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With the recent advances in the biogeotechnics field and specifically microbially induced calcite precipitation (MICP), cone penetration testing (CPT) has become a valuable tool to overcome the challenges associated with intact sampling of improved soils, evaluate the spatial extent and magnitude of the applied MICP treatment, and assess the consequential improvement of engineering properties. Although the CPT cone tip resistance (qc) can effectively monitor the improvement of densified clean sands, no relationship exists to estimate cementation and strength parameters in MICP-treated sands. This paper proposes a relationship between the apparent cohesion (c) stemming from the MICP-induced cementation bonds at particle contacts and the change in tip resistance (qc) in initially loose sands. To develop a broadly useful correlation, available experimental CPT data in biocemented soils were used to guide computation simulations using a direct axisymmetric model of cone penetration in biocemented sands. The CPT numerical model uses the finite-difference method with a rezoning algorithm for large-deformation problems along with the Mohr-Coulomb constitutive model. The biocemented sand was characterized by Mohr-Coulomb strength parameters and an elastic shear modulus informed by shear-wave velocity measurements (Vs). The correlation parameters of interest were identified (c, qc, and Vs), and results of the numerical simulations were validated against available experimental data. Once validated, the numerical simulations were extended to different initial conditions, and the trends between parameters of interest were analyzed and interpreted. Results from the simulations are consistent with experimental data and show an increase in the cone tip resistance as the cementation level increases. The cementation level is modeled through apparent cohesion and the shear stiffness model parameters, which both increase as the cementation level increases. A linear relationship is proposed between the apparent cohesion and the change in cone tip resistance as a function of the confining stress.

Lateral spreading of an interlayered deposit adjacent to a meandering stream channel in Wufeng, Taiwan, during the 1999 Chi-Chi Earthquake is evaluated using two-dimensional (2D) nonlinear dynamic analyses (NDAs) with geostatistical modeling of the subsurface to assess their ability to approximate the observed magnitude and spatial extent of ground deformations, as well as identify the key factors and mechanisms that most contributed to the overall system response. In-situ data from borings and cone penetration tests (CPTs) depict thinly stratified overbank deposits of low-plasticity silty sands, silts, and clays, interlayered with laterally discontinuous channel-deposited sands. The three-dimensional (3D) subsurface is simulated using transition probability-based indicator geostatistics, conditioned on available CPT data and geological inferences. The NDAs are performed using the PM4Sand and PM4Silt constitutive models, within the FLAC finite difference program. Sensitivity analyses are performed to understand the influence of uncertainties in the stratigraphy, channel conditions, soil properties, input ground motions, constitutive model calibration protocols, and numerical boundary conditions, as well as the performance of alternate channel transects. Most analysis cases generally matched the maximum displacements observed near the channel but overestimated the extent of displacements away from the channel. The most favorable results were largely influenced by nonstationary stratigraphic trends and cyclic softening of fine-grained soils, in addition to the liquefaction of coarse-grained soils. This case history demonstrates the capabilities and limitations of current subsurface and NDA modeling procedures for predicting ground deformation patterns.

This case study presents an application of a conditional transition probability method for interpreting subsurface stratigraphy for the interbedded alluvium underlying Perris Dam, and evaluating the effects of stratigraphic uncertainty on nonlinear dynamic analysis (NDA) results for design earthquake loading. The challenges involved in synthesizing information from different sources (i.e., geologic conditions, site investigation tools, lab data, field classifications) into soil categories for interbedded alluvium were examined. The application of conditional transition probability methods for developing three-dimensional (3D) realizations of the upper Holocene and lower Pleistocene alluvial strata over a 305-m-wide interval along the dam alignment is described, including challenges with insufficient data and limitations involved with utilizing a stationary, geostatistical method for approximating nonstationary geologic conditions. Two-dimensional (2D) NDA models of Perris Dam were created by slicing the 3D transition probability realizations into five 2D cross sections. The constitutive models PM4Sand and PM4Silt were used to model the sand and clay soil categories in the alluvial strata, as well as the different zones in the embankment. The deformations and variability in deformations for each cross section were compared, and sensitivity studies were completed to examine the impact of several factors, including impacts of the small-strain shear modulus for the alluvium, mean lengths and sills for the alluvium categories, strengths for each alluvium soil category, and different ground motions. NDA cross sections of Perris Dam with uniformly (noncategorical) distributed properties were performed with and without additional deterministic embedded soil lenses, and the deformations were compared with transition probability models and deterministic models completed by others. The use of conditional transition probability models for NDAs of Perris Dam, along with implications and lessons for practice, are discussed.

