Nonlinear Soil Behavior Research Articles

Insights on nonlinear soil behavior and its variation with time at strong-motion stations during the Mw7.8 Kaikōura, New Zealand earthquake

To the end of investigating the potential nonlinear soil behavior at 44 strong motion stations during the 2016 Mw7.8 Kaikōura, New Zealand earthquake, we analyzed the modifications of the site response under the strong mainshock recording based on the horizontal-to-vertical spectra ratio, including the shift of the predominant frequency, and three nonlinearity indicators, DNL, ADNL, and PNL. Significant modifications to site response were observed at more than half of the stations, where the predominant frequency generally shifted to the lower one, and the DNL, ADNL, and PNL values were generally greater than 4.0, 0.3, and 10%, respectively. The strain proxy represented by PGV/Vs30 was found in high level as the nonlinearity indicators were high. The deformation proxy may be a better indicator predicting the nonlinear soil behavior at sites with available shear-wave velocity. After the nonlinear soil behavior occurred, the soil structure completely recovered and the nonlinearity vanished after a period of time. The recovery process was dependent on the ground motion intensity immediately after the strong ground shaking, and the soil condition.

Analytical solution for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading

This paper presents analytical solutions for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading. Analytical solutions are derived for one-dimensional nonlinear consolidation of multi-layered soil subjected to constant loading and ramp loading. The proposed solutions are verified through the comparison with the existing solutions for double-layered soil and single-layered soil, which shows the proposed solutions are more general ones for one-dimensional nonlinear consolidation of saturated soils subjected to time-dependent loading. Based on the proposed solutions, nonlinear consolidation behavior of saturated multi-layered soil under time-dependent loading is investigated.

Influence of the variability of soil profile properties on weak and strong seismic response

Characterizing the potential effect of local site conditions on the amplification of ground motions is a critical aspect of seismic hazard and risk assessment. The aim of this study is to investigate the reliability and the limit of using the average shear wave velocity in the upper 30m of the soil profile vs,30, as single proxy, to characterize seismic site effects for weak and strong events.To this regard, a dataset of 300 one-dimensional soil profiles with a given vs,30 are generated through a Monte Carlo approach. Their seismic responses are computed for a set of 40 real accelerograms, with different seismic features. The vertical propagation from the bottom of the generated columns is modeled using a finite element spatial discretization, accounting for both linear and nonlinear soil behavior.The site dominant frequency f0 and the shear wave velocity gradient in the profile B30 are proposed as proxies to characterize seismic site effects and the variability of the response spectra for the numerical signals, at the free surface of the set of columns, is discussed. Correlations between site-specific amplification factors deduced using the numerical response spectra and the proposed site proxies are analyzed for different sub-ranges of periods. The obtained amplification factors are then compared to those proposed by different international and national design codes. The results, obtained under assumption of linear and nonlinear behavior of soil, emphasize the need to introduce complementary site parameters proxies, in addition to vs,30, to characterize the expected site effects in design response spectra.

Seismic fragility analysis of URM buildings founded on piles: influence of dynamic soil–structure interaction models

The impact of adopting different dynamic soil–structure interaction (SSI) models on the assessment of seismic fragility functions for buildings with pile foundations is studied herein. Given the importance on seismic response of the coupling of structure, foundation and soil, and the challenges posed on modelling dynamic SSI, especially when soil nonlinearity plays a significant role, the linear substructure approach is initially adopted by implementing two different models, followed by the use of a nonlinear pile-head macro-element. The first model is one-dimensional and includes, between the foundation node and the ground, only a translational elastic spring and a dashpot, whose stiffness and viscous damping are retrieved from the real and imaginary parts of the dynamic impedance at the first natural frequency of the structure. The second and more refined model is a Lumped-Parameter Model accounting for frequency dependence of the coupled horizontal and rotational impedances in a two-dimensional response. A nonlinear pile-head macro-element model is introduced afterwards to explore the sensitivity of fragility functions to the linearity assumption. This approach models the soil nonlinear behaviour at near-field, as well as the far-field dynamic impedance and energy dissipation through radiation damping, by condensing the entire soil-foundation system into a single nonlinear element at the base of the superstructure. In all models, the superstructure is represented in a simplified way as a nonlinear single-degree-of-freedom system. The comparison between the adopted approaches is evaluated in terms of their effects on the characterisation of fragility functions for unreinforced masonry buildings with pile foundations.

