Shear Modulus Degradation Research Articles

Dynamic properties of two historically liquefiable sands in the Lisbon area

The stiffness properties of soils, particularly shear modulus and damping ratio, play a fundamental role in predicting the ground deformation during cyclic and dynamic loading. The dynamic properties can be used for the assessment of seismic ground response and the analysis of soil–structure interaction. This study provides a detailed dynamic characterisation of two liquefiable sandy soils, which have experienced earthquake-induced liquefaction, as historically documented. The soils were collected in the greater Lisbon area, in the south of Portugal. For this purpose, a comprehensive laboratory testing programme, which included a series of bender-element and resonant-column tests, was conducted. During the study, the effects of void ratio and mean effective stress on the soil stiffness were examined, focusing on the small-strain response. Results show shear modulus degradation and damping ratio curves, at small and intermediate shear strain levels, for saturated reconstituted samples under different stress conditions. Data obtained in the laboratory of both materials were fitted into normalised models to estimate the dynamic properties for different stress and state conditions. In addition, damping ratio curves were compared against the typical bounds of quartz materials. Stress-dependent models for estimating the maximum shear modulus and threshold shear strain amplitudes of both sands are proposed in this paper. The data provided in this study are useful for numerical analyses and geotechnical design, particularly when involving dynamic or seismic approaches.

Effect of mean grain size on shear modulus degradation and damping ratio curves of sands

Determination of shear modulus and damping ratio from small to large strains is essential to understand the non-linear stress–strain and damping behaviour of sand. The shear modulus and damping rat...

Prediction of large seismic sliding movement of slopes using a 2-body non-linear dynamic model with a rotating stick-slip element

In the present work a new cost-effective dynamic method predicting large seismic displacement along slip surfaces is proposed. For this purpose, the 1-D propagation of horizontal shear waves on a soil stratum with a horizontal stick-slip element at some depth is considered. State-of-the-art equations modeling (a) the coupled 1-dimesional dynamic response of soils with slippage both above and below the slip element, (b) the rotation of the sliding mass with displacement effect and (c) the non-linear soil response for both the dry and saturated cases are combined in a unique manner. No other cost-effective dynamic method was found in the bibliography that simulates all the above effects. The new method is applied for some particular geometries for both the linear and non-linear cases. In the linear case the effects of the stiffness of the soil layers both above and below the slip element and of the rotation of the sliding mass on the permanent seismic displacement are illustrated and interpreted. Likewise, in the non-linear case, the effects of (i) the shear modulus degradation in dry soil profiles and (ii) the additional effect of excess pore pressure build-up in saturated soil profiles on the permanent seismic displacement are illustrated and interpreted.

Ground subsidence and its implication on building seismic performance

Ground subsidence due to underground water extraction leads to changes in dynamic properties such as shear wave velocity distribution and shear modulus degradation and damping curves, and more importantly, soil layer thickness and shape. These effects modify site predominant periods, frequency content, and spectral accelerations in both the free field and soil-structure systems during an earthquake. These variations can be substantial in highly compressible very soft clays, such as those found in the Mexico City basin. This paper examines the complex role that ground conditions, including settlement variability and structural tilting due to regional ground subsidence, had in the seismic performance of buildings during the Mw 7.1 2017 Puebla-Mexico City earthquake. A numerical study was undertaken to simulate the seismic response of conventional buildings supported by a compensate box-like foundation in soft clay, representative of those that exhibited major damage or collapse. Sets of three-dimensional finite difference models were developed with FLAC3D. Initially, the overall static behavior of the soil-structure system was assessed, considering both ground settlement and structure tilting due to ground consolidation, resembling the conditions prevailing right before the earthquake. Then, the seismic performance evaluation during the dynamic event was conducted at several consolidation times (i.e. 0, 25, 32 and 45 years). From the results gathered herein, it was clearly established the effect of the variation of the fundamental period of the soil deposit, and the initial ground deformation and structural tilting, on the seismic demand acting on the structure during the earthquake, which in turn, lead to most of the observed failures.