The Canterbury Earthquake Sequence produced a spatial pattern of liquefaction-induced surface ejecta at an open field along Palinurus Road in Christchurch, New Zealand, that would not be ex...

Two-dimensional nonlinear dynamic analyses (NDAs) are performed for a series of hypothetical embankment dams on a spatially variable liquefiable foundation layer to evaluate the utility of representing the foundation layer with random fields conditioned on different levels of site characterization information. A set of two-dimensional parent models (PMs), each representing a true foundation condition, were generated using unconditional random fields of equivalent clean sand, corrected standard penetration test (N1)60cs values. Different levels of site characterization were then represented by combining different numbers of local borings (i.e., columns of data from the PM) with the optional inclusion of constraints on the geostatistical properties that might come from sitewide explorations. NDAs were performed using the same input motions for the PM (which represents perfect knowledge of soil conditions), a set of realizations conditioned on the local borings alone, and a set of realizations conditioned on the local borings with sitewide statistics. Embankment deformations obtained for the conditional realizations are compared to those for the PM to evaluate the potential benefits of increasing levels of site characterization in terms of deformation prediction accuracy. Parametric analyses include varying the embankment size, scales of fluctuation in the foundation stratum, number of conditioning borings, and ground motions. The results of these comparisons illustrate that the beneficial effects of using conditional random fields were generally limited to cases with the horizontal scale of fluctuation approaching the scale of the embankment base width and to cases with a large number of borings (more than three borings per horizontal scale of fluctuation), which may not be practical in many situations. Additional potential benefits and limitations of using conditional random fields for representing spatial variable liquefiable foundation layers in embankment dam NDAs are discussed.

Centrifuge modeling was used to study the performance of loose sand treated with microbial-induced calcium carbonate precipitation (MICP) to improve liquefaction resistance to triggering an...

A broad diversity of biological organisms and systems interact with soil in ways that facilitate their growth and survival. These interactions are made possible by strategies that enable organisms to accomplish functions that can be analogous to those required in geotechnical engineering systems. Examples include anchorage in soft and weak ground, penetration into hard and stiff subsurface materials and movement in loose sand. Since the biological strategies have been ‘vetted’ by the process of natural selection, and the functions they accomplish are governed by the same physical laws in both the natural and engineered environments, they represent a unique source of principles and design ideas for addressing geotechnical challenges. Prior to implementation as engineering solutions, however, the differences in spatial and temporal scales and material properties between the biological environment and engineered system must be addressed. Current bio-inspired geotechnics research is addressing topics such as soil excavation and penetration, soil–structure interface shearing, load transfer between foundation and anchorage elements and soils, and mass and thermal transport, having gained inspiration from organisms such as worms, clams, ants, termites, fish, snakes and plant roots. This work highlights the potential benefits to both geotechnical engineering through new or improved solutions and biology through understanding of mechanisms as a result of cross-disciplinary interactions and collaborations.

Nonlinear dynamic analyses (NDAs) of embankment dams of different heights founded on a spatially variable, liquefiable alluvial layer are used to examine factors influencing embankment defo...