Sensitivity of 1-D ground motion predictions to analysis codes and material models using KiK-net vertical arrays

One-dimensional (1-D) ground response analysis (GRA) predictions are highly sensitive to the analysis methods and dynamic soil models employed, contributing to significant scatter in analysis outputs. In this paper, a parametric study of 1-D GRA is conducted to evaluate the performance of various models using 60 ground motion records of varying intensity from five Kiban-Kyoshin (KiK-net) downhole array stations in Japan. Four GRA codes are considered, including the equivalent-linear (EL) method, a modified EL method using frequency-dependent soil parameters (FDEL), and two nonlinear (NL) models computed in OpenSees and DEEPSOIL. The soil constitutive models are constrained using a set of five material curves representing a wide range of nonlinear soil behaviour. It was found that all models are sensitive to the material curves at high frequencies, and the NL models are highly sensitive to the parametrization of Rayleigh damping. As the levels of soil nonlinearity increase, all GRA methods tend to over-damp the higher frequency content of ground motions, with substantial discrepancies across the model predictions. Interestingly, the FDEL method displays a lower sensitivity to material curves and reduces the biases at high frequencies. The results of this study suggest that GRA codes and material curves contribute evenly to the overall dispersion when simulating strong ground motions. To quantify the variability of GRA models, along with the epistemic uncertainties, a linear regression relationship in bi-logarithmic space is established across all records between the total standard deviation and the shear strains developed within the soil profiles.

Shaking table test and numerical simulation of eddy-current tuned mass damper for structural seismic control considering soil-structure interaction

This paper firstly investigates the vibration control performance of eddy current tuned mass damper (ECTMD) on structure considering soil-structure interaction (SSI) subjected to seismic loads, and shaking table tests of a six-story steel frame model equipped with ECTMD in SSI system are conducted. By comparison with the undamped TMD, the effectiveness of eddy current damping is also studied. The experimental results in the seismic cases clearly reveal that ECTMD mitigates the maximum displacement response both in rigid base and SSI situations, but it may amplify the peak floor acceleration considering SSI effects. On the whole, SSI decreases the mitigation effects of ECTMD on the structural maximum response, and eddy current damping can improve TMD’s control performance, especially in SSI system. Furthermore, a three-dimensional finite element model on the shaking table tests is established. The numerical model utilizes two different analysis procedures - equivalent linear method and bounding surface plasticity model, to simulate the nonlinear behavior of soil, and the concept of an equivalent eddy current damping is used to simulate ECTMD. A comparison of experimental and simulated results shows that the proposed model can accurately estimate the dynamic response of structure equipped with ECTMD in SSI system under earthquake excitations.

The behaviour of geosynthetic-reinforced pile foundation under long-term dynamic loads: model tests

In order to reduce the effects of the low strength and high compressibility of soft soil, geosynthetic-reinforced pile foundations (GRPF) are widely applied for the construction of high-speed railways. Though its reinforcement effect is proved acceptable in practices so far, it is unclear whether it will keep this performance as the train speed continues increasing. Since it is impossible to study the problem in field tests, only mathematical and physical models can be used. However, the nonlinear behaviour of the soft soil complicates the use of analytical models. Therefore, this paper presents a small-scale model test to study the possible changes in stress distribution and deformation in the GRPF under increasing dynamic loads. One test with a natural foundation, without piles or geosynthetic, shows the difference with a similar construction with GRPF foundation. Furthermore, three GRPF tests show the influence of the embankment thickness. The results show the long-term dynamic loading significantly affects the dynamic stress and displacements of the subsoil between the piles of the GRPF. This effect can be divided into three stages with an increasing level of load amplitude: no impact, advantageous impact, and adverse impact. When the dynamic load reaches the adverse impact stage, the long-term dynamic loads reduce the dynamic pile–soil stress ratio, which means that more soil settlement will develop, because more dynamic stress is applied to the soft soil. The test results show that the reduction in dynamic stress on the subsoil in the GRPF construction is clearly lower than the dynamic stress on the natural foundation, due to the existence of rigid piles. Moreover, a thicker embankment gives significantly lower dynamic stresses on the subsoil between the piles. For the thickest embankment tested, the adverse impact stage was not found at all: the arching kept enhancing under long-term dynamic loading with high load amplitudes.

