts. The first part consists of stress controlled cyclic triaxial tests under different stress amplitudes that were conducted to estimate the modulus reduction and the thresholds between nonlinear elastic, elasto-plastic and viscoplastic behavior. The second part involves the investigation of the undrained stress–strain behavior of fine grained soils under irregular cyclic loadings. The results showed that the elastic threshold is approximately equal to 90% of G_max. Another transition point was defined as the flow threshold where the value of tangent of shear modulus ratio changes for the second time. Simple empirical relationships to estimate the dynamic shear modulus and damping ratio was formulated and compared with the similar empirical relationships proposed in the literature. The results provide useful guidelines for preliminary estimation of dynamic shear modulus and damping ratio values for fine grained soils based on laboratory tests.     

A practical method for utilization of commercial cyclic testing apparatuses for computation of site response in central Adapazari

We suggest a practical method for estimating strain–modulus–damping relationships for utilization in equivalent-linear site response analyses, so that the necessity for more sophisticated sampling and testing procedures can be justified. The method employs the commercial cyclic testing apparatuses, which have limitations in low-strain ranges, and the in-situ seismic tests. The shear modulus at about 1% cyclic shear strain amplitude and the shear-wave velocity measured in-situ is used for building a hyperbolic relationship between shear stress and shear strain. An extension of Masing׳s rule and the constraint on hysteretic damping at 1% cyclic shear strain amplitude leads to a strain–damping relationship. By putting a particular emphasis on the soils of Adapazarı, a city famous for the concentrated damage on alluvium basin during the 1999 Kocaeli (Mw7.4) earthquake, we demonstrated the usefulness of the method, and concluded that the shear-modulus reduction and damping characteristics of Adapazarı soils can yield to site amplification factors greater than those predicted by strain–modulus–damping relationships presented in literature, and can more efficiently explain the concentration of damage on the alluvium basin. Through the comparisons of spectral amplification factors computed by equivalent-linear site response analyses, we justified the necessity to run a more sophisticated testing program on determination of cyclic stress–strain behavior of Adapazarı soils, and consequently to consider transient nonlinear site-response analyses in order to reduce the possible bias in calculation of spectral amplification factors.     

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.     

Nonlinear identification of the soil response at Dahan downhole array site during the 1999 Chi–Chi earthquake

Records of the 1999 Chi–Chi earthquake, provided by the Dahan downhole array were analyzed, and nonlinear hysteretic stress–strain relations in the soil layers were estimated by the method previously used for studying the response of soils during the 1995 Kobe and the 2000 Tottori earthquakes. The obtained models of the soil behavior were applied for evaluating changes of the shear moduli in the soil layers and for the nonlinear identification of the soil behavior at Dahan site during the Chi–Chi earthquake. We found that reduction of the shear moduli in the soil layers did not exceed 5%, and the soil response was virtually linear. The content of the nonlinear components in the soil response was about 5% of the intensity of the response, and it was mostly due to the odd-order nonlinearities. A similarity in the stress–strain relations describing the behavior of soils during the 1995 Kobe earthquake, the 2000 Tottori earthquake, and the 1999 Chi–Chi earthquake was found, which indicates the possibility to describe the behavior of similar types of soils at different sites by similar stress–strain relations and predict soil behavior in future earthquakes.     

Simultaneous identification of time and space variant dynamic soil properties during the 1995 Hyogoken-Nanbu earthquake

Time and space variant soil properties at a liquefied site were simultaneously identified in the time domain by using borehole array strong motion records. During soil liquefaction at a site, soils usually show a wide variety of non-linear behavior along the depth as well as non-stationary behavior. Strong ground motion records were obtained at Port Island borehole array observatory, Kobe, during the 1995 Hyogoken-Nanbu earthquake. In this study, the instrumented soil was modeled by the equivalent linear MDOF system, and an extended Kalman filter with local iteration was employed for the identification of the soils. The identification process was successfully conducted, and the stress–strain relationships of the soils at the liquefied site were obtained from different depths all at once.     

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.     

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.     