Author(s): Boulanger, RW; Wilson, DW; Kutter, BL; DeJong, JT; Bronner, CE | Abstract: The 9-m and 1-m radius geotechnical centrifuges at the Natural Hazards Engineering Research Infrastructure (NHERI) facility at the University of California at Davis provide the national research community with open access to unique and versatile modeling capabilities for advancing methods to predict and improve the performance of soil and soil-structure systems affected by earthquake, wave, wind, and storm surge loadings. Large-scale centrifuge models are particularly effective for the building of basic science knowledge, the validation of advanced computational models from the component to the holistic system level, and the validation of innovative soil remediation strategies. The capabilities and unique role of large-scale centrifuge modeling are illustrated using three example research projects from the shared-use NHERI facility. Education impacts stemming from operations activities and coordination of activities by the center’s user base are discussed. Future directions and opportunities for research using the NHERI facilities are discussed.

Author(s): Oathes, TJ; Boulanger, RW | Abstract: The performance of geotechnical structures founded on normally consolidated (NC) clays under static or dynamic loading is dependent on the soil's strain-softening tendency and the potential for localizations to develop. Prior studies of the localization phenomenon have demonstrated that the addition of viscous (or strain-rate dependent) shearing resistance suppresses the onset of localization and provides a measure of regularization for the numerical simulation of the localization process. The onset of localization is delayed when the reduction in strength due to strain softening is counteracted by the increase in strength due to the increased strain rate that develops within a potential localization zone. Understanding localization tendencies is further complicated by spatial variability in clay properties. This paper presents a numerical study that investigates the combined effects of strain-rate, sensitivity, rate of strain softening, and varying strength profiles on the localization tendencies and the global stress-strain behavior of NC clays. The analyses were performed using the finite difference program FLAC 8.0 with the user-defined constitutive model PM4Silt modified to incorporate strain-rate effects. Parametric analyses examine the influence of strain rate, strength profile variations, local soil brittleness, and mesh size on the global post-peak stress-strain behavior of clays.

Numerical simulations of a centrifuge model test of an embankment on a liquefiable foundation layer treated with soil-cement walls are presented. The centrifuge model was tested on a 9-m radius centrifuge and corresponded to a 28 m tall embankment underlain by a 9 m thick saturated loose sand layer. Soil-cement walls were constructed through the loose sand layer over a 30 m long section near the toe of the embankment and covered with a 7.5 m tall berm. The model was shaken with a scaled earthquake motion having peak horizontal base accelerations of 0.05 g, 0.26 g, and 0.54 g in the first, second, and third events, respectively. The latter two shaking events caused liquefaction in the loose sand layer. Crack detectors embedded in the soil-cement walls showed that they developed only minor cracks in the second shaking event, but sheared through their full length in the last shaking event. The results of the centrifuge model test and two-dimensional nonlinear dynamic simulations are compared for the two stronger shaking events using procedures common in engineering practice. The effects of various input parameters and approximations on simulation results are examined. Capabilities and limitations in the two-dimensional simulations of soil-cement wall reinforcement systems, with both liquefaction and soil-cement cracking effects, are discussed. Implications for practice are discussed.

This paper presents the development, implementation and experimental evaluation of a new crack detection mechanism for centrifuge modelling. The proposed mechanism is a brittle conductor bonded to cement providing a binary indication of if, and when, a sensor is cracked. The results of a pair of large centrifuge tests were used to evaluate the effectiveness of the proposed crack detection mechanism. Each test model included a soil profile consisting of a 23 m thick layer of lightly over-consolidated clay, underlain and overlain by thin layers of dense sand. The centrifuge models had two separate zones, a zone without reinforcement and a zone with an ‘embedded’ soil–cement grid, which had a unit cell area replacement ratio Ar = 24%. Models were subjected to 13 different shaking events with peak base accelerations ranging from 0·01 to 0·55g. The performance of the proposed crack detection mechanism was examined using (i) post-test crack mapping in the soil–cement grids, (ii) results of the crack detection system and (iii) time series of accelerations, displacements and footing rotation. The results from the centrifuge test showed that the proposed crack detection method accurately captured if, and when, cracking occurred in the soil–cement grid at the locations of the sensors.

