Probabilistic Models for Cyclic Straining of Saturated Clean Sands

A maximum likelihood framework for the probabilistic assessment of postcyclic straining of saturated clean sands is described. Databases consisting of cyclic laboratory test results including maximum shear and postcyclic volumetric strains in conjunction with relative density, number of stress (strain) cycles, and “index” test results were used for the development of probabilistically based postcyclic strain correlations. For this purpose, in addition to the compilation of existing data from literature, a series of stress-controlled cyclic triaxial and simple shear tests were performed on laboratory-constituted saturated clean sand specimens. The variabilities in testing conditions (i.e., type of test, consolidation procedure, confining pressure, rate of loading, etc.) were corrected through a series of correction schemes, the effectiveness of which were later confirmed by the discriminant analyses results. Volumetric and shear strain boundary curves were developed in the cyclic stress ratio versus N1,60,CS or qc,1 domain. In addition to being based on significantly extended and higher quality databases, contrary to the existing judgmentally derived deterministic ones, proposed correlations have formal probabilistic bases, and so provide insight regarding uncertainty of strain predictions or probability of exceeding a target strain value. Probabilistic uses of the proposed correlations were illustrated by three sets of examples. A companion paper applied and calibrated the proposed volumetric strain correlation to semiempirically evaluate postearthquake settlement of level, free-field sites. For the calibration, case history soil profiles, composed of a broad range of sand types and depositional characteristics, shaken by a number of earthquakes, were used. Superior predictions of field settlements by this laboratory data-based cyclic strain assessment approach were concluded to be strongly mutually supportive.     

Unified Catastrophic Model for Collapsible Loess

A unified model considering the microstructure instability and a set of complete constitutive relations, which describes the volumetric collapse and shearing collapse simultaneously, is developed for collapsible loess in the framework of the catastrophe theory. The validity of the model is verified by comparing the results calculated using the model with the data of triaxial compression tests performed on Lanzhou loess. The following characteristics of collapsing deformation are explained and reproduced successfully using the model: (1) the existence of two turning points on each deformation curve, (2) the shear curves under various stress ratios intersect one another, (3) the ratio of the shear strain to the volumetric strain is a function of the stress ratio, and (4) the initial collapse condition is approximately a circle.     

Performance of a Three-Dimensional Hvorslev–Modified Cam Clay Model for Overconsolidated Clay

It is well established that critical state soil mechanics provides a useful theoretical framework for constitutive modeling of soil. Most of the critical state models, including the popular modified Cam clay (MCC) model, predict soil behavior in the subcritical region fairly well. However, the predictions for heavily overconsolidated soils, in the supercritical region, are not so satisfactory. Furthermore, the critical state models were developed from triaxial test data and extension of these models into three-dimensional (3D) stress space has not been investigated thoroughly. In the present work, experiments were carried out to obtain stress–strain behavior of overconsolidated soil in triaxial compression, extension, and plane strain conditions. A novel biaxial device has been developed to conduct the plane strain tests. The experimental results were used to formulate Hvorslev–MCC model which has MCC features in the subcritical region and Hvorslev surface in the supercritical region. The model was generalized to 3D stress space using the Mohr–Coulomb failure criterion. A comparison of the model predictions with test results has indicated that the Hvorslev–MCC model performs fairly well up to the peak supercritical point, during which deformations are fairly uniform and the specimens remain reasonably intact. Limitations of this simple model in predicting postpeak localization are also discussed. The model’s predictions for volumetric response in different shear modes seem to agree reasonably well with test results.     

