Nonlinear Soil Model Research Articles

Nonlinear interaction behaviour of plane frame-layered soil system subjected to seismic loading

The foundation of a tall building frame resting on settable soil mass undergoes differential settlements which alter the forces in the structural members significantly. For tall buildings it is essential to consider seismic forces in analysis. The building frame, foundation and soil mass are considered to act as single integral compatible structural unit. The stress-strain characteristics of the supporting soil play a vital role in the interaction analysis. The resulting differential settlements of the soil mass are responsible for the redistribution of forces in the superstructure. In the present work, the nonlinear interaction analysis of a two-bay ten-storey plane building frame- layered soil system under seismic loading has been carried out using the coupled finite-infinite elements. The frame has been considered to act in linear elastic manner while the soil mass to act as nonlinear elastic manner. The subsoil in reality exists in layered formation and consists of various soil layers having different properties. Each individual soil layer in reality can be considered to behave in nonlinear manner. The nonlinear layered system as a whole will undergo differential settlements. Thus, it becomes essential to study the structural behaviour of a structure resting on such nonlinear composite layered soil system. The nonlinear constitutive hyperbolic soil model available in the literature is adopted to model the nonlinear behaviour of the soil mass. The structural behaviour of the interaction system is investigated as the shear forces and bending moments in superstructure get significantly altered due to differential settlements of the soil mass.

Static and Dynamic Axial Response of Drilled Piers. II: Numerical Simulation

Realistic time history simulation of drilled pier/pile-soil systems under dynamic and static loading is essential for the development of effective performance-based earthquake designs of deep foundations. This paper presents the results of the numerical simulation of a series of static and dynamic tests on drilled piers performed at the University of California, Berkeley. A nonlinear soil model was implemented based on multiaxial cyclic bounding-surface plasticity within a general finite-element framework, OpenSees. The model requires a small number of parameters that can be easily obtained through conventional site investigations. The results of the simulations show that the model can reasonably simulate nonlinear response of the soil and that it does a good job of capturing the actual load deformation curves obtained from in situ dynamic and static pier load tests. Although the model is suitable for a fully nonlinear total stress analysis of soil-pile systems under multidirectional shaking, further studies are needed to enhance the model capacity by incorporating the cyclic stiffness and strength degradation caused by full stress reversals.

Configuration Optimization of Drilled Shafts Supporting Bridge Structures: Three Case Studies

A common approach to estimating the point of fixity is to utilize the results of a single pile lateral analysis. Although no universal agreement exists as to the definition of the location of the point of fixity, it is generally accepted that its location will affect the computed stresses and displacements of a bridge structure. This study summarizes a method to determine a cantilever’s equivalent length of drilled shaft foundation elements supporting a bridge. Results from an equivalent frame model are compared to those for bents modeled using the finite element method and nonlinear soil models for three bridges in North Carolina. Results indicated that the equivalent frame model provides responses that are comparable to those obtained from more rigorous finite element analyses. The study presents the results of the optimization of the support system by reducing the number, or size, of the shafts while maintaining an acceptable level of safety.

Nonlinear Site Response and Liquefaction Analysis in the New Madrid Seismic Zone

Many existing highway bridges in the New Madrid Seismic Zone are located in the Mississippi Embayment, consisting of deep soil deposits and liquefaction susceptible near surface soils. It is important to understand the comprehensive impact of deep soil deposits and liquefaction on the response of the bridge foundations under seismic loading. A nonlinear soil model is then presented to study the impacts of the deep soil deposit and liquefaction on response analysis. The soil model has the advantage of using input parameters that can be obtained from conventional field and laboratory testing methods, which makes it attractive to engineering practice. The model calibrations used field recorded motions and laboratory test data, which indicate that the model provides an acceptable outcome based on simple input parameters. The model is implemented into the site response analysis for a typical Missouri highway bridge site in this seismic zone. The effect of the deep soil deposit and liquefaction on the site response analyses is discussed.

Calculation of Damping Ratio Using Non-Linear Soil Models and Comparison between Measured and Predicted Data

Several theoretical soil nonlinear models to predict damping ratio, which is one of the typical dynamic properties of soils, it is impractical to predict damping ratio. The resonant column and torsional shear test(RC-TS) is used to represent the dynamic behavior of soils from intermediate to medium shear strains. A limitation of RC-TS is measure precise shear strain in large strains and the modified equivalent radius() was obtained using both modified hyperbolic model and Ramberg-Osgood model. Bonneville clays were tested using RC-TS test to obtain rotation and torque. The measured rotation and torque were then compared with calculated rotation and torque using curve-fitting method. Then, the nonlinear soil model parameters were obtained and the equivalent radius was calculated using the model parameters.