Centrifuge model tests are used to examine the dynamic response of structures supported by shallow foundations on soft clay reinforced by soil-cement grids. The centrifuge models involved a deep, lightly over-consolidated clay profile with three different soil-cement grid configurations. Structures on square shallow foundations were located over the central part of each soil-cement grid system. The models were subjected to multiple shaking events with peak base accelerations ranging from 0.006 to 0.546 g. The recorded responses of the structures and reinforced soil profiles were used to define the dynamic moment-rotation-settlement responses of the shallow foundations across the range of imposed shaking intensities. While the soil-cement grids were effective at controlling foundation settlements in most cases, the more significant foundation settlements which developed for the weakest soil-cement grid configuration under the stronger shaking intensities produced a rocking response of the structure and caused extensive crushing of the soil-cement below the edges of the shallow foundations. Analysis methods for predicting the demands imposed on the soil-cement grids by the inertial loads from the overlying structures and the kinematic loading from the soil profile's dynamic response are evaluated for consistency with the observed damage patterns. The experimental data have been archived and provide a basis for future studies to evaluate numerical and design analysis methods.

A plasticity model for representing clays and plastic silts, as opposed to purely nonplastic silts or sand, in geotechnical earthquake engineering applications is presented. The PM4Silt model builds on the framework of the stress-ratio controlled, critical state based, bounding surface plasticity PM4Sand model, and is coded as a user defined material for use with the program FLAC. The model was developed to provide reasonable approximations of monotonic undrained shear strength, cyclic undrained shear strength, and shear modulus reduction and hysteretic damping responses. The model does not include a cap, and therefore is not suited for simulating consolidation or reconsolidation settlements (i.e., volumetric strains) or strength evolution with consolidation stress or seismic loading history. The primary input parameters are the undrained shear strength ratio (or undrained shear strength), the shear modulus coefficient, and the contraction rate parameter. All secondary input parameters are assigned default values based on a default calibration, but may be adjusted when calibrating against advanced laboratory test data or performing sensitivity studies. The calibration process is described and illustrated by calibrations for three different normally consolidated, fine-grained soils with plasticity indices ranging from 4 to 20. The model is shown to provide reasonable approximations of behaviors important to many earthquake-engineering applications and to be relatively easy to calibrate.

Two-dimensional nonlinear dynamic analyses (NDAs) of Austrian Dam in the 1989 Mw=6.9 Loma Prieta earthquake are presented using the finite-difference program FLAC with the user-defined constitutive model PM4Silt and following engineering procedures common in practice. This relatively homogeneous, 55-m high embankment dam is comprised primarily of low-plasticity clayey sands and clayey gravels. The dam experienced estimated peak ground accelerations of 0.4-0.6g during the earthquake and developed extensive cracking with crest settlements up to 859 mm. The engineering properties of the compacted embankment materials are estimated based on the available isotropically consolidated undrained triaxial compression and resonant column test data. NDAs were performed using two alternative calibrations for the PM4Silt model and four different input motions. Sensitivity of the computed deformations to various modeling parameters and assumptions was examined. The computed responses are shown to be in reasonable agreement with the observed crest settlements, embankment deformation patterns, and excess pore pressures. Limitations in the material characterizations and analysis procedures and their possible effects on the analysis results are discussed. The results of this study provide support for the use of these analysis methods and engineering procedures in seismic evaluations of compacted earthfill embankments.

The effects of soil plasticity and penetration rate on cone penetration resistance in low-plasticity fine-grained soils are evaluated. A series of centrifuge tests with in-flight variable rate cone penetration soundings was performed on models of four slurry deposited mixtures of nonplastic silica silt and kaolin clay (0%, 2.5%, 5%, and 20% kaolin by dry mass) with plasticity indices ranging from 0 to 6. Cone penetration resistances for an effective overburden stress of 100 kPa ranged from 26 to 40 MPa (260 to 400 atm) in the nonplastic silica silt to 0.4-1.8 MPa (4-18 atm) in the silt-clay mixture with a plasticity index of 6. The addition of a small amount of clay (as little as 2.5% by dry mass) to nonplastic silt resulted in an order of magnitude decrease in drained penetration resistance. Faster penetration rates produced partially drained and undrained conditions, with negative excess pore pressures developing in the nonplastic silica silt and positive excess pore pressures developing in the mixtures with 5% and 20% kaolin.