Non-linear modulation of site response: Sensitivity to various surface ground-motion intensity measures and site-condition proxies using a neural network approach

The impact of non-linear soil behavior on site response may be described by the non-linear to linear site response ratio RSRNL introduced in Régnier et al. (2013). This ratio most often exhibits a typical shape with an amplitude above one below a site-specific frequency fNL, and an amplitude below one beyond fNL. This paper presents an investigation of the correlation between this RSRNL ratio and various parameters used to characterize the site (Site Condition Proxies: SCPs) and the seismic loading level (Ground Motion Intensity Measures: GMIMs).The data used in this analysis come from sites of the Japanese Kiban–Kyoshin (KiK-net) network, for which the nonlinear to linear site-response ratio (RSRNL) is obtained by comparing the surface/down-hole Fourier spectral ratio for strong events and for weak events. The five SCPs are VS30, the minimum velocity of the soil profile (Vsmin), an index of the velocity gradient over the top 30 m (B30), the fundamental frequency f0HV, as measured from the H/V earthquake ratio, and the corresponding amplitude A0HV. The seven GMIMs are PGA, PGV, PGV/VS30 (peak strain proxy), IA (Arias Intensity), CAV (Cumulative Absolute Velocity), arms (Root Mean Square Acceleration) and Trifunac-Brady Duration (DT). The original data set consists of a total of 2927 RSRNL derived from KiK-net recordings at 132 sites. To assign an equal weight to each site, and to avoid any bias linked to sites with many recordings, for each GMIM, this original data set is grouped in 15 different intervals corresponding to fixed fractiles of the statistical distribution of the considered GMIM (every 10% from F10 to F50, and every 5% from F55 to F100). In each group, the average RSRNL-GM for each site is computed. For each of these seven advanced data sets, a neural network approach is used to predict the behavior of RSRNL-GM as a function of the corresponding GMIM, and one or two SCPs. The performance of each model is quantified through the average variance reduction coefficient μ(Rc) in a fixed frequency range. This sensitivity study is performed in the normalized frequency (f/fNL) domain to identify the best combinations (GMIM, SCPs) providing the largest variance reduction, and then in the absolute frequency domain for the final optimal combination. The optimal combinations [GMIM, two-SCPs] are triplets [PGV/VS30, VS30-f0HV; μ(Rc) = 18.6%], [PGV/VS30, VS30-A0HV; μ(Rc) = 18.16%], [PGV, VS30-f0HV; μ(Rc) = 17.3%] and [PGA, B30-A0HV; μ(Rc) = 17.2%]. The final absolute frequency model with the best triplet makes it possible to predict the non-linear response of a given site knowing its linear, weak-motion response, and two site proxy parameters, for wide ranges of the considered ground motion parameters.

Nonlinear Behavior of Marine Soil on the Dynamic Stability of Upper Wharf Structures: A Numerical Simulation Approach

Shen, C.; Qian, J.; Chen, X.; Xie, F., and Zhu, J., 2021. Nonlinear behavior of marine soil on the dynamic stability of the upper wharf structures: A numerical simulation approach. Journal of Coastal Research, 37(1), 149–155. Coconut Creek (Florida), ISSN 0749-0208.This paper investigates the influence of mechanical behavior of marine soil on the dynamic stability of the upper wharf. A series of triaxial consolidation undrained shear tests and one-dimensional consolidation compression tests was conducted to analyze the influence of fine particle content on the nonlinear behavior of marine soil. It was found that the relationship between stress and strain, the undrained shear strength, and residual strength of soil samples strongly correlated with the content of fine particles. In addition, the content of illite soil had a significant impact on the characteristic of the stress–strain curves, with a threshold of about 10%. A numerical model of the foundation-pile-superstructure under wave load was established. The results showed that the dynamic response of a wharf under wave load depended on the strength and nonlinear behaviors of the marine soil foundation. The strain-softening foundation with high peak strength led to more damage on the wharf. However, the strain-hardening characteristics resulted in more damage on the wharf when the peak strength was low. This suggests that the mechanical properties of soil foundation should be taken into account for the long-term durability and stability in the design of the wharf.