On-Site Nonlinear Hysteresis Curves and Dynamic Soil Properties

Strong motion records at five vertical array sites in Japan are used to examine soil shear modulus and material damping as a function of shear strain during large earthquakes. Acceleration data from the sites are processed directly for evaluation of site shear stress-strain hysteresis curves for different time windows of the record. Results of the analysis demonstrate a significant nonlinear ground response at the sites with surface peak ground accelerations exceeding 90 gal. The results of shear stress-strain hysteresis curves are also used to estimate variation of soil shear modulus and material damping characteristics with shear strain amplitude at each site. The identified shear modulus-shear strain and damping ratio-shear strain relationships are in general agreement with published laboratory results. These response interpretations are also compared with the results of a frequency-domain analysis by using the spectral ratio (uphole∕downhole) technique. There is general agreement between the time- and frequency-domain results. The results illustrate the significance of the site nonlinearity during strong ground motions as well as the accuracy of the dynamic soil properties obtained from laboratory tests.     

Sequential Analysis of Ground Movements at Three Deep Excavation Sites with Mixed Ground Profiles

Field measurements of settlement and lateral deformation obtained from three deep excavation sites constructed in mixed ground profiles are presented and analyzed. Settlement measurements were obtained throughout the construction process, categorized in three stages as: (1) preexcavation (i.e., preliminary site work and support wall installation); (2) main excavation and bracing/anchor installation; and (3) postexcavation (i.e., removal of bracing as basement construction proceeds). Maximum preexcavation stage settlements of 0.03%Hw to 0.06%Hw (where Hw = wall or trench depth) were measured at two sites, with the maximum settlements occurring adjacent to the wall during its installation. Maximum ground surface settlements during the main excavation stage ranged from about 0.15%He to 0.30%He (where He = final excavation depth) and the distribution of ground settlement extended to a distance of 1.5He to 2.0He from the wall. Maximum settlements occurred at distances of about 0.3He to 0.5He from the wall at two sites where the wall consisted of concrete cast in situ (concrete diaphragm and concrete secant pile walls), creating a significant reverse curvature in the settlement distribution. The maximum postexcavation stage settlements ranged from 0.07%He to 0.10%He for the three sites, representing roughly 10 to 60% increases in settlement over the main excavation settlements, depending greatly on the specific support removal methods as well as the basement floor construction details employed at an individual site. Lateral deflections during the main excavation stage were consistent with trends reported in the literature, ranging from 0.12%He to 0.23%He, while lateral movement during postexcavation stage ranged from 0.03%He to 0.09%He. Finally, the settlements measured during the main and postexcavation stages are related to the support system stiffness.     

Effects of Disturbance on Undrained Strengths Interpreted from Pressuremeter Tests

Although the cylindrical cavity expansion theory should provide a sound basis for obtaining the undrained shear strength of clays from pressuremeter tests, the interpreted strengths are often inconsistent with data measured in high-quality laboratory tests. This paper investigates how the pressuremeter results are affected by disturbances that inevitably occur during device installation. The installation of self-boring and displacement-type pressuremeters is simulated using strain path analyses, with realistic effective stress-strain-strength properties described by the MIT-E3 model. Derived strengths obtained from the simulated expansion of displacement-type pressuremeters tend to underestimate the in situ∕cavity expansion strength by amounts that depend on the relative volume of soil displaced, the time delay prior to testing, and the initial overconsolidation ratio of the clay. Interpretation procedures using the simulated contraction curves give much more reliable estimates of the true undrained shear strength. The simulated disturbance effects of self boring lead to derived peak shear stresses that are significantly higher than the reference undrained shear strengths. This overestimate depends on the volume of soil removed during installation and is enhanced when the finite membrane length is included in the analyses. Self-boring pressuremeter data from a well-documented test site in Boston confirm the general character of the predicted pressuremeter stress-strain behavior. The theoretical analyses underestimate the peak strengths derived from self-boring pressuremeter (SBPM) expansion tests, but match closely the measured postpeak resistance in the strain range of 3–6% (saddle point condition). Saddle point strengths are similar in magnitude to the shear strengths measured in laboratory undrained triaxial compression tests at this site. The current predictions are not able to explain the very high shear strengths derived from the SBPM contraction curves.     