Nonlinear, Effective-Stress Ground Motion Response Analyses following AASHTO Specifications for Load and Resistance Factor Design Seismic Bridge Design

Nonlinear, effective-stress ground motion response analyses were conducted for a bridge site north of Seattle, Washington. This site was characterized by silt and sand layers in the upper 90 ft (27.4 m) of the soil profile that were expected to liquefy during a 975-year seismic event. Procedures described in the 2009 AASHTO Guide Specifications for LRFD Seismic Bridge Design were followed when site-specific analyses of ground motion response were conducted. Two one-dimensional, nonlinear effective-stress computer programs, D-MOD2000 and PSNL, were used to perform the analyses. Field and laboratory tests were conducted to define soil parameters for the nonlinear soil models. Results of the analyses were used to identify soil layers that were likely to liquefy as well as changes in design response spectra that could result from liquefaction. These results demonstrated important differences in site-response prediction from subtle changes in soil modeling, including the potential for shielding of upper liquefiable soil layers and the importance of soil dilation when lower layers liquefy. This paper provides a summary of the analyses and discusses observations made from comparison of the two sets of analyses. The paper also highlights uncertainties that can occur when nonlinear, analyses of effective-stress ground motion response are conducted.

A Case Study of Passive Piles Failure in Open Excavation

This paper presents a case study in West Malaysia for passive piles failure in very soft marine clay in open excavation. In this particular case, the thickness of the very soft marine clay ranges from 5 m to 7 m (16 ft to 23 ft) from the ground surface. Preliminary site investigation reported SPT ‘N’ value of zero for the very soft marine clay. The design was based on a deep foundation utilizing driven piles to support the superstructure. During pile cap construction, the piles were subjected to uncontrolled open excavation, inducing bending moment in the piles, resulting in some cracked and broken piles. Analyses were carried out using an existing three-dimensional finite element code with a non-linear soil model to predict the response of these piles during excavation. Finally, the predictions of pile responses during excavation were compared satisfactorily with the observed results.

A field investigation of vertical footing response on sand

This paper presents the results from an experimental programme that studied the factors affecting the bearing resistance of shallow footings in sand. In particular, the tests considered the effects of the footing width and embedment depth on the pressure–settlement response. By comparing the results with field tests on full-scale footings, simple correlations between the bearing pressure mobilised at normalised settlement levels of 5% and 10% of the footing width and the cone penetration test qc value were studied. These correlations were found to be independent of footing size, embedment depth and sand state, although they were affected by creep. The rate of mobilisation of the footing resistance at low settlements was found to be strongly dependent on the initial soil state and the previous loading history. A simple non-linear elastic soil model was found to adequately predict this response.

Side effect of using response spectral amplification ratios for soil sites—variability and earthquake-magnitude and source-distance dependent amplification ratios for soil sites

We investigate a special type of variability in response spectral amplification ratios computed from numerical “engineering” models for a soft soil site. The engineering models are defined by shallow soil layers over “engineering” bedrock with a shear-wave velocity over 600–700 m/s and the model is subjected to vertical propagating shear waves. The variability, perhaps unique in earthquake engineering, is a result of the “perfectly accurate” computational procedure. For example, an engineering soil site model, subjected to two rock site records or the two horizontal components of a rock site record, produces different response spectral amplification ratios. We use a large number of strong-motion records from “engineering” rock sites, with a reasonably balanced distribution with respect to magnitude and source distance, generated by subduction earthquakes in Japan, to investigate the nature of the variability. In order to avoid any approximation in removing the effect of soil nonlinear response, we use a simple model, a single horizontal soil layer over a bedrock, modelled as elastic. We then demonstrate that a similar type of variability observed in the one- or two-dimensional nonlinear soil models is caused by the nature of response spectral amplification ratios, not a direct result of soil nonlinear response. Examination of variability reveals that the average of response spectral amplification ratios systematically depends on both earthquake magnitude and source distance. We find that, at periods much longer than the site natural periods of the soil sites, the scatter of the amplification ratios decreases with increasing magnitude and source distance. These findings may have a potential impact in establishing design spectra for soft soil sites using strong-motion attenuation models or dynamic numerical modelling.

