Elastic Soil Properties Research Articles

Probabilistic Analysis of Strip Footings Resting on Spatially Varying Soils and Subjected to Vertical or Inclined Loads

A probabilistic analysis of vertically and obliquely loaded strip footings resting on a spatially varying soil is presented. The system responses are the footing vertical and horizontal displacements. The deterministic computation of these system responses is based on numerical simulations using the software FLAC3D. Both cases of isotropic and anisotropic random fields are considered for the soil elastic properties. The uncertainty propagation methodology employed makes use of a nonintrusive approach to build up analytical equations for the two system responses. Thus, a Monte Carlo simulation approach is applied directly on these analytical equations (not on the original deterministic model), which significantly reduces the computation time. In the case of the footing vertical load, a global sensitivity analysis has shown that the soil Young's modulus E mostly contributes to the variability of the footing vertical displacement, the Poisson ratio being of negligible weight. The decrease in the autocorrelation distances of E has led to a smaller variability of the footing displacement. On the other hand, the increase in the coefficient of variation of E was found to increase both the probabilistic mean and the variability of the footing displacement. Finally, in the inclined loading case, the results of the probability of failure against exceedance of a vertical and/or a horizontal footing displacement are presented and discussed.

Non‐invasive characterization of pore‐related and elastic properties of soils in linear Biot–Stoll theory using acoustic‐to‐seismic coupling

SummarySoil structure, moisture content and strength have profound effects on plant growth. Traditional methods for monitoring soil condition are invasive and therefore may affect the samples of interest. We have demonstrated the potential of a non‐invasive measurement technique for the in situ monitoring of soil physical properties in the field. When soils are regarded as porous and elastic media, sub‐surface wave propagation can be indicative of the soil status. Such propagation can be initiated by airborne sound through acoustic‐to‐seismic (A–S) coupling. Measurements of near‐surface sound pressure and acoustically induced soil particle motion can be exploited to estimate the pore‐related and elastic properties of soils. We have conducted laboratory measurements on dry and wet sand and field measurements on an arable soil growing wheat using a compression driver, microphones and a laser Doppler vibrometer. The excitation levels were chosen so as to reduce the influence of soil non‐linearity while still yielding sufficient signal‐to‐noise ratios. Measured data were compared with model predictions based on wave propagation in layered homogeneous isotropic poro‐elastic media described by linear Biot‐Stoll theory. Soil properties were estimated through an optimization process minimizing the differences between the measurements and predictions. Latin hypercube sampling was adopted to ensure uniform seeding for optimization throughout the multi‐dimensional search space. The fitted soil characteristics are air permeability, porosity, P‐/S‐wave speeds (related to bulk and rigidity moduli) and a loss factor. Layer depth was also estimated for multi‐layered samples. The current work has demonstrated that soil can be characterized non‐invasively by using A–S coupling. It is also shown that field soils can be represented adequately by multiple homogeneous layers.

Application of Piezoceramic Elements for Determining Elastic Properties of Soils

Elastic modulus and Poisson’s ratio of soils are two important parameters required for safe design of various civil engineering structures. The elastic modulus and shear modulus of the soils are generally obtained from the resonant column, torsional shear tests and geophysical methods. Though, from these parameters the Poisson’s ratio can be determined, these tests are quite elaborate, cumbersome, time consuming and require skilled manpower particularly for data interpretation. Moreover, direct determination of the Poisson’s ratio by employing micro-strain gauges, which measure axial and lateral strains using Wheatstone bridge circuits, is difficult for soils due to the problems associated with their fixing on the surface of the sample. Under these circumstances, application of piezoceramic elements, which can generate shear and compression waves, seems to be an excellent alternative. Using these wave velocities, the Poisson’s ratio can be computed easily and precisely. However, how this (computed) value of the Poisson’s ratio compares vis-a-vis that obtained from the conventional triaxial tests (i.e., strain controlled uniaxial compression tests), which yield stress–strain relationship, needs to be established. With this in view, investigations were conducted on soils of different types (clays and sands) in their disturbed and undisturbed forms by resorting to piezoceramic tests and the triaxial tests. Details of the methodology are presented in this paper and it has been demonstrated that application of piezoceramic elements yields the Poisson’s ratio and the elastic modulus of the soils quite easily, particularly for the soft clays and sands.