Different Approaches for Estimating Ground Strains from Pile Driving Vibrations at a Buried Archeological Site

Ground strains were estimated from vibrations measured during pile driving operations at a buried, prehistoric archeological site to monitor potential construction impacts. Subsurface characteristics of the site were investigated using multiple cone penetration test (CPT) soundings and the shear wave velocity profile was measured using the seismic CPT method. Embedded geophones and surface accelerometers were then used to measure ground vibrations during pile driving. Displacement gradients were estimated from the vibrations using the following three methods: (1) the difference between adjacent displacements divided by sensor spacing; (2) peak particle velocity divided by depth-dependent wave velocity (i.e., at the depth where the sensor was placed); and (3) peak particle velocity divided by frequency-dependent wave velocity from a measured dispersion curve. Methods (1) and (3) agreed well, while method (2) caused errors that depended on depth of embedment of the sensors and distance from pile driving. Errors in (2) were attributed to a mismatch between the depth-dependent wave velocity and the wave velocity on the frequency band that carried the largest velocity pulse through the dispersive soil profile. Ground strains were related to displacement gradients based on theoretical solutions of harmonic body waves and Rayleigh waves in dispersive elastic media. The peak estimated ground strains were smaller than the threshold volumetric shear strain, but a few centimeters of settlement were nevertheless observed at the site. The spatial extent of the settlement is characterized using attenuation rules fit to the vibration data, and by calibration with a settlement gauge. Ground cracking and vertical offsets that could potentially mask the archaeological history of the site were neither observed nor predicted from the observed vibration amplitudes. Estimated impact on archeological interpretation of artifacts in their stratigraphic context was likely insignificant except in the immediate region where the piles were driven. This insight will assist in future planning at sites with similar subsurface stratigraphy.     

Experimental Study of Wellbore Instability in Clays

This paper presents the results of an extensive program of laboratory model wellbore tests that have been performed to study wellbore instability in saturated clays. The tests were conducted on resedimented Boston blue clay (RBBC) anisotropically consolidated to vertical effective stresses up to 10?MPa by using two custom-built thick-walled cylinder (TWC) devices with outer diameters Do = 7.6 and 15.2?cm. The experimental program investigated the effects of specimen geometry, mode of loading, strain rate, consolidation stress level, and overconsolidation ratio (OCR) on deformations of the model wellbore measured during undrained shearing. Results indicate that for normally consolidated clays most of the change in cavity pressure occurs at volumetric strains less than 5% after which the borehole becomes unstable. Increases in outer diameter and strain rate led to a reduction in the minimum borehole pressure. Stress-strain properties were interpreted by using an analysis procedure originally developed for undrained plane strain expansion of hollow cylinders. The backfigured undrained strength ratios from these analyses for normally consolidated specimens range from su/σvc′ = 0.19–0.22. Overconsolidation greatly improves the stability of the borehole, and interpreted undrained strength ratios from the TWC tests are consistent with well-known power law functions previously developed for elemental shear tests.     

Probabilistic Model for the Assessment of Cyclically Induced Reconsolidation (Volumetric) Settlements

A maximum likelihood framework for the probabilistic assessment of cyclically induced reconsolidation settlements of saturated cohesionless soil sites is described. For this purpose, over 200 case history sites were carefully studied. After screening for data quality and completeness, the resulting database is composed of 49 high-quality, cyclically induced ground settlement case histories from seven different earthquakes. For these case history sites, settlement predictions by currently available methods of Tokimatsu and Seed (1984), Ishihara and Yoshimine (1992), Shamoto et al. (1998), and Wu and Seed (2004) are presented comparatively, along with the predictions of the proposed probabilistic model. As an integral part of the proposed model, the volumetric strain correlation presented in the companion paper is used. The accuracy of the mean predictions as well as their uncertainty is assessed by both linear regression and maximum likelihood methodologies. The analyses results revealed that (1) the predictions of Shamoto et al. and Tokimatsu and Seed are smaller than the actual settlements and need to be calibrated by a factor of 1.93 and 1.45, respectively; and (2) Ishihara and Yoshimine, and Wu and Seed predictions are higher than the actual settlements and need to be calibrated by a factor of 0.90 and 0.98, respectively. The Wu and Seed procedure produced the most unbiased estimates of mean settlements [i.e., their calibration coefficient (0.98) is the closest to unity], but the uncertainty (scatter) of their predictions remains high as revealed by the second to last smaller R2 value, or relatively higher standard deviation (σε) of the model error. In addition to superior model predictions, the main advantage of the proposed methodology is the probabilistic nature of the calibration scheme, which enables incorporation of the model uncertainty into mean settlement predictions. To illustrate the potential use of the proposed model, the probability of cyclically induced reconsolidation settlement of a site after a scenario earthquake to be less than a threshold settlement level is assessed.     