Dynamic Load Sharing of Combined Pile Raft Foundation (CPRF) for Reinforced Concrete Structures

Combined pile raft foundation (CPRF) is one of the emerging concepts for providing a cost-effective and efficient solutions for heavily-loaded structures. However, predicting the behaviour of such foundations, especially the load sharing between raft and pile is a challenge due to its inherent complex interactions. Existing analysis methods are either bound within a range of simplifying assumptions or sometimes computationally demanding. Hence, an attempt has been made to evolve a simple and easily implementable methodology, considering non-linear degrading behaviour of soil in a rational manner. The approach has first been validated with measured response during an experimental centrifuge testing of a CPRF in soft Malaysian kaolin clay and an instrumented bridge (Impulsora) founded in soft clayey soil. Subsequently, a range of comparative parametric evaluation of load sharing and settlement characterstics has been carried out which has indicated the importance of pile layout, length and numbers to arrive at a safe and economic design.

Regional correlations for estimating seismic amplification. Implications for loss assessment in SW Iberia

Most earthquake-related losses are enhanced by soil amplification phenomena, especially in areas where high vulnerability assets coexist. These mechanisms are frequently inferred from empirical formulas. These procedures are based on the average shear-wave velocity to 30 m depth (Vs30) as a proxy for amplification events. However, past analysis of spatial relationships between the Vs30 and nonlinear soil behaviour has frequently resulted in poor correlations, affecting all onward analysis. In this research, these relationships are further analysed using an Earthquake Loss Estimation Software. In this framework, the Algarve region and associated ground motion have been depicted based on a certified seismic catalogue. This region has a moderate seismic hazard but possesses a complex geology and dissimilar seismogenic sources. The source data for this research has been Vs30 data collected from geologic surveys made for the region in 2010 in the framework of the Study of Seismic Risk and Tsunamis in Algarve (ERSTA) coordinated by the Portuguese Civil Protection. Other data collected has been the Vs30 topography compiled by the USGS and geologic information available by the OneGeology collaborative project. The goal of this research is to identify inaccuracies that potentially occur in estimating the site effects by different approaches. In this framework three amplification factors based on different sources - Vs30 field-data, Vs30 using slope as proxy and Vs30 using geology as proxy – have been tested. The results have shown a good correlation between Vs30-field-data and geologic based Vs30 and a minor correlation between the former and slope based Vs30. However, regarding the seismic losses - building damage and human losses - the final results show similar values for all three amplification factors analysed.

A new simplified meta-model to evaluate the transmission of ground movements to structures integrating the elastoplastic soil behavior

Many buildings may suffer damage due to ground movements associated to underground excavations like tunneling, mines or urban excavations. The level of damage depends upon the rate of ground movements transmitted to structures that is affected by the soil-structure interaction (SSI) conditions and parameters such as the soil elastoplastic behavior. The purpose of this paper is to integrate the soil elastoplasticity while investigating the response of a structure sitting on a soil subjected to a ground movement. Analytical and numerical approaches are applied to examine the effect of the non-linear soil behavior. The analytical approach is based on modified Winkler and Pasternak elastic models under the assumption of limiting the soil reaction by its bearing capacity; the numerical approach is based on finite element models, using Plaxis 2D that consider an elastoplastic soil behavior. Results display the discrepancy in the structural response between considering an elastic or an elastoplastic soil behavior. Based on a significant number of iterations, the artificial neural network technique is used to propose a new simplified meta-model that integrates the soil elastoplasticity to evaluate the transmission of ground movements to structures. In addition, a procedure, which can be used by engineers and designers, is developed to evaluate the transmission ratio for any structure sitting on any type of soil.

Foundation design taking into account non-linear soil behavior in karst-hazardous areas

The article solves the problem of stress and strain state of the subgrade waned by cylindrical neckline, modeling the karst pothole area. The solution was obtained taking into account nonlinear behavior of the soil subgrade based on using the A.I.Bonkin bilinear subjection. In the article are presented the visual results of calculations as the isofields of stresses and strains. The obtained solution allowed us to offer for consideration an updated analytical model of karst-resisting foundations of buildings and constructions. In the proposed analytical model was adopted a variable coefficient of subgrade reaction, varying according to the bilinear law.