Near-Fault Earthquake Ground-Motion Simulation in the Grenoble Valley by a High-Performance Spectral Element Code

Near-fault effects are known to produce specific features of earthquake ground motion (such as long-period velocity pulses and directivity) that cannot be predicted by numerical approaches involving vertical plane wave propagation in one-dimensional (1D) soil models that are used as a standard in engineering applica- tions. Coupling near-fault conditions with site effects induced by complex geological structures (such as deep alluvial basins or steep topographic irregularities) further con- tributes to the complexity of earthquake ground motion and to the difficulty to provide reliable predictions without making use of large-size 3D numerical simulations. In this article, we present a parametric study of the seismic response of the Grenoble Valley, France (due to an Mw 6 seismic source at some 10 km epicentral distance from the urban area) that was carried out in the framework of an international benchmark for earthquake ground-motion prediction. The spectral element code GeoELSE for seismic-wave propagation analyses in 3D heterogeneous media, in the linear and non- linear range, was used for this purpose; full advantage was taken of its implementation on parallel computer architectures. After introducing GeoELSE and its parallel per- formance, and after introducing some of its validation benchmarks, the spatial varia- bility of the seismic response of the Grenoble Valley is quantitatively investigated taking into account two effects: (i) the hypocenter location and (ii) the nonlinear soil behavior through a nonlinear viscoelastic soil model. Finally, numerical results are compared with available data and attenuation relationships of peak values of ground motion in the near-fault region. Based on the results of this work, the unfavorable interaction between fault rupture, radiation mechanism, and complex geological con- ditions may give rise to large values of peak ground velocity (exceeding 1 m=sec) even in low-to-moderate seismicity areas; it may therefore considerably increase the level of seismic risk, especially in highly populated and industrially active regions, such as the Alpine valleys.

RESPONSE OF SOFT CLAY STRATA AND CLAY-PILE-RAFT SYSTEMS TO SEISMIC SHAKING

The behavior of pile foundations under earthquake loading is an important factor affecting the performance of structures. Observations from past earthquakes have shown that piles in firm soils generally perform well, while the performance of piles in soft or liquefied ground can raise some questions. Centrifuge model tests were carried out at the National University of Singapore to investigate the response of pile-soil system under three different earthquake excitations. Some initial tests were done on kaolin clay beds to understand the pure clay behavior under repetitive earthquake shaking. Pile foundations comprising of solid steel, hollow steel and hollow steel pile filled with cement in-fill were then embedded in the kaolin clay beds to study the response of clay-pile system. Superstructural inertial loading on the foundation was modeled by fastening steel weight on top of the model raft. The model test results show that strain softening and stiffness degradation feature strongly in the behaviour of the clay. In uniform clay beds without piles, this is manifested as an increase in resonance periods of the surface response with level of shaking and with successive earthquakes. For the pile systems tested, the effect of the surrounding soft clay was primarily to impose an inertial loading onto the piles, thereby increasing the natural period of the piles over and above that of the pile foundation alone. There is also some evidence that the relative motion between piles and soil leads to aggravated softening of the soil around the pile, thereby lengthening its resonance period of the soil further. The centrifuge model tests were back-analyzed using the finite element code ABAQUS. The analysis shows that the simple non-linear hypoelastic soil model gave reasonably good agreement with the experimental observations. The engineering implication arising from this study so far is that, for the case of relatively short piles in soft clays, the ground surface motions may not be representative of the raft motion. Other than the very small earthquakes, the raft motion has a shorter resonance period than the surrounding soil.

Numerical analysis of nonlinear soil–pile group interaction under lateral loads

A nonlinear p – y element was provided which can simply model the behavior of a pile group foundation subjected to lateral loading. Its elasto-plastic side soil is expressed as a Winkler-type distributed model. Despite the simplification involved in modeling such a complex phenomenon the proposed nonlinear soil model can reproduce the system behavior as computed by more rigorous 3D finite element methods. The numerical results are also compared with those from available physical model data to confirm that our simulations can predict the behavior of pile groups with good accuracy.