Fatigue life prediction of shear failure dominated foam cored sandwich composite hull panels under variable water-slamming conditions

This paper presents a hybrid computational-empirical fatigue failure prediction model for shear failure dominated foam cored sandwich hull structures subjected to variable water slamming conditions. The proposed approach combines finite element analysis with core material experimental characterization published in the literature. Core shear stress and stress rate histograms are constructed by interpolation of simulated finite element results using experimentally determined hydrodynamic pressure distribution. An exponential fatigue damage accumulation model based on core shear modulus degradation is presented and implemented to predict slamming fatigue life of sandwich panels. As a result of the present study, it was determined that sandwich panels experienced the highest core shear stresses and stress rates in the proximity of the right-hand support. Results demonstrated that under variable slamming conditions, fatigue performance of cored sandwich panels is stress-sequence dependent. Sandwich panel fatigue life showed a significant reduction with increasing impact velocity and decreasing deadrise angle.

Dilatancy-triggering surface for advanced constitutive modelling of sand

This paper presents, for sand, a formulation for a surface in stress space defining the onset of dilatancy based on the volumetric threshold strain concept, the expression for the small-strain shear modulus in terms of soil state and an expression for secant shear modulus degradation with increasing shear strain. The size of the surface depends on both density (void ratio) and mean effective stress. The use of the proposed surface is demonstrated for Toyoura sand. The paper also presents a multiaxial formulation for the surface that can include kinematic hardening. The proposed surface can be useful in constitutive modelling, especially to capture seismic or cyclic loading conditions.

A methodology for estimation of site-specific nonlinear dynamic soil behaviour using vertical downhole arrays

System identification (SI) techniques have been widely used in Geotechnical Engineering to understand the characteristics of soils. In this study, system identification techniques with and without using a constitutive model were examined using three downhole array sites in California, US. Shear wave velocities (VS) and maximum shear moduli (Gmax) of soils were obtained using SI techniques without using a constitutive model and low-amplitude earthquake records. Average shear moduli and average damping ratios of soil layers were estimated through SI technique using a linear constitutive model and relatively high amplitude records. Finally, a practical methodology was proposed for predicting site-specific shear modulus degradation (G/Gmax) and damping curves (ξ) using nonlinear constitutive models and high amplitude earthquake data recorded in some arrays. The proposed methodology predicts site-specific dynamic characteristics by using the recorded earthquake data and iterating the reference strain (γr) in the nonlinear constitutive model. From the results, it can be inferred that average shear modulus values estimated using the linear constitutive model might not predict the dynamic soil behaviour properly for high amplitude earthquakes. However, the acceleration time histories obtained using the site-specific G/Gmax and ξ curves predicted by the proposed methodology using nonlinear constitutive model were in good agreement with the recorded acceleration data.

Pile Side Resistance in Sands for the Unloading Effect and Modulus Degradation

A total of 36 groups of sand-concrete interface loading and unloading direct shear tests were used to analyze the mechanical properties of the pile side-soil interface. The test results show that the interface residual shear stress for the same applied normal stress tends to be constant for the rough sand-concrete interface. The initial shear modulus and peak shear stress of the interface both decrease with the degree of unloading and increase with the interface roughness. The maximum amount of interface shear dilatancy increases with the degree of unloading, and the maximum amount of interface shear shrinkage decreases with unloading for the same interface roughness. A pile side resistance-displacement model is established using the shear displacement method. The proposed function considers both the radial unloading effect and modulus degradation of soil around the pile. The effect of radial unloading and interface roughness on the degradation of the equivalent shear modulus is analyzed using a single fitting parameter b. Good agreement of the proposed model is confirmed by applying the direct shear tests of the 36 groups.