Equivalent seismic coefficients for caisson foundations supporting bridge piers

Safety of a foundation under seismic loading is strongly dependent on the inertial forces transmitted by the superstructure, exchanged with the surrounding soil and acting into the foundation itself. The latter contribution, typically neglected for shallow and pile foundations, should be considered for caisson foundations, much more massive and rigid than the foundation soil. In this paper, the inertial forces acting in caisson foundations during seismic shaking are extracted from the results of a parametric study where different caissons supporting bridge piers are subjected to severe ground motions. The parametric study was carried out in the time domain via 3D Finite Element (FE) dynamic analyses performed in terms of effective stresses but assuming an undrained response of the foundation soil. Non-linear and inelastic soil behaviour was described in the analyses by an elastic-plastic constitutive model with isotropic hardening.In the framework of a pseudo-static approach, the caisson inertia is represented by equivalent horizontal and rotational seismic coefficients, kh eq and krot eq, relating the generalised inertial forces to the caisson weight. The coefficient kh eq turns out to be always remarkably smaller than the maximum value computed at ground surface in free-field conditions, kh max(g.s.). The equivalent seismic coefficients kh eq and krot eq are expressed via empirical relationships as a function of the dynamic properties of the whole system and the seismic input, through dimensionless parameters. Calculation examples are finally given, where safety assessment of bearing capacity is made for different systems using the pseudo-static approach, showing that use of the seismic coefficients computed by the proposed relationships yields results consistent with the ones obtained from the dynamic analyses.

Simulation of fully non-stationary spatially varying ground motions considering nonlinear soil behavior

Taking the nonlinear soil behavior into consideration, a novel method for simulating fully non-stationary spatially varying earthquake ground motions (SVEGMs) was proposed. Based on the one-dimensional (1D) wave propagation model, time-varying shear modulus and damping ratio were introduced into the classical transfer function model, where the evolution characteristics of soil properties (i.e., shear modulus and damping ratio) during earthquake were obtained by using a two-dimensional (2D) site response analysis. By using an example of application, the out-of-plane and in-plane fully non-stationary SVEGMs on ground surface were simulated. The acceleration and displacement time-histories were observed, and the auto power spectral density functions (PSDFs) and coherency loss functions of simulated motions were compared with corresponding targets, respectively. The normalized time-frequency spectra of simulated motions were presented to exhibit the spectral non-stationarity. It was shown that the evolution tendency of predominant frequency of simulated motions reflected similar characteristics with that of shear modulus of soil, which demonstrated the validness of the proposed method.

Site Characterization Using Microtremor Array and Seismic Hazard Assessment for Jakarta, Indonesia

AbstractSite characterization is one of the most important components in seismic hazard analysis because it accounts for the important effects of near‐surface geology on ground motion. It is usually quantified based on the time‐averaged S‐wave velocity (VS) for the top 30 m of the profile (VS30). In this study, we estimate the site class in Jakarta based on VS structure estimated using microtremor array observations. The results show that microtremor‐derived VS profiles agree well with standard penetration test‐derived profiles at nine sites. The site‐class estimates in the Jakarta area can be divided into two National Earthquake Hazards Reduction Program classes: (a) site class E (soft soil) located in alluvium, beach ridge, and alluvial fan deposits in northern and western Jakarta, and (b) site class D (stiff soil) found mainly in alluvial fan deposits in southeastern Jakarta. The variation of VS30 in Jakarta leads to different soil amplification factors that will impact the seismic hazard at the surface. We show that the seismic hazard resulting from selected ground‐motion models (GMMs) illustrates a clear influence of site effects at long periods (>1 s). However, the effect on peak ground acceleration and response spectra for short periods (0.2 s) appear to be less pronounced, due to the GMMs’ treatment of basin effects and nonlinear soil behavior. Available GMMs may not accurately account for such effects in the Jakarta basin, and GMMs specific to Indonesia should be developed to accurately assess seismic hazard there.