Application of experimental results on cyclic deforming of soils to seismic response analysis

It is shown in this paper that experimental results on stiffness and damping corresponding to cyclic deforming of soils can be well approached theoretically on an interval of strain variation from zero to arbitrary large values of strains. For this purpose, the following two methods are recommended: a modification of the hysteretic model obeying Masing's rule by adding elastic stresses to pure hysteretic stresses that do not change the corresponding backbone curve; and, as the second method, a non-linear model with frequency independent loss of energy in periodic processes. It is shown that in the area close to the free surface of soil, normalized strains resulting from propagation of seismic waves can be very large, even in the case of an input motion of relatively low intensity. Therefore, a using analytical approximations for experimental stress–strain relationships, which are suitable only for an interval of small and medium values of normalized strains, is insufficient in seismic response analysis.     

Dynamic properties and liquefaction resistance of two soil materials in an earthfill dam—Laboratory test results

Results are presented of laboratory resonant column and cyclic triaxial tests on specimens of two compacted soils (a sandy–silty clay and a sand–gravel mixture), planned to be used in the core and the shells, respectively, of a proposed earthfill dam. The values of low-amplitude shear modulus of the clayey material were found to increase with increasing confining pressure and decreasing water content, with deviations of ±20% from the predictions of the “Hardin equation”. On the other hand, the low-amplitude damping ratio was found to be at least four times higher than the values corresponding to natural undisturbed cohesive soils. The proposed G/G₀−γ_c curve for the compacted cohesive soil was found to be independent of confining pressure and small variations of the water content on either side of the optimum value and showed a remarkable agreement with recently published similar curves for natural cohesive soils. For the case of the sand–gravel mixture, normalized G/G₀–γ_c and D–γ_c curves are proposed, based on recently published results for gravelly soils and the limited data of the present study. The liquefaction resistance of the saturated sand–gravel mixture was found to be strongly dependent on its relative density, especially for high values of cyclic stress ratio. A relative density of at least 55% was found to be necessary to assure safety against earthquake-induced liquefaction of the material. The results presented herein may be used (directly or as guide) in the seismic analysis of (new or existing) earth dams constructed from similar soil materials and in addition they provide insight into the dynamic behavior of compacted soils.     

A practical numerical method for large strain liquefaction analysis of saturated soils

Accurate prediction of the liquefaction of saturated soils is based on strong coupling between the pore fluid phase and soil skeleton. A practical numerical method for large strain dynamic analysis of saturated soils is presented. The u–p formulation is used for the governing equations that describe the coupled problem in terms of soil skeleton displacement and excess pore pressure. A mixed finite element and finite difference scheme related to large strain analysis of saturated soils based on the updated Lagrangian method is given. The equilibrium equation of fluid-saturated soils is spatially discretized by the finite element method, whereas terms associated with excess pore pressure in the continuity equation are spatially discretized by the finite difference method. An effective cyclic elasto-plastic constitutive model is adopted to simulate the non-linear behavior of saturated soils under dynamic loading. Several numerical examples that include a saturated soil column and caisson-type quay wall are presented to verify the accuracy of the method and its usefulness and applicability to solutions of large strain liquefaction analysis of saturated soils in practical problems.     

Probabilistic pseudo-static analysis of pile foundations in liquefiable soils

This paper presents the development, implementation, and application of a probabilistic framework for the pseudo-static analysis of pile foundations in liquefied and lateral spreading soils. The framework allows for rigorous consideration and propagation of the large uncertainties regarding quantification of seismic loads and soil–pile interaction relationships, which exist in the pseudo-static method. Building upon previous relationships proposed by others, the key features of the presented framework are outlined. In particular, the uncertainty estimation of the induced lateral soil displacements; superstructure inertia loads; and stiffness and strength of the liquefied soils are discussed in detail. The results of applying the pseudo-static method to a case study bridge structure are compared to that obtained using a rigorous seismic effective stress analysis within a similar framework. It is illustrated that the consideration of uncertainties in the pseudo-static framework provides enhanced communication of the foundation's seismic performance to end-users, and that the pseudo-static method provides seismic performance prediction consistent with that obtained using advanced seismic effective-stress analyses.     

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.     