Modelling effects of recent suction history on small-strain stiffness of unsaturated soil

Recent suction history has been found to affect shear modulus of unsaturated soil at small strains (i.e., from 0.001% to 1%). In this study, a bubble model for unsaturated soil is developed within the framework of kinematic hardening and bounding surface plasticity. An elliptical elastic bubble is defined inside a modified Cam-clay bounding surface. Being a key feature of the proposed model, the size of the elastic bubble is modelled as a function of suction, degree of saturation, and plastic volumetric strain. Translation of the elastic bubble is governed by suction, degree of saturation, and stress increments. Moreover, hardening modulus depends on not only stress and void ratio, but also suction, degree of saturation, and relative position of the elastic bubble and the bounding surface. The proposed model is evaluated using suction-controlled constant-p shear tests on completely decomposed tuff (silt). It is evident that the new model is capable of capturing well the effects of recent suction history on nonlinear stress–strain relation and shear modulus degradation at small strains.

Degradation of the In-plane Shear Modulus of Structural BFRP Laminates Due to High Temperature.

The behavior of fiber reinforced polymer (FRP) composites at high temperature is a critical issue that needs to be clearly understood for their structural uses in civil engineering. However, due to technical difficulties during testing at high temperature, limited experimental investigations have been conducted regarding the thermal behavior of basalt fiber reinforced polymer (BFRP) composites, especially for the in-plane shear modulus of BFRP laminates. To this end, both an analytical derivation and an experimental program were carried out in this work to study the in-plane shear modulus of BFRP laminates. After the analytical derivation, the in-plane shear modulus was investigated as a function of the elastic modulus in different directions (0°, 45° and 90° of the load-to-fiber angle) and Poisson’s ratio in the fiber direction. To obtain the in-plane shear modulus, the four parameters were tested at different temperatures from 20 to 250 °C. A novel non-contacting digital image correlation (DIC) sensing system was adopted in the high-temperature tests to measure the local strain field on the FRP samples. Based on the test results, it was found that the elastic moduli in different directions were reduced to a very low level (less than 20%) from 20 to 250 °C. Furthermore, the in-plane shear modulus of BFRP at 250 °C was only 3% of that at 20 °C.

Dynamic properties of sand-EPS bead mixtures

Soils modified with Expanded Polystyrene (EPS) beads are typically used as lightweight mixtures to solve many geotechnical challenges. In seismically active areas, understanding the relationship between dynamic properties and strain levels of such mixtures is important for geotechnical applications. The aim of the study is to evaluate the shear modulus and material damping of sand-EPS bead mixtures over a wide range of strains to provide a basis for evaluation of using such mixtures as seismic buffers behind earth retaining structures and for base isolation in seismic areas. Dynamic properties of sand-EPS bead mixtures are evaluated from resonant column and cyclic triaxial tests at small and large strains, respectively. Sand-EPS bead mixtures with varying EPS bead content, up to 2.5% by weight, have been tested at confining pressures of 50, 100 and 200 kPa. Results were analyzed to calculate the small-strain shear modulus, minimum damping ratio, shear modulus degradation curves, and damping curves. Results indicate a decrease in shear stiffness with increasing bead content at all strain levels. Material damping is relatively unaffected at small shear strains; however, it increases at larger strains. The dynamic testing performed yielded properties that can be reflected on applicability of the mixture in geotechnical applications.

STATIC AND DYNAMIC PROPERTIES OF SOILS IN CATANIA (ITALY)

The analysis of the historical reports and previous research projects allowed us to describe high-level seismic risk scenarios for the city of Catania, located on the eastern coast of Sicily (Italy). The geotechnical zonation of the subsoil of the city of Catania suggests a high seismic hazard added to a soil amplification of the ground motion. To this aim field and laboratory tests allowed the definition of a geotechnical characterisation in the city of Catania. For the site characterisation of soils deep site investigations have been undertaken. Borings and dynamic in situ tests have been performed in some selected test sites with the aim to evaluate the soil profiles of shear wave velocity and to retrieve undisturbed samples for laboratory tests. The testing programme consisted of standard classification tests, Oedometer tests, Direct shear tests, Resonant Column and Torsional shear tests. Two equations to draw the complete shear modulus degradation with strain level and the inverse variation of damping ratio with normalized shear modulus respectively have been also proposed. Shear wave velocity profiles experimentally obtained were compared with both in situ and laboratory tests.