Back-calculation of elastic modulus of soil and subgrade from portable falling weight deflectometer measurements

In the field of nondestructive testing of pavement, the portable deflectometer devices have gained, in the recent years, a wide use for in situ assessment of elastic properties of soils, subgrade and pavement foundations. However, if the use of the elasto-static model based on the Boussinesq’s theory does not constitute a shortcoming in the back-calculation procedure of homogenous elastic modulus, questions have been arose about the reliability and accuracy of the peak value method commonly used to extract the static stiffness of soils and subgrade from the dynamic transient data. This paper deals with the use of minimization technique, based on least square algorithm as an alternative method for data analysis and soil elastic stiffness identification. Details of the mathematical basis, the implementation and different steps for elastic modulus back calculation, are presented. In this method, an equivalent spring-mass-dashpot system, where the complex dynamic soil behavior is reduced to a viscoelastic one-dimensional wave propagation problem, is used for modeling the loading plate/soil system. The comparative study shows the suitability and the accuracy of the minimization method for soil elastic stiffness identification and elastic modulus back calculation.

Elastic Parameters of Intermediate Soils Based on Bender-Extender Elements Pulse Tests

The elastic behaviour of compacted soils subjected to very small strains (smaller than 10 －5) is essential, because the serviceability of most geotechnical structures depends on soil elastic properties. Small-strain stiSness of soils was studied in the past years using diSerent experimental devices (mainly resonant columns). However, the results have been relatively inconsistent. The bender elements technique, now extensively used in soil mechanics, oSers an e‹cient non destructive alternative, since it is based on the propagation of shear waves. To enrich the common bender elements testing results providing only shear modulus values, an evolution of the bender elements technique, named bender-exten-der element's is used in this paper. This device allows the simultaneous measurement of the shear and compression wave velocities. As a result, the two independent elastic constants are measured for the same sample in order to avoid indirect estimations. Also, for unconˆned sample's the GrindoSonic test is performed: this test is based on the transient vibrational response of the sample to a slight shock. The present study provides new results about the elastic properties of intermediate unsaturated soils made of mixtures of sand and clay. The results for the elastic properties are presented as a function of the suction level. Finally, a model relating the elastic behaviour of these unsaturated soils is proposed.

Influence of organic matter on rheological properties of soil

Recently rheological methods have been used to investigate the mechanical properties of soil micro-structure. Rheological techniques provide a number of quantitative physically based measurements and offer a better understanding of how soil micro-structure behaves when subject to stress. Here a rotational rheometer with a parallel-plate measuring device was used to explore the viscoelastic properties of soil as a function of soil organic carbon (SOC). We used samples from the long-term experimental site at Broadbalk, Rothamsted, UK. Data from amplitude sweep tests (AST) with controlled shear deformation are reported as well as mineralogical data. In general, water content, and SOC content, in addition to soil texture, clay mineralogy, carbonate, and cations all have an effect on stiffness, structural stability, and shear behavior. Storage modulus G′ and loss modulus G″, yield point, the linear viscoelastic range (LVE), loss factor tan δ, and integral z characterize micro-structural properties of soil on the particle-to-particle scale. Long-term applications of farmyard manure (FYM) lead to a significant increase in soil organic carbon (SOC), in comparison with the application of ammonium nitrate in form of mineral NPK fertilizer and bare fallow. For wet soils, increased SOC provided greater resistance to deformation and improved soil elastic properties allowing greater deformation before a yield point was reached. In drier soils however, (−6 and −15kPa) this relationship was less clear.

