Soil Dynamic Constitutive Model for Characterizing the Nonlinear-Hysteretic Response

A simplified analysis procedure for the nonlinear hysteretic dynamic response of soil or structural systems, or both, is presented. The method is based on a Galerkin formulation of the equations of motion in which the solution is expanded using basis functions defined over the spatial domain occupied by the soil system. The basis functions are selected as the normal eigenmodes of the linearized problem. The hysteretic stress-strain behavior is modeled by using elastoplastic constitutive equations based on multi-surface kinematic plasticity theory. Accuracy and versatility of the technique are demonstrated by applying it to analyze the nonlinear dynamic response of an earth dam. The dam is modeled as a one-dimensional hysteretic shear wedge. Parametric studies assessing the influence of the nonlinearities on the response are presented. Finally, comparisons are made with results obtained through a more elaborate finite element representation of the dam.

To investigate the effect of the slenderness ratio (L/d) of the specimen, resonant column (RC) tests were conducted on dry sand specimens by using three different values of L/d, namely 2, 3, and 4, keeping the same diameter (d = 50 mm) to measure the shear moduli and material damping associated with the shear strain varying approximately from 0.0004 to 0.03 %. For the sake of the comparison, bender element (BE) tests were also performed on the same specimens to examine the effect of L/d on the shear moduli. Different combinations of relative densities and isotropic confining pressures were employed. The current experimental findings based on the simplified theory, which is widely used for analyzing the RC test results, reveal that the measured shear moduli of the specimens become higher for a slender specimen. On the other hand, the damping values were found to be only marginally affected with the changes in L/d. For greater L/d, generally the damping values were found to be slightly higher, especially with greater relative densities. The BE tests, on the other hand, hardly illustrate any variation in shear moduli with the changes in L/d. The shear wave velocities (Vs) from the BE tests were found to be a little greater as compared with the RC tests, and the difference between two sets of results becomes narrower with an increase in L/d. This study reveals that it will be more appropriate to use a L/d equal to 4 rather than 2, especially when testing at isotropic confining pressure ≥ 500 kPa.

Nonlinear vibration analysis of the resonant column test of granular materials

Many reports describe overestimation of liquefaction resistance based on sounding data related to ground materials containing coarse particles such as gravel and cobbles. Better methods of liquefaction potential estimation must be developed using investigation data other than those from sounding. Gathering perfect and undisturbed samples is difficult, but using seismic methods such as PS logging might be effective for assessing liquefaction potential. For this study, bender element (BE) tests and local small strain (LSS) tests were conducted, respectively, to measure the dynamic and static shear moduli of gravel – mixed sand specimens. Subsequently, relations between liquefaction strength and secant shear moduli were examined to provide reliable estimation of liquefaction in gravel – mixed sand. Although the liquefaction resistance increased considerably with overconsolidation, the initial shear modulus exhibited only a slight change with the same overconsolidation. The experimentally obtained results elucidated that the important shear strain level, for which secant shear modulus has a strong relation with liquefaction strength, was not a linear elastic region of 0.001%: it was about 0.01%.

Resonant column tests, corresponding to a given input voltage of the drive mechanism, were conducted in torsional mode to examine the effect of vibration cycles on shear modulus (G) and damping (D) of dry sand with shear strain amplitude in a range of 0.0005–0.05%. Two different relative densities, approximately 61 and 85%, and effective confining pressures, 300 and 500 kPa, were used. The specimens were subjected to a number of vibration cycles ranging from 1,000 to 50,000. The shear modulus and damping ratio, before and after the application of vibration cycles, were determined for several input voltages. An induction of the vibration cycles leads to a continuous increase in shear strain, which causes (1) a decrease in the shear modulus and (2) an increase in the damping ratio. This effect becomes especially more prominent for lower values of relative densities and confining pressures. The modulus reduction and damping curves remained the same after applying vibration cycles.

Shear modulus and damping ratio are considered essential soil parameters for ground response analyses under dynamic loading. The dependency of these two key parameters on the amplitude of induced strain for several types of soil has been studied in the laboratory and in situ tests under a limited set of controlled environmental factors, mainly soil confinement, plasticity, and moisture content. The present research investigates the influence of an additional potential critical factor, i.e., soil temperature. The thermo-controlled resonant column (RC) tests were conducted on low plastic clays (CL), and the effects of rising temperature on the soils' dynamic parameters were thoroughly investigated, with particular emphasis on the shear moduli degradation and variations in damping ratios (D) vs. G/Gmax under thermally controlled conditions. The results suggest that the ground temperature might not play a significant role in the assessment of suitable values of the shear modulus and damping ratio for ground response analyses.