3D modelling of sprayed-concrete-lined tunnels in clay

Realistic finite element (FE) modelling of the tunnel construction process has been restricted by the computational effort needed to incorporate the three-dimensional (3D) aspects of the tunnelling operation. Two-dimensional (2D) plane-strain models have therefore been widely adopted by practitioners and researchers in their studies of the effects of tunnelling. However, 2D modelling suffers the drawback whereby a volume loss must be assumed at the outset as the input for the FE model. This paper presents an analysis of measured surface ground movements induced by a sprayed concrete lined tunnel in London Clay. This was achieved using computationally efficient, non-linear, 3D modelling and Oasys LS-DYNA software. By modelling the problem using a non-linear small strain BRICK soil model, which incorporates anisotropic behaviour, good agreement with the actual Gaussian distribution of surface settlement was obtained. This was achieved without any initial assumptions regarding volume loss, but rather by realistically modelling the excavation sequence and time-dependent gain in lining strength. On the basis of this work it is considered that 3D modelling techniques can provide an effective means to estimate ground settlement and the associated effects on nearby structures, without dependence on empirical methods alone.

Behavior of strip footing on geogrid-reinforced sand over a soft clay slope

The potential benefits of reinforcing a replaced layer of sand constructed on near a slope crest was studied. Model tests were carried out using model footing of 75 mm width and geogrids. Several parameters including the depth of replaced sand layer and the location of footing relative to the slope crest were studied. Particular emphasis is paid on the reinforcement configurations including number of layers, spacing, layer length and depth to ground surface. A series of finite element analyses were performed on a prototype slope using two-dimensional plane strain model using the computer code Plaxis. The soil was represented by non-linear hardening soil model, which is an elasto-plastic hyperbolic stress–strain model while reinforcement was represented by elastic elements. A close agreement between the experimental and numerical results is observed. Test results indicate that the inclusion of geogrid layers in the replaced sand not only significantly improves the footing performance but also leads to great reduction in the depth of reinforced sand layer required to achieve the allowable settlement. However, the efficiency of the sand–geogrid system increases with increasing number of geogrid layers and layer length. Based on the theoretical and experimental results, critical values of the geogrid parameters for maximum reinforcing effects are established.

Load Transfer Mechanisms between Underground Structure and Surrounding Ground: Evaluation of the Failure of the Daikai Station

The Daikai Station, a cut and cover structure in the subway system in Kobe, collapsed during the Hyogoken-Nambu earthquake of January 17, 1995 in Japan. The Daikai Station is the first well-documented underground structure not crossing an active fault that has completely collapsed during an earthquake without liquefaction of the surrounding soil. What makes this case even more interesting is that tunnel sections adjacent to the station, with similar structural characteristics and analogous soil conditions, did not collapse. Dynamic numerical analyses have been conducted to investigate the load transfer mechanisms between the underground structure and the surrounding soil and to identify the causes for different behavior of similar sections of the station subjected to the same seismic loading. A hysteretic nonlinear soil model has been used for the analysis. The model captures well the soil's shear modulus degradation and the increase of damping with strain. The results from the analyses show that, for a given earthquake, there are two key factors that determine the response of an underground structure: the relative stiffness between the structure and the degraded surrounding ground, and the frictional characteristics of the interface. A stiff structure has small deformations; because the adjacent soil movement is restricted by the structure, the shear modulus degradation of the soil is limited which contributes to reduce further deformation of the soil and thus decreases the displacement demand on the structure. A strong interface is capable of transmitting larger shear to the structure but in turn increases the confinement of the soil surrounding the structure which limits the soil's shear modulus degradation. The model predicts larger deformations in the section that collapsed because this section had a smaller stiffness, and thus triggered drifts in critical structural elements which were larger than at other sections of the station which remained stable.

Impedance-Based Winkler Spring Method for Soil-Pile group Interaction Analysis

A simple numerical model is presented for handling both linear and nonlinear soil-pile interactions. In the present method, the diagonal terms of the exact soil impedance matrix define the elastic characteristics of Winkler side soil springs. When its off-diagonal terms are described as a function of the pile’s active length, they were found less dependent on the other secondary factors. Despite the simplification, the proposed nonlinear soil model can reproduce piles’ behaviors computed by more rigorous finite element methods.