Learning of Dynamic Soil Behavior from Downhole Arrays

An increasing number of downhole arrays are deployed to measure motions at the ground surface and within the soil profile. Measurements from these arrays provide an opportunity to improve site response models and to better understand underlying dynamic soil behavior. Parametric inverse analysis approaches have been used to identify constitutive model parameters to achieve a better match with field observations. However, they are limited by the selected material model. Nonparametric inverse analysis approaches identify averaged soil behavior between measurement locations. A novel inverse analysis framework, self-learning simulations (SelfSim), is employed to reproduce the measured downhole array response while extracting the underlying soil behavior of individual soil layers unconstrained by prior assumptions of soil behavior. SelfSim is successfully applied to recordings from Lotung and La Cienega. The extracted soil behavior from few events can be used to reliably predict the measured response for other events. The field extracted soil behavior shows dependencies of shear modulus and damping on cyclic shear strain level, number of loading cycles, and strain rate that are similar qualitatively to those reported from laboratory studies but differ quantitatively.     

Double Strain Softening and Diagonally Crossing Shear Bands of Sand in Drained Triaxial Tests

A comprehensive understanding of the shear behavior of sand in the context of shear band development has not been achieved yet in spite of many detailed research works on each specified subject. In order to observe the entire drained shear behavior of Toyoura sand from the macromechanical point of view, conventional triaxial tests were performed and analyzed up to an axial strain of 30% for various void ratios, initial confining stresses, and stress paths, paying particular attention to volume changes. The strong correlation was found between “double strain softening” and “diagonally crossing shear bands” as a remarkable result. Finally, a qualitative explanation of relations among the stress–strain curve, the failure shape, the dilatancy index–strain curve and the strain localization, could be clearly made. Also, it is concluded that the dilatancy index is an indicator not only of the ratio of the volumetric strain increment to the axial strain increment but also the condition of the strain localization.     

Effect of Sampling Disturbance on Properties of Singapore Clay

This paper examines results from triaxial unconfined compression tests and undrained compression tests on reconsolidated samples of a Singapore marine clay retrieved using two sampling methods that offer differing quality of samples. Both local internal strain measurements using a Hall-effect transducer and external strain measurements using LVDTs were employed in the triaxial tests. Bender elements were embedded in some of the samples to establish the maximum shear modulus. If the samples are not reconsolidated, the shear strength and stiffness determined from triaxial tests are found to be sensitive to the quality of the samples, and generally lower than that determined by in situ tests. However, if the samples are subjected to isotropic or K0 consolidation to the estimated in situ condition, there is little difference between the shear strengths of samples retrieved using different samplers, and also consistent with results from vane shear tests. However, for the maximum shear modulus, even with reconsolidation, there is still a 10% difference between the results from samples retrieved using different samplers. Further, the laboratory determined maximum shear moduli are about 10% lower than the value determined in an in situ seismic cone test.     