A new parameter to empirically describe and predict the non-linear seismic response of sites derived from the analysis of Kik-Net database

We evaluate the non-linear site response at the stations of the Japanese Kik-Net network by computing the ratio between the Fourier spectra of the recordings at the surface and at the downhole station. When the amplitude of the input signal increases, we observe a shift of the resonance peaks towards lower frequencies, characteristic of non-linear soil behavior. We propose a new parameter called fsp to characterize this shift. We observe that fsp is a good proxy for the shear modulus reduction by comparing fsp and the modulus reduction curve obtain by both laboratory test measurements and numerical approaches. The fsp is used to correct the linear site response and surface ground motion in frequency domain in order to take into account the non-linear soil behavior. We show that the procedure we established reduces the error in predicting the main frequency peak by 50% compared to an elastic evaluation of the site response during the 2016 Kumamoto earthquake (Mw = 7.1).

Respuesta sísmica local de la presa Las Dos Bocas utilizando un análisis no lineal

Uno de los problemas más importantes y comúnmente encontrados en la ingeniería sísmica es la evaluación de la respuesta del terreno donde se ubicala edificación. La respuesta dinámica del suelo es un fenómeno sumamente complejo, que depende de un gran número de variables, tanto de las propiedades del mismo suelo como de la excitación a la que se encuentre sometida. El comportamiento no lineal del suelo durante un evento sísmico tiene un papel predominante en el análisis actual de la respuesta del sitio, lo que indica que su relación esfuerzo-deformación es no lineal e histerética, debido a esto, el enfoque lineal debe ser modificado para proporcionar estimaciones razonables de respuesta del terreno para los problemas prácticos de interés.
 En el presente artículo se muestra la influencia, en el análisis de la respuesta sísmica local de la presa de tierra "Las Dos Bocas", ejercida al considerar distintas excitaciones sísmicas, así como las propiedades dinámicas del suelo en función del nivel de deformación inducido. Demostramos cómo la no linealidad puede afectar la amplificación del suelo en función de diferentes fuentes de excitación. Aquí, el comportamiento no lineal con un enfoque en la respuesta del sitio 1-D se desarrolla aplicando un método iterativo para lograr la aproximación lineal equivalente del suelo, basada en las propiedades no lineales del material.

Stiffness Decay in Structured Soils by Seismic Dilatometer

The small-strain stiffness modulus G0 is not directly applicable to evaluate deformation in most practical engineering problems, and therefore, nonlinear soil behavior curves have been developed in terms of Young modulus E or shear modulus G. These curves were successfully obtained for sedimentary soils, while for residual soils, the available data from intertional community is still scarce. Residual soils are considered structured soils and often classified as problematic soils since they do not fit into the behavior of remolded or unstructured soils. In fact, the role of bonding and fabric affects both the strength and the stiffness of the soil. This article illustrates the use of the seismic dilatometer test (SDMT) for the determination of in situ stiffness decay curves with strain level (G-γ curves or similar) in a granitic residual soil of the Northeastern region of Portugal (Guarda), showing its adequacy to solve these kinds of problems. In situ and laboratory tests were performed on these granitic residual soils. The adopted approach relies on the ability of SDMT to provide a small-strain modulus G0 (from the shear wave velocity Vs) and a “working strain” modulus GDMT (derived from the constrained modulus MDMT in accordance with the theory of elasticity). Thus, in situ G-γ decay curves were tentatively constructed by fitting curves through these two points using a hyperbolic model. However, it was observed that the results obtained by the hyperbolic model for the cemented soils are not satisfactory. Based on the SDMT parameters, a logistic curve was derived for the reproduction of reference stiffness curves obtained from the triaxial test results.

Predicting resilient modulus of fine-grained subgrade soils considering relative compaction and matric suction

The resilient modulus has been used to characterise the stress-strain non-linear behaviour of subgrade soils and is an important parameter for pavement design and analysis. This study aims at developing an accurate and efficient methodology to estimate the resilient modulus of subgrade soils. Therefore, repeated load triaxial tests were carried out in this study. The soil matric suction was measured by the pressure plate test and the soil-water characteristic curve (SWCC) was described using the Fredlund & Xing model. Then, the influence of stress state, matric suction and relative compaction on the resilient modulus were analysed. Subsequently, a new resilient modulus model was proposed to incorporate the relative compaction and matric suction in addition to the stress state. The new model matched 7 sets of experimental data well and the coefficients of determination were high, which indicates that this new model is reasonable and widely applicable. Finally, the correlations between the basic properties variables of soil samples and the regression coefficients of the new model were established.