Prediction of Nonlinear Soil Effects

Mathematical models of soil nonlinearity in common use and recently developed nonlinear codes are compared to investigate the range of their predictions. We consider equivalent linear formulations with and without frequency-dependent moduli and damping ratios and nonlinear formulations for total and effective stress. Average velocity profiles to 150 m depth with midrange National Earthquake Hazards Reduction Program site classifications (B, BC, C, D, and E) in the top 30 m are used to compare the response of a wide range of site conditions from rock to soft soil. Nonlinear soil models are compared using the amplification spectrum, calculated as the ratio of surface ground motion to the input motion at the base of the velocity profile. Peak input motions from 0.1 g to 0.9 g are considered. For site class B, no significant differences exist between the models considered in this article. For site classes BC and C, differences are small at low input motions (0.1 g to 0.2 g ), but become significant at higher input levels. For site classes D and E the overdamping of frequencies above about 4 Hz by the equivalent linear solution with frequency-independent parameters is apparent for the entire range of input motions considered. The equivalent linear formulation with frequency-dependent moduli and damping ratios under damps relative to the nonlinear models considered for site class C with larger input motions and most input levels for site classes D and E. At larger input motions the underdamping for site classes D and E is not as severe as the overdamping with the frequency-independent formulation, but there are still significant differences in the time domain. A nonlinear formulation is recommended for site classes D and E and for site classes BC and C with input motions greater than a few tenths of the acceleration of gravity. The type of nonlinear formulation to use is driven by considerations of the importance of water content and the availability of laboratory soils data. Our average amplification curves from a nonlinear effective stress formulation compare favorably with observed spectral amplification at class D and E sites in the Seattle area for the 2001 Nisqually earthquake. Manuscript received 18 June 2004.

Two-Dimensional Analyses of Thermoplastic Culvert Deformations and Strains

Tests have been performed in a biaxial pipe test cell to develop baseline information on profiled pipe behavior under biaxial loading. These include a lined corrugated high-density polyethylene pipe and a helically wound ribbed polyvinyl chloride pipe. Results of the tests are utilized to examine the effectiveness of the two-dimensional methods of buried pipe analysis. Calculations of pipe responses by the two-dimensional finite element method and a set of simplified design equations are compared with the measurements of pipe strains and deflections. The study reveals that the two-dimensional finite element analysis can effectively be used to calculate pipe deflections and circumferential strains. The simplified equations appear suitable as design tools for standard buried thermoplastic pipe installations. Janbu’s nonlinear soil model with Mohr–Coulomb plasticity provided an effective simulation of the nonlinear soil behavior A study of pipes with low stiffness soil support under the haunches shows that this leads to strain concentrations in the pipe walls near that zone. Higher values of empirical strain factor, Df, are estimated to include this strain concentration during design.

Development and Validation of Nonlinear Dynamic Analysis in Seismic Performance Verification of Underground RC Structures

Large shake table test and subsequent numerical analysis correlation were conducted to develop and validate a suitable nonlinear FEM model for the seismic performance evaluation of underground RC structures, enhancing the existing skeleton and hysteresis rules for RC members. A trilinear nonlinear RC member model that represents the effect of reinforcing bar pullout was developed and validated through numerical correlation analysis using past static loading tests. The shake table test results demonstrate that the deformation of model RC structure is fully governed by ground deformation both in the elastic and inelastic ranges. The FEM model developed here derives estimations that show good correlation with test results in terms of such parameters as structural deformation, shear stress distribution on the upper slab surface and concrete cracks and reinforcing bars yielding events, because of the successful parameter identification of nonlinear soil and RC member models.

Advanced numerical investigation of Terzaghi's superposition theory

Traditionally the analysis of footings embedded in granular soils has been one of the most difficult finite element simulations to be attempted in geomechanics. This is particularly noticeable by a general lack of published work in foundation analysis using finite elements in the literature. Because of the difficulties involved most of the work performed in this area has concentrated on the use of simple linear elastic, perfectly plastic Mohr–Coulomb constitutive soil models. This paper advances the state-of-the-art by describing the use of a non-linear elastic multi-surface kinematic soil model for the simulation of circular foundations embedded in a particular granular soil. The paper first computes the bearing capacity factors N γ and N q separately, then checks Terzaghi's superposition theory by simulating an embedded foundation (modelled as a surface foundation with an initial surcharge). It is well known that the bearing capacity factor N γ is a function of the foundation width. The paper confirms this, and also shows that the bearing capacity factor N q is actually related to the foundation depth.