The effects of partial drainage on the cyclic strength of saturated sand in a set of dynamic centrifuge model tests were evaluated. Three models of level profiles of saturated Ottawa F-65 sand with initial relative densities of 25%, 43%, and 80% were tested using a 9-m-radius centrifuge. Models were subjected to multiple sinusoidal shaking events with acceleration amplitudes ranging from 0.03g to 0.55g. The cyclic resistance ratios (CRR) obtained from inverse analyses of dense accelerometer and pore pressure transducer arrays were correlated with cone penetration resistances (qc1N) from in-flight cone penetration tests. Time histories of volumetric strain and surface settlement due to partial drainage were determined by inverse analyses of the array data and compared with measured surface settlements. The effect of volumetric strain on cyclic strength is examined through single-element simulations using the constitutive model PM4Sand version 3. Results of these simulations are compared to prior laboratory and numerical studies investigating the effect of partial saturation on cyclic strength. The magnitude of the volumetric strains developed in the centrifuge models due to partial drainage and their effects on the centrifuge CRR-qc1N correlation are examined.

Mechanistic approaches to developing cone penetration test-based liquefaction triggering correlations are presented and evaluated with an application to Ottawa sand. The mechanistic approaches utilize combinations of data from undrained cyclic direct simple shear tests, dynamic geotechnical centrifuge tests with in-flight cone penetration profiles, and cone penetration simulations. Cyclic direct simple shear tests on Ottawa sand characterize the relationship between cyclic resistance ratio (CRR) and relative density (DR). Relationships between cone tip resistance (qc) and DR are developed from geotechnical centrifuge tests and cone penetration simulations. Penetration simulations using the MIT-S1 constitutive model with three different calibrations for Ottawa sand examine the role of critical state line shape and position on simulated qc values. The CRR-DR relationship from laboratory tests is composed with measured and simulated qC-DR relationships via common DR values to develop CRR-qc relationships. An alternative CRR-qc relationship is developed from inverse analyses of centrifuge test sensor array data (i.e., arrays of accelerometers and pore pressure sensors). The results of these different approaches are compared to case history-based correlations for clean sand and their relative merits discussed. Recommendations are provided for future application of these mechanistic approaches to developing liquefaction-triggering correlations of poorly characterized or unique soils.

A set of saturated Ottawa sand models was treated with microbially induced calcite precipitation (MICP) and subjected to repeated shaking events using the 1-m radius centrifuge at the UC Davis Center for Geotechnical Modeling. Centrifuge models were constructed to initial relative densities (DR0) of approximately 38% and treated to light, moderate, and heavy levels of cementation (calcium carbonate contents by mass of approximately 0.8%, 1.4%, and 2.2%, respectively) as indicated by shear wave velocities (light≈200 m/s, moderate≈325 m/s, and heavy≈600 m/s). The cemented centrifuge models were compared to a pair of uncemented saturated Ottawa sand models with initial DR0≈38 and 53% and subjected to similar levels of shaking. Cone penetration resistances and shear wave velocities were monitored throughout shaking to investigate (1) the effect of cementation on cone penetration resistance, shear wave velocity, and cyclic resistance to liquefaction triggering; and (2) the effect of shaking on cementation degradation. Accelerometers, pore pressure transducers, and a linear potentiometer were used to monitor the effect of cementation on liquefaction triggering and consequences. Cone penetration resistances and shear wave velocities were sensitive to light, moderate, and heavy levels of cementation (increases in penetration resistance from 2 to 5 MPa, from 2 to 10 MPa, and from 2 to 18 MPa and increases in shear wave velocity from 140 to 200 m/s, from 140 to 325 m/s, and from 140 to 660 m/s, respectively), and were able to capture the effects of cementation degradation.