Experimental Characterization of Stress- and Strain-Dependent Stiffness in Grouted Rock Masses.

Grouting of fractured rock mass prior to excavation results in grout-filled discontinuities that govern the deformation characteristics of a site. The influence of joint characteristics on the properties of grouted rocks is important in assessing the effects of grouting on jointed rock mass. However, grouting remains a predominantly empirical practice and the effects of grouting on rock joint behavior and material properties have yet to be accurately assessed. Granular materials, including jointed rocks, typically display nonlinear strain-dependent responses that can be characterized by the shear modulus degradation curve. In this study, the effects of grouting on the strain-dependent shear stiffness of jointed rock mass were investigated at the small-strain (below 10−5) and mid-strain (10−5 to 10−3) ranges using the quasi-static resonant column test and rock mass dynamic test devices. The effects of curing time, axial stress, initial joint roughness, and grouted joint thickness were examined. The results show that (1) grouting of rock joints leads to decreased stress sensitivity and increased small-strain shear stiffness for all tested samples; (2) the grouted rock samples display similar modulus degradation characteristics as the applied grout material; (3) the initial joint roughness determines the stress-dependent behaviors and general stiffness range of the jointed and grouted rocks, but the strain-dependent behaviors are dependent on the properties of the grout material; (4) increased grouted joint thickness results in larger contribution of the grout properties in the overall grouted rock mass.

Earthquake Response Analysis of Sites in State of Haryana using DEEPSOIL Software

Earthquake response analysis has been carried out for various locations in the State of Haryana (India) adopting the equivalent linear approach. For this purpose, geotechnical data have been collected from different government and private organizations. Based on the provisions of National Earthquake Hazards Reduction Program (NEHRP), all the sites have been classified using average N-value (N30) for the soil profile. The shear modulus (Gmax) values of the layers in a soil profile have been estimated using standard correlations. Cyclic Response has been accounted for using the standard shear modulus degradation and damping curves. Time histories from Himalayan Thrust System have been used as an input and soil amplification has been estimated at the surface using DEEPSOIL software. The results of the study have been formulated in terms of soil amplification map, response spectra, PGA along the depth, surface time histories and strain along the depth. These results can be used for dynamic analyses and design of structures, planning of advanced dynamic lab test etc. Moreover, it has been observed that sites in Haryana can significantly amplify ground motions and hence a site-specific design approach must be adopted for important structures.

Scaling Shear Modulus from Small to Finite Strain for Unsaturated Soils

AbstractThe stress-dependent curve of shear modulus degradation with increasing shear strain amplitude is a fundamental mechanical property of soils. Although it is well known that the degree of sa...

Regional subsidence effects on seismic soil-structure interaction in soft clay

Regional subsidence effects on dynamic soil properties and ground layering deformation are often ignored in practice, when dealing with seismic soil-structure interaction analyses. Nevertheless, these effects can substantially change the frequency content and spectral accelerations in both free field and in the soil-structure system. Pore pressure variations over the project economic life are due to both regional subsidence as well as dissipation of excess pore pressure caused by the structure weight. These variations lead to changes in effective stresses, which in turn, modify the dynamic properties such as shear wave velocity distribution and modulus degradation and damping curves, as well as soil layer thickness and shape. These changes can be substantial in highly compressible very soft clay, such as that found in Mexico City valley. This paper presents a numerical study on the seismic response of a conventional five-story building supported by a compensated box foundation built in soft clay, considering these effects. Three-dimensional finite difference models were developed with the software FLAC3D. Initially, the evolution of effective stresses with pore pressure was established based on in-situ piezometer measurements of an instrumented site, and laboratory data. Then, changes in dynamic properties were taken into account based on the results gathered from series of resonant column tests conducted for several effective consolidation stresses, and a PS suspension logging test. The static behavior of the soil-structure system was assessed. For the cases studied herein, the complex interplay between soil nonlinearities, which lead to fundamental period elongation of the soil deposit, Tp, and the overall tendency of ground consolidation to shorten it, controls the variations in the spectral ordinates depending on how close Tp is of the predominant period of the excitation.