FINITE ELEMENT PROCEDURE FOR MODELING SOILSTRUCTURE- FOUNDATION INTERACTION IN BUILDING SEISMIC DAMAGE RESPONSE

A finite element based computational procedure is presented for soil-structure interactionmodelling in building due to seismic damage response. Attention is focused on a combinationof contact surfaces at the soil-foundation interface, nonlinear soil material response, andinfinite elements as transmitting boundary conditions. A rationale for efficient mesh design isoffered for the detailed building/foundation/soil system model based on computational wavepropagation studies using infinite elements.To evaluate the performance of the proposed procedure for handling SSI, a completecomparison between four models for a 3-story office building were performed. The modelsclassified as one fixed base model without any effect of soil, second with the conventionaltreatment of the foundation and soil as discrete linear springs, the third incorporating theproposed procedure with elastic properties of soil, and the fourth proposed procedure withnon-linear properties of soil.This evaluation was based on the capability of the model to capture the different columndamage indices. These indices are: acceleration time history, the floors drift ratio, andmoment-curvature plot for the column. The strategy adopted for the analysis is performed aseismic dynamic analysis for the four models by using the general purpose finite element codeABAQUS. Conclusions that can help in clearing and analyze the system response werecleared out.

Elasto-plastic long-term behavior of granular soils: Experimental investigation

The experimental and phenomenological investigation of the elasto-plastic long-term behavior of soils under dynamic loading is an important contribution for development of risk analysis tools and numerical models for settlement prediction due to dynamic long-term impacts. Thereby elastic soil properties as well as long-term accumulation characteristics of the soil are of major importance for correct description of the soil behavior. This paper delivers insight in the experimental investigation of strain accumulation in granular soils due to dynamic loading in the small strain region through combined bender element and cyclic triaxial testing. Test results are presented illustrating the evolution of elastic parameters during long-term cyclic loading and the influence parameters on strain accumulation. A subsequent discussion focuses on difficulties in adapting cognitions out of laboratory investigations on accumulation properties of soil to in situ conditions and draws conclusions out of achieved test results.

Reliability-Based Analysis of Strip Footings Using Response Surface Methodology

A reliability-based analysis of a strip foundation subjected to a central vertical load is presented. Both the ultimate and the serviceability limit states are considered. Two deterministic models based on numerical simulations are used. The first one computes the ultimate bearing capacity of the foundation and the second one calculates the footing displacement due to an applied load. The response surface methodology is utilized for the assessment of the Hasofer-Lind reliability indexes. Only the soil shear strength parameters are considered as random variables while studying the ultimate limit state. Also, the randomness of only the soil elastic properties is taken into account in the serviceability limit state. The assumption of uncorrelated variables was found to be conservative in comparison to the one of negatively correlated variables. The failure probability of the ultimate limit state was highly influenced by the variability of the angle of internal friction. However, for the serviceability limit state, the accurate determination of the uncertainties of the Young's modulus was found to be very important in obtaining reliable probabilistic results. Finally, the computation of the system failure probability involving both ultimate and serviceability limit states was presented and discussed.

Attenuation and Velocity Structure for Site Response Analyses via Downhole Seismogram Inversion

A seismic waveform inversion algorithm is proposed for the estimation of elastic soil properties using low amplitude, downhole array recordings. Based on a global optimization scheme in the wavelet domain, complemented by a local least-square's fit operator in the frequency domain, the hybrid scheme can efficiently identify the optimal solution vicinity in the stochastic search space, whereas the best-fit model detection is substantially accelerated through the local deterministic inversion. Results presented for selected aftershocks of the Mw 7.0 Sanriku-Minami earthquake in Japan, recorded by the Kik-Net Strong Motion Network, illustrate robustness of the impedance structure estimation. By contrast, the attenuation structure is shown to be sensitive to the frequency content of seismic input data, attributed to the deterministic description of the continuum in the forward model that cannot simulate late arrivals of multiple-scattered energy. Sensitivity analyses illustrate that for the same forward model, results can be substantially different based on the definition of the objective function. It is concluded that even for engineering purposes, inversion should aim to decouple intrinsic and scattering attenuation mechanisms.