The performance of Çark Canal in the 1999 M=7.5 Kocaeli earthquake was evaluated using common liquefaction vulnerability index (LVI) methods, a nonlinear dynamic analysis (NDA) method, and a Newmark sliding block method to examine possible factors contributing to why different analysis approaches often overestimate liquefaction effects in interbedded deposits. The characterization of the interbedded fluvial stratum based on cone penetration test (CPT) data utilized an inverse filtering procedure to correct CPT data for thin-layer and transition zone effects. Common LVIs computed using the measured and inverse-filtered CPT data with a site-specific fines content calibration showed that the combination of these two steps reduced the LVIs by 30%-50% for this site and seismic loading. Two-dimensional NDAs were performed using stochastic realizations for the interbedded stratum and the PM4Sand and PM4Silt constitutive models for the sandlike and claylike portions, respectively. Computed deformations were evaluated for their sensitivity to stochastic model parameters, the cyclic strength assigned to the sandlike soils, the undrained shear strengths assigned to the claylike soils, the level of shaking, and other input parameters. Newmark sliding block analyses were performed with different allowances for the influence of interbedding on the composite strength of the interbedded stratum. The differences between results obtained with these analysis methods, along with those presented by others, provided insights into how the various factors can contribute to an overestimation of ground deformations in interbedded deposits of sands, silts, and clays.

Equivalent-static pushover analyses with a three-dimensional (3D), nonlinear, finite-difference model are used to investigate the static and seismic stresses imposed on soil-cement grid reinforcements in soft clay profiles by overlying structures supported by shallow footings. The goal is to evaluate the potential stress concentrations in the soil-cement grid during foundation rocking and the potential for large foundation settlements associated with the local crushing of the soil-cement. The numerical analyses are first validated using data from dynamic centrifuge experiments that included cases with and without large foundation settlements and localized crushing of the soil-cement grids. The experimental and numerical results indicate that the stresses imposed on the soil-cement grid by the overlying structures must account for foundation rocking during strong shaking and stress concentrations at the soil-cement grid intersections. The numerical analyses provide reasonable predictions of the structural rocking loads and the zone of the expected crushing or lack of crushing, but underestimate the accumulation of foundation settlements when the seismic demands repeatedly exceed the soil-cement strength. The simulated moment-rotation and uplift behavior of the footings under monotonic lateral loading are reasonably consistent with the dynamic centrifuge test results. Parametric analyses using the validated numerical model illustrate how the stress transfer varies with the area replacement ratio, the thickness of the top sand layer, the properties of the bearing sand layer, and the relative stiffness of the soil-cement and the surrounding soil. A design model for estimating the stresses imposed on a soil-cement grid by rocking foundations was developed and shown to provide a reasonable basis for assessing whether or not local damage to the soil-cement grid is expected.

A direct axisymmetric cone-penetration model developed for use with a user-written implementation of the MIT-S1 constitutive model is presented. The penetration model uses a finite-differen...

The effects of shaking history on cone penetration test (CPT)-based liquefaction triggering correlations for clean saturated sand are examined by using cone penetration resistance and cyclic strength data pairs from dynamic centrifuge model tests. Three model tests on a 9-m-radius centrifuge examined the liquefaction responses of level profiles of saturated Ottawa F-65 sand subjected to multiple (17-29) shaking events that produced successive changes in density and model response characteristics. Inverse analysis of data from dense accelerometer arrays were used to define time series of cyclic stress ratios and shear strains throughout the profile. Cyclic resistance ratios against triggering of ~100% excess pore pressure ratio in 15 equivalent uniform cycles were computed at multiple depths based on weighting of the cyclic stress ratio time series up to the time of triggering. Cone penetration tests performed at select times during each model test were used to define the variation in cone tip resistances with depth and shaking history. The resulting data pairs, with normalized cone tip resistances ranging from 20 to 340 and cyclic resistance ratios ranging from 0.1 to 2.0, show that both quantities progressively increase as a result of recurrent liquefaction events and generally follow the trends predicted by case history-based liquefaction triggering correlations. Three 1-m-radius centrifuge tests of similar configurations produced consistent results. Implications for the interpretation of case histories and engineering practice are discussed.