Damping formulation for nonlinear 1D site response analyses

Measurements and observations of ground shaking during large earthquakes have demonstrated the predominant role of site effects in the response of infrastructure during a seismic event. Despite significant efforts to model the hysteretic response and nonlinearity of soils due to medium and large ground motions, the most widely accepted nonlinear site response methods are not able to represent simultaneously the changes of stiffness and energy dissipation (damping) observed in both laboratory tests and during earthquake events. This paper presents two new soil damping formulations implemented in nonlinear one-dimensional site response analysis for small and large strains. The first formulation introduces an approach to construct a frequency-independent viscous damping matrix which reduces the over-damping at high frequencies, and therefore, the filtering at those frequencies. The second formulation introduces a reduction factor that modifies the extended Masing loading/unloading strain–stress relationship to match measured modulus reduction and damping curves simultaneously over a wide range of shear strains. A set of examples are introduced to illustrate the effect of using the two proposed formulations, separately and simultaneously, in nonlinear site response analyses.     

Modeling and cyclic behavior of segmental bridge column connected with shape memory alloy bars

This paper examines the quasi-static cyclic behavior,lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy(SMA) link-bars.Moment-curvature constitutive relationships are formulated and analysis tools are developed for the PT column,including a modified four-spring model prepared for the SMA bars.The suggested system is exemplified using a column with an aspect ratio of 7.5 and twelve 36.5 mm diameter NiTi martensitic SMA bars.A post-tensioning force of 40% to 60% of the tendon yield strength is applied in order to obtain a self re-centering system,considering the residual stress of the martensitic SMA bars.The cyclic response results show that the lateral strength remains consistently around 10% of the total vertical load and the equivalent viscous damping ratios reach 10%-12% of critical.When large diameter NiTi superelastic SMA bars are incorporated into the column system,the cyclic response varies substantially.The creep behavior of the superelastic SMA bar is accounted for since it affects the re-centering capability of the column.Two examples are presented to emphasize the modeling sensitivities for these special bars and quantify their cyclic behavior effects within the column assembly.     

Shear moduli of volcanic soils

The shear modulus of soils is one of the important parameters in small strain level geotechnical problems (i.e. the study of earthquake effects and soil–structure interaction). In this paper, the shear moduli of crushable volcanic soils at small strain level were investigated in bender element and cyclic undrained triaxial tests. Comparison of results shows that the shear moduli from bender element tests agree well with those determined in cyclic triaxial tests. The influence of particle breakage, effective confining pressure, consolidation time, void ratio and fines content on the shear modulus are also discussed. In the present study, empirical equations for evaluating the shear modulus of granular materials with particle breakage are proposed based on the test results.     

System identification estimation of soil properties at the Lotung site

Dynamic properties of the soils at the Lotung test site, Lotung, Taiwan, are estimated from seismic vertical array measurements (input–output data sets) using both time-invariant and time-variant parametric modeling methods (system identification). Soil properties are directly mapped from model parameters to an equivalent lumped mass model of the soil interval. Shear stiffness and damping ratios were calculated for 8 events with M_L ranging from 4.5 to 7.0. Shear stiffness ranged between 0.5 and 6 MN/m, inversely proportional to PGA. The equivalent viscous damping ratio varied from 2 to 30% of critical damping, proportional to PGA. Degradation of soil behavior, while less pronounced with increasing depth, consistently occurs above a peak input acceleration of 0.07 g. Although “non-linear” behavior is evident above 0.17 g, Event 7 (0.21 g) is accurately predicted using a linear constant parameter model estimated from the smaller Event 8 aftershock ground motions.     

Simulation of torsional shear test results with neuro-fuzzy control system

In the first part of this study, a series of stress-controlled hollow cylinder cyclic torsional triaxial shear tests were conducted on loose to medium dense saturated samples of clean Toyoura sand to investigate its liquefaction behavior. A uniform cyclic sinusoidal loading at a 0.1 Hz frequency was applied to air-pluviated samples where confining pressure and relative density was varied. Cyclic shear stress–strain changes, the number of cycles to reach liquefaction and pore pressure variations were recorded. Results indicate that the liquefaction resistances of uniform sands are significantly affected by the method of sample preparation and initial conditions.     

等幅循环荷载作用下土的动剪模量和阻尼

本文根据我国南方8个场址81个试样的动三轴试验资料，对土在等幅循环荷载作用下，其动模量和阻尼与应变幅值的关系进行了分析研究，并与现场测试结果进行对比，分析结果，本文提出一种广义双曲线模型，能更满意地描述各类寺应力应变关系，该模型保持了形式简便，参数物理意义明确等优点，文中还分别对砂土和粘土，给出了模型中参数的统计关系式，这些表达式能明显的映粘性土和非粘性土的特性及其差别。