Volumetric Strains of Clean Sands Subject to Cyclic Loads

We utilize simple shear testing to investigate the volume change of clean sands subject to cyclic loads. We examine the effects of a number of compositional and environmental factors on the vertical strain at 15 uniform shear strain cycles and on the cycle-to-cycle variation of vertical strain. The compositional factor found to principally affect seismic compression susceptibility is relative density. Compositional factors found to not significantly affect cyclic volume change include gradation parameters (mean grain size and uniformity coefficient), particle angularity, soil fabric, mineralogy, and void ratio “breadth” e-emin. An environmental factor found to affect seismic compression susceptibility is confining stress, with volumetric strains decreasing with increasing stress. Environmental factors that do not significantly affect seismic compression susceptibility for clean sands are saturation and age. Stress history can decrease vertical strains from seismic compression for certain conditions, but we find such effects to be insignificant for the levels of overburden stress where compacted fills are typically overconsolidated from compaction-induced stresses. An empirical model is developed to represent the major trends of the data for application in engineering practice, which improves upon an earlier model that is based on a much smaller database and does not account for the aforementioned environmental factors.     

Volumetric Threshold Shear Strain for Cyclic Settlement

The volumetric cyclic threshold shear strain for cyclic settlement, γtv, is evaluated for seven different sands and clays at different degrees of saturation, S, from the results of 11 Norwegian Geotechnical Institute-type direct simple shear, multistage cyclic settlement tests. Each test included several cyclic strain-controlled stages at cyclic shear strain amplitudes, γc, slightly smaller and slightly larger than γtv, such that γtv could be evaluated from each single test. At γc<γtv, specimens did not experience a permanent change in volume or settle even after a large number of cycles, while at γc>γtv they did. The data show that γtv is larger for clays than for sands and that it generally increases with the soil’s plasticity index (PI). For example, γtv ≈ 0.01–0.02% was obtained for sands and γtv ≈ 0.04–0.09% was obtained for clays having PI ≈ 30. A rather consistent γtv versus PI correlation for cyclic settlement is presented. No obvious trends were found between γtv and S and vertical stress.     

Liquefaction-Induced Lateral Spreading in Near-Fault Regions during the 1999 Chi-Chi, Taiwan Earthquake

We document and analyze incidents of liquefaction-induced lateral ground deformation at five sites located in the near-fault region of the 1999 Chi-Chi Taiwan earthquake. Each of the lateral spreads involved cyclic mobility of young alluvial soils towards a free face at creek channels. In each case, the lateral spreading produced relatively modest lateral displacements (approximately 10–200?cm) in parts of the spreads not immediately adjacent to channel slopes. For each site, we present displacement vectors across the spread features, which are based on mapping performed within three weeks of the earthquake. We review the results of detailed subsurface exploration conducted at each site, including cone penetration test soundings, borings with standard penetration testing, and laboratory index tests. We back-analyze the field displacements using recent empirical and semiempirical models and find that the models generally overestimate the observed ground displacements. Possible causes of the models’ overprediction bias include partial drainage of the liquefied soils during shaking, low but measurable plasticity of some of the soils’ fines fraction, and the absence of nonspread sites in the empirical databases used to develop existing empirical and semi-empirical lateral spread displacement prediction models.     

Undrained Shear Strength of Pleistocene Clay in Osaka Bay

This study presents the undrained shear characteristics of Holocene and Pleistocene clay samples from depths of 20–200 m under the seabed in Osaka Bay. Automated triaxial K0 consolidation tests and anisotropically consolidated-undrained triaxial compression and extension tests are conducted using the recompression method. The average undrained strength ratio (su/σv0′) is 0.33 (SD = 0.03) when the extension strength is defined as the peak strength or the strength at an axial strain of 15%, while su/σv0′ is 0.29 (SD = 0.04) when the extension strength is defined as the shear stress at the axial strain corresponding to the peak compression strength. Circular arc stability analyses are carried out with the modified Fellenius and Bishop methods for the design cross section of the seawall structure of the Kansai International Airport to study the effects of different definitions of shear strength. The seawall is founded on 19 m of soft Holocene clay and 10 m of Pleistocene sand overlying the Pleistocene clay. The stability analyses show that the factor of safety and depth of the critical circle (i.e., above versus below the sand layer) are sharply affected by both the value of su/σv0′ (0.33 versus 0.29) and the method of slices (Fellenius versus Bishop). The marginal stability calls for careful monitoring of construction with field instrumentation.     