Author(s): Boulanger, RW; Brandenberg, SJ | Abstract: Two methods to account for strain rate dependence of clay behavior in computing settlement due to consolidation and secondary compression are compared. The first method explicitly accounts for strain rate effects during primary consolidation using a visco-plastic relationship and nonlinear finite difference solution. The second method indirectly accounts for strain rate effects during primary consolidation by using analytical solutions for consolidation and secondary compression in combination with a time-line based procedure for selecting the analysis parameters. The second method is computationally simpler, and potentially useful for more complicated soil layering and loading conditions. These two analysis methods are described, along with a third, traditional approach for comparison. Results are presented for one-dimensional analyses of a single clay layer for a range of stress history and loading conditions. The time-line based method is shown to provide a reasonable approximation of the more rigorous nonlinear analysis method, indicating that various traditional analysis methods can approximately account for strain rate effects (or creep) during primary consolidation through the appropriate selection of input properties.

Nonlinear deformation analyses of an embankment dam on a spatially variable (stochastic), liquefiable alluvial deposit are presented and compared to results of analyses using uniform properties for the same deposit. The results are used to examine the basis for selecting representative properties (as a percentile of the stochastic distributions), which when used in uniform models, produces embankment deformations consistent with the median response of the stochastic models. Analyses are performed for four different sets of realizations for the stochastic alluvial deposit and a range of shaking intensities. The results suggest that the use of 33rd percentile properties for representing stochastic deposits in uniform models is reasonable to slightly conservative for cases where the length scale of the deformation mechanism is significantly greater than the scale of fluctuation in the deposit.

The formulation of the constitutive model PM4Sand [7] is modified to improve simulations of liquefaction-induced deformations of sloping ground subjected to uniform and irregular cyclic loading. Existing laboratory test data on the response of liquefiable sand under sloping ground conditions subjected to uniform cyclic loading are reviewed and additional experimental data from undrained cyclic direct simple shear (DSS) tests of liquefiable sand under sloping ground conditions subjected to irregular cyclic loading are presented. The previous version of the PM4Sand model (Version 2) and its limitations in modeling liquefaction effects in sloping ground with uniform and irregular cyclic loading are described. Evidence from the laboratory tests show that it is the effect of loading history on the dilation and stiffness characteristics of the response that is not properly captured by Version 2 of the model. The modifications made in Version 3 include a revised dependency of dilation and plastic modulus on the fabric tensor and its history. These modifications are introduced using irregular cyclic DSS test results to illustrate the motivations for the changes in the constitutive equations. Finally, two examples of calibration are presented: one against a specific laboratory test result for a single sand and one against an engineering correlation describing trends observed for many sands across a broader range of relative densities, confining stresses, and loading conditions. The updated formulation in Version 3 of the model is shown to better approximate liquefaction behaviors for sloping ground and irregular cyclic loading conditions.

Inverse analyses were used to evaluate the degree of partial drainage occurring during dynamic shaking of liquefying soil profiles in a set of centrifuge model tests. Three tests were performed using the 9-m radius centrifuge at the UC Davis Center for Geotechnical Modeling on saturated Ottawa sand models with initial relative densities of 25, 43, and 80%. Models were subjected to multiple sinusoidal shaking events with acceleration amplitudes ranging from 0.03 to 0.55g. Densely spaced pore pressure transducer arrays provided profiles of pore pressure generation and dissipation; inverse analyses of the pore pressure data were used to obtain volumetric strain profiles during shaking and dissipation. Surface settlements computed by integrating the volumetric strain profiles are compared to surface settlements measured from linear potentiometers. The magnitude of the volumetric strains due to partial drainage and their potential effects on liquefaction responses are discussed.