Dynamic shear modulus and damping of cemented and uncemented lightweight expanded clay aggregate (LECA) at low strains

This paper investigates the undrained shear stiffness of sand–bentonite specimens (with 0 %, 3 %, and 5 % bentonite by dry mass of the sand) prepared at the same skeleton void ratio (Drsk = 35 % to 40 %) using a dry pluviation technique. The experimental program consisted of (1) small strain tests using a resonant column apparatus and (2) large strain tests using a cyclic triaxial apparatus. The resonant column tests were performed at three confining stress levels (50, 100, and 193 kPa) under drained and undrained conditions. A comparison of the shear modulus reduction with shear strains for both drained and undrained conditions is presented; the effects of changes in effective stresses and the rate of modulus reduction as a function of the effective stress are discussed to describe the discrepancy between the two sets of data. The results show a marginal decrease in Gmax for specimens with bentonite, which is attributed to the presence of bentonite at the sand grain contacts. However, the presence of bentonite increases the linear elastic threshold, particularly in the case of undrained tests, in which a noticeable delay in excess pore pressure generation was measured. The strain level required in order to initiate excess pore pressure generation increased with increasing bentonite content. A similar trend was noted in cyclic triaxial tests, in which, for a given strain, specimens with bentonite generated lower excess pressure than sand specimens tested under similar conditions. Finally, a combined normalized G/Gmax curve from both tests is presented for specimens with 0 %, 3 %, and 5 % bentonite at 100 kPa.

A series of dynamic behavior tests on Nanjing flake-shaped fine sand were performed by using the WFI cyclic triaxial apparatus made in England. The dynamic behaviors of Nanjing flake-shaped fine sand under different static deviator stress levels and cyclic stress ratios were studied. Through comparing the effective stress path under cyclic loading with static loading, the processes of liquefaction of saturated Nanjing flake-shaped fine sand with development of dynamic pore-water pressure, including the initial compact state, compression state and dilative state, were investigated. The variation of the shear stiffness with the number of cycles and cyclic strain was investigated by analyzing the secant shear modulus in each unload-reload loop of dynamic stress-strain relationship. And by means of the exponential function, the empirical equations of the relationship between secant shear modulus Gsec, shear modulus ratio Gsec/Gmax and cyclic strain e were established based on series of test results. The results show that according to different combinations of static deviator stress and cyclic stress, two kinds of failure patterns with deviator stress reversal or no deviator stress reversal are observed in the samples tested in this series, including cyclic mobility and the failure of accumulation residual strain. In addition, the degradation of dynamic shear modulus is due to the development of vibration pore-water pressure and it is observed that the shear modulus reduces with the progressive number of cycles.

This paper presents an experimental investigation of the concept of effective density for the propagation of small-strain shear waves through saturated granular materials. Bender element tests and resonant column tests were conducted on various granular materials in dry and saturated conditions. Values of small-strain shear modulus for the dry condition are compared with corresponding values for the saturated condition, which are calculated using saturated density and effective density. For bender element tests, the use of saturated density produced errors as high as 28% in the shear modulus, whereas the use of effective density resulted in errors generally less than 5%. For resonant column tests, errors in the shear modulus that were obtained using saturated density were smaller than those for bender element tests because of the lower range of excitation frequency and effect of mass polar moment of inertia of the loading system. A quick chart is provided to help users determine if effective densi...

The threshold shear strain is a fundamental property of the soil behavior subjected to cyclic loading. Starting from the unloading and reloading hysteretic curves of dynamic Ramberg-Osgood model, construct small-strain dynamic dissipation function and explain small-strain dynamic characteristics by use of the skeleton curve back stress assumption. The plotting results of yield curves in true stress space indicate that there exist two threshold shear strains which are defined as the first threshold shear strain and the second threshold shear strain respectively which represent boundaries between fundamentally different dynamic characteristics of cyclic soil behavior. The yields of soil are controlled by the constant friction coefficient, the variable friction coefficient and dilatancy-related microstructural changes respectively. Both the first threshold shear strain and the second threshold shear strain do depend significantly on the maximum dynamic shear modulus coefficient and exponent. Comparison between the two threshold shear strain values and shear modulus reduction curves obtained on exactly the same soils confirms that the soil behavior is considerably at nonlinear at , the secant shear modulus, Gs, of the four soils studied is between 0.6 and 0.8 of its maximum value.