古砖塔子结构压剪复合受力性能分析

为研究古塔子结构的受力性能,设计制作了3件不同楼层的子结构缩尺模型试件,进行低周反复加载试验,观察试件的开裂、变形及破坏现象;建立数值模型进行计算,得到了试验荷载作用下各试件的等效塑性应变、荷载?位移曲线,将计算结果与试验结果进行对比,分析竖向压应力对古塔砌体抗震性能的影响。结果表明,特征荷载的计算值相对试验值的误差均小于21%,等效塑性应变的分布与试件开裂破坏区域一致;当竖向压力保持恒定时,随着水平荷载的增大,塔体沿砌筑缝逐渐开裂破坏,裂缝宽度亦随之增大,在塔体洞口周围的破坏更为明显,且试件残余变形增大;随着压剪比的增大,古塔砌体开裂破坏的范围减小,抗剪承载力、刚度以及耗能能力均有所提高,但延性和变形能力略有降低。研究结果为砖石古塔建筑结构损伤及抗震能力评定提供参考。      

Evaluation of Laminated Circular Elastomeric Bearings

This paper evaluates the behavior and performance of laminated circular elastomeric bearings and compares them to those of square and rectangular bearings. The study included an experimental evaluation and a nationwide survey of state Department of Transportations on the use and performance of circular bearings and bearings in general in their states. The experimental investigation studied the bearings' behavior in compression, compression and rotation, and compression and shear. Results from this limited study showed that the three bearings have similar stress-strain behavior in compression and they are in agreement with the AASHTO LRFD guide stress–strain curves. In compression and rotation, the AASHTO LRFD substructure moments are slightly less than the measured values for circular bearings and rectangular bearings rotated about their strong axis for a compressive stress of 10.3?MPa (1.5?ksi) and slightly higher than those of rectangular bearings rotated about their weak axis. In compression and shear, the shear stiffness of circular and square bearings is in agreement with theoretical values within the range of design displacements. Results from the survey showed that many states are using circular bearings and more states would consider using them, however no maintenance or monitoring data were available on their short-term and long-term performance.     

Nonlocal Multilaminate Model for Strain Softening Analysis

A constitutive model formulated within the multilaminate framework is described in this paper. The basic model, incorporating deviatoric and volumetric hardening, was developed for normally consolidated or slightly overconsolidated clay. This model has been extended to account for shear softening by using a nonlocal formulation. The nonlocal plasticity is based on weighted average of plastic strains taken from neighboring material points within a certain distance which is a function of an internal length parameter. This parameter is related to the mean grain size that restricts the element size. By using a softening scaling this restriction can be eliminated and the model is therefore capable of simulating geotechnical boundary value problems. The capability of the model for simulating strain softening behavior is shown by numerical simulation of biaxial tests. Finally, the ground response curve obtained from the proposed model for excavation of a tunnel in soil is discussed.     

Plasticity Model for Sand under Small and Large Cyclic Strains

A plasticity constitutive model for sands is proposed, which combines a bounding surface framework for large cyclic strains with a Ramberg-Osgood-type hysteretic formulation for relatively smaller strains. The distinction between small and large cyclic strains is based on the volumetric threshold cyclic shear strain γtv, a well-established geotechnical parameter. The state parameter ψ is used explicitly to interrelate the critical, peak, and dilatancy deviatoric stress ratios. The plastic modulus is expressed as a particular function of accumulated plastic volumetric strain, which simulates empirically the effect of fabric evolution during shearing. Extensive comparisons with experiments show accurate simulation of the basic aspects of cyclic behavior for a wide range of cyclic strain amplitudes, specifically, (1) the degradation of shear modulus and increase of hysteretic damping with cyclic shear strain amplitude; (2) the evolving rates of shear strain and excess pore pressure (or volumetric strain) accumulation with number of cycles; and (3) the resistance to liquefaction. The 14 model parameters are proven independent of initial and drainage conditions, as well as the cyclic shear strain amplitude. The simulation of monotonic shearing is equally accurate.