Calibrations of the PM4Silt constitutive model are presented for two low-plasticity fine-grained soils that exhibit significantly different cyclic loading behaviors. The PM4Silt model is a stress-ratio controlled, critical state compatible, bounding surface plasticity model that was recently developed for representing low-plasticity silts and clays in geotechnical earthquake engineering applications. The low-plasticity clayey silt and silty clay examined herein were reconstituted mixtures of silica silt and kaolin with plasticity indices (PIs) of 6 and 20. Undrained monotonic and undrained cyclic direct simple shear (DSS) tests were performed on normally consolidated, slurry deposited specimens. Calibration of the PM4Silt model was based on the monotonic and cyclic DSS test data, plus empirical relationships for strain-dependent secant shear moduli and equivalent damping ratios. The calibration process and performance of the PM4Silt constitutive model are described for each soil. The results illustrate that PM4Silt is capable of reasonably approximating a range of monotonic and cyclic loading behaviors important to many earthquake engineering applications and is relatively easy to calibrate.

A revised magnitude scaling factor (MSF) relationship for CPT-based and SPT-based liquefaction triggering analyses is presented in this paper. The revised MSF relationship incorporates functional dependency on the soil characteristics [represented by clean sand equivalent penetration resistances in the present form] as well as on earthquake magnitude. The revisions in MSF are based on the examination of cyclic testing results for a broad range of soil types and densities, analyses of strong ground motion records to develop relationships for the equivalent number of loading cycles for different soil properties, and the synthesis of those results into an MSF relationship suitable for implementation in practice. A separate study [2] showed that use of the revised MSF relationship in CPT-based and SPT-based liquefaction triggering procedures is well-supported by the case history databases. Other factors known to fundamentally influence the MSF are discussed.

The liquefaction database describing the response of the Christchurch area in the 2010–2011 Canterbury Earthquake Sequence (CES) provides a unique basis for evaluating the regional application of various liquefaction analysis procedures, from liquefaction triggering analyses through to liquefaction vulnerability parameters. This database was used to compare the Robertson and Wride [17] , Moss et al. [15] and Idriss and Boulanger [7] liquefaction triggering procedures as well as evaluate the impact of the 2014 versus 2008 Cone Penetration Test (CPT)-based liquefaction triggering procedure by Idriss and Boulanger on four liquefaction vulnerability parameters (SV1D, LPI, LPIISH and LSN), the correlation of those parameters with observed liquefaction-induced damage patterns in the CES, and the mapping of expected damage levels for 25, 100 and 500 year return period ground motions in Christchurch. The effects on SV1D, LPI, LPIISH and LSN were small relative to other sources of variability for the majority of the affected areas, particularly where liquefaction was clearly severe or clearly not. Nonetheless, considering the separation of the land damage populations as well as consistency between the events, the the IB-2008 liquefaction triggering procedures appears to give a slightly better fit to the mapped liquefaction-induced land damage for the regional prediction of liquefaction vulnerability for the Christchurch soils. The Boulanger and Idriss [1] triggering procedure produces improved agreement between the liquefaction vulnerability parameters and observations of damage for: areas south of the Central Business District (CBD) where there tends to be higher soil Fines Content (FC), and localized areas that experienced liquefaction during the smaller Magnitude (M) earthquake events. Implementation of the 2014 liquefaction triggering procedure for mapping of expected liquefaction-induced damage at 25, 100 and 500 year return period ground motions is shown to require use of representative Peak Ground Acceleration (PGA)-M values consistent with the de-aggregation of the seismic hazard. Use of equivalent magnitude-scaled PGA-M7.5 pairs, where the equivalency relates to previously published MSF relationships, with the 2014 liquefaction triggering procedure is shown to be unconservative for certain situations.