Laboratory test and empirical model for shear modulus degradation of soft marine clays

The change in the shear modulus of clays under repeat environmental loads is an important factor in the design of offshore and onshore foundations. A degradation model for the shear modulus of soft clays that considers the effects of the number of cycles, the cyclic stress ratio, the loading frequency and the plasticity index is proposed. A series of undrained cyclic triaxial tests on undisturbed Shanghai marine clays were conducted. Experimental results reveal that the shear modulus degradation index has a logarithmic relationship with the number of cycles, decreases linearly with the cyclic stress ratio, and increases linearly with the loading frequency when plotted in log-log coordinates. Further study using existing data from other research shows that the degradation index decreases with plasticity index, IP. Based on the test results, a new degradation model is proposed which considers these factors explicitly. The main feature of the new model is that only one set of parameters for each type of clay is required for the prediction of shear modulus degradation. The applicability of the present model is verified by five soft clays with different plasticity indices and loading conditions.

Modelling of non-linear seismic ground response using elasto-plastic constitutive framework within a finite element soil column model

The prediction of seismic ground response is conditioned by the knowledge of each material behavior of soil deposits. The recourse to plasticity criterion to simulate cyclic behavior of soils under seismic loading is becoming more realistic. In this study, an elasto-plastic constitutive equation is cast within the framework of one dimensional finite element (FE) soil column model to account for the spatial and material nonlinearity of the secant shear modulus. To account of the spatial non linearity, shear modulus is written in terms of rigid base shear modulus and height of the soil column, while for material nonlinearity, the shear modulus degradation is deducted by the application of the isotropic evolution of the Von Misès criterion. Obtained results proved the efficiency of the proposed methodology and the predictive capability of the elaborated elastoplastic model which captures both small- and large-strain behaviors. They likewise highlight the important roles that play the spatial and material shear modulus variation in the prediction of the seismic soil responses.

Monotonic, cyclic and post-cyclic behaviour of an unsaturated clayey soil

Geotechnical design for unsaturated soils requires an understanding of their fundamental characteristics. In this paper, in order to study the monotonic, cyclic and post-cyclic behaviour of an unsaturated clayey soil, monotonic and cyclic triaxial tests were carried out on Tehran oil refinery’s disturbed unsaturated clayey soil (CL). Tests were conducted on the specimens with different initial matric suctions and net confining pressures with the same dry density under constant pore-air pressure and undrained conditions for water. No reconsolidation was allowed after cyclic loading of specimens. Tests results showed that cyclic loading degrade the undrained shear strength and deformation modulus of specimens during the post-cyclic monotonic loading. It was observed that shear modulus degradation is more pronounced than that of the shear strength due to cyclic loading. Also, the shear strength and shear modulus of soil generally increased with increasing the net confining pressure and initial matric suction.

Improved Approach for Modeling Nonlinear Site Response of Highly Strained Soils: Case Study of the Service Hall Array in Japan

A nonlinear ground response analysis is conducted for the Niigata-ken Chuetsu-oki earthquake recorded at a free-field vertical array near the Kashiwazaki-Kariwa Nuclear Power Plant in Japan. A bidirectional site response analysis is carried out using LS-DYNA which allows user defined stress-strain relationships to dictate soil behavior subjected to dynamic loading. Dynamic soil behavior is characterized using a two-stage hyperbolic backbone curve implemented with modifications to consider the peak strength of soil layers as well as the strain at which the peak strength is fully mobilized. The effects of bidirectional input motions, strain rate, and the shape of the shear modulus degradation curves are investigated, and it is demonstrated that each factor can have a significant influence on the results.