Isothermal and adiabatic shear moduli have been measured countless times. Adiabatic shear moduli which are generally considered to be the same as isothermal shear moduli are shown here to be unstable, so they cannot exist. A constitutive law that avoids adiabatic moduli is found to apply to polycrystalline isotropic solids. The equation is a power law in the volume per unit mass time the shear modulus. The volume is in turn a function of temperature T and pressure p in the system. The adiabatic moduli are established in shear stress versus strain space using a construction from isothermal elastic shear moduli. The derivation of this law replaces adiabatic with isochoric conditions in linear elastic, sheared solids. It is widely reported that the shear thermal expansion coefficient is zero since isotropic solids do not change the shape when heated. All solids with applied shear stresses and temperature dependent shear moduli change the shape and have shear thermal expansion coefficients. The thermal expansion coefficient is coupled into the shear component of the entropy and the T dependence of the isothermal shear modulus. In a sheared solid, only the single point τ = 0, γ = 0 has no shear entropy contributions and no thermal expansion and is mechanically unstable in adiabatic constructions. The exact form of the proposed constitutive law is based on solutions from a second order differential equation based on shear contributions from the entropy.

Numerical simulations of earthquake fault rupture propagation can be used to design structures to resist damage from induced ground deformations. Several researchers have developed numerical models for analyzing the responses of soil and structures to underlying fault movement. Often, however, a relatively simple Mohr-Coulomb constitutive model that is modified to incorporate strain softening or other material nonlinearity is used. In this work, a modification of the UBCSAND soil constitutive model, one that has been shown to capture well the nonlinear shear response of soil for many stress paths, was used. The UBCSAND model was modified to add postpeak strain softening with a response that is dependent on the mode of fault rupture, a nonlinear failure envelope that is stress dependent, and a modified flow rule that is dependent on the mode of shear deformation. The numerical simulations captured well the observed trends in carefully performed geotechnical centrifuge experiments. The Modified-UBCS...

To evaluate the effect of the excitation frequency on the dynamic properties of soils, the elastic modulus \(E\), shear modulus \(G\), and Poisson’s ratio \(\nu \) for three Mexican compacted clayey soils were determined using two techniques: laser ultrasonic and resonant column (RC) tests. For the first, the parameters were determined by measurements of the P- and S-waves at ultrasonic frequencies and variations of the height of the cylindrical soil specimens and for the second one, a harmonic excitation between 5 Hz and 7 Hz was applied. Large variations in the elastic parameters through an ultrasonic axial scanning of the soil specimens were observed; this reveals the heterogeneity of these materials, while a decrease of the sample aspect ratio mainly affects the determination of Poisson’s ratio. The ultrasonic data were integrated with those from RC data to obtain a shear modulus profile covering both high and low frequencies. The interpolation on whether the data are either linear or not is an indication of the viscoelastic behavior of the compacted clayey soils. The specimens were: (a) clay from Texcoco Valley, (b) clay from Mexico Valley, and (c) granular soils from the Parota. Experimental determination of the mechanical properties of soils is very important because soil constitutive models are traditionally calibrated from global boundary measurements taken from laboratory soil specimens. The most difficult parameter to obtain is the Poisson’s ratio, as well as the shear modulus, which is a fundamental parameter for establishing the soil response under low amplitude vibrations and it is extremely important to foundation design.

This study compares results from three different testing methods: Resonant Column, TorsionalSimple Shear, and Bender Element tests to determine shear modulus. The resonant column and torsionalshear tests were performed on the same hollow cylinder specimen. The bender element test was performed ona triaxial specimen with the same void ratio and confining stress as well as others. Several effects werestudied, among them confining stress, shear strain amplitude and for the bender element, anisotropicconfinement. Testing methods and data analysis are discussed in the paper because data interpretation is veryimportant in these tests. Results showed that the shear modulus values were almost identical between theresonant column and torsional shear but varied somewhat with the bender element results. Further researchwill focus on influence of stress anisotropy preparation methods.