Estimation of Nonlinear Time-dependent Soil Behavior in Strong Ground Motion Based on Vertical Array Data

To improve our understanding of nonlinear elastic properties of soils, a method is proposed of estimation of stress-strain relations of soils in situ in strong ground motion based on vertical array data. Strong motion records provided by seismic vertical arrays allow estimation of nonlinear stress-strain relations in soil layers at different depths, from the surface down to the location of the deepest device. As an example, records obtained during the main shock of the 1995 Kobe earthquake at Port-Island, SGK, and TKS sites were used to estimate the stress-strain relations in the soil profiles. For different layers, different types of nonlinear stress-strain relations were selected, according to the profiling data. To account for temporal changes in the soil behavior, consecutive parts of records were examined, and for successive time intervals, the relations were found showing the best-fit approximation to the observed data. At Port Island and SGK sites, where the strongest accelerations were recorded, the obtained stress-strain relations showed systematic changes in the upper layers (0–14 m), such as, a progressive reduction of the slopes of the stress-strain curves due to liquefaction at Port Island and reduction and recovery of the slopes at SGK and TKS sites. At the three sites, the stress-strain relations remained stable in layers below 11–14 m. Thus, the proposed approach gives us a representation of the soil behavior in layers at different depths in strong ground motion; it allows calculation of the propagation of arbitrary seismic signals in the studied profiles and estimation of nonlinear components in the ground response by the nonlinear system identification technique. The method can also be applied to evaluate the ground response at sites where profiling data are available and an imposed motion can be estimated.

Winkler Coefficient for Beams on Elastic Foundation

Using the elastic continuum approach for the analysis ofbeam on elastic foundation, a method is developed to calculate an equivalent coefficient of subgrade reaction k to use in the Winkler model. It is shown that dividing the contact pressure produced from elastic continuum model by the corresponding settlement along the beam length generates length dependent coefficient of subgrade reaction that accurately describes the interaction between the beam and the supporting soils. Results from the developed I equivalent k parameter are compared with those from elastic continuum model and by using different k values predicted by other methods that are currently in use. For uniformly loaded beam, graphs and regression equations are provided from which an equivalent k value at different positions along the beam length (eg, at the center and the edge of the beam) can be calculated as a function of the elastic soil properties and the rigidity of the beam

Elastic Properties of Soils

A triaxial apparatus to measure small strains in the range between 10 −6 and 10 −2 has been set up to investigate the reversible behavior of various types of soils (sands, gravels, clays). Reversible behavior, along compression and extension triaxial paths, was demonstrated for strain amplitudes lower than 10 −5 . Elasticity was found to be nonlinear, since the Young's modulus depended on the mean effective stress. We also studied the influence of such parameters as deviatoric stresses, void ratio, stress and strain history, and soil structure on the elastic coefficients of these soils. A general equation was proposed for determining the Young's modulus E in initially isotropic soils, which was modified by further loading. In granular materials, strain hardening increased the value of E , while in structured materials, a decrease of E was observed due to internal structure damage.

Simplified Analysis of Long-Span Soil-Metal Structures

To analyze and design long-span soil-metal structures and other structures involving soil or reinforced soil, it is important to estimate accurately the soil properties. Triaxial tests are carried out on reinforced as well as unreinforced Lake Erie sand specimens. A hyperbolic stress-strain relation is proposed to represent the soil elastic properties. Expressions are deduced to evaluate the modulus of elasticity of the soil as well as the coefficient of soil reaction that is required for the proper design of soil-metal structures. The proposed expressions are valid for both reinforced and unreinforced soils. A simplified finite-element model is presented for the analysis of long-span unreinforced and reinforced soil-metal structures. Results from the simplified model are compared to those from a plane-strain finite-element analysis. The results are also verified using results obtained from tests carried out on reduced-scale models.

Validation of small strain properties from recorded weak seismic motions

During the last decade, there has been an increased interest in the computations of surface ground motions from known rock outcrop motions. The main advantage of the procedure is to allow for the actual variation of strength and stiffness properties of heterogeneous soil profiles, eventually accounting for non-linear soil behavior. The main questions raised against the adequacy of such a procedure lie upon the reliability of the computational scheme and in the representativity of the soil constitutive relationship. The present paper addresses both aspects by comparing the motions computed assuming standard assumptions in the state of practice of earthquake engineering. Since until now, the downhole array recorded only weak motions (horizontal peak ground accelerations smaller than 0·04 g), the paper focuses on elastic soil properties. It is demonstrated that a carefully conducted geotechnical survey yields an accurate shear wave velocity profile and that rate-independent soil damping might not be appropriate to represent the soil behavior in the small strain range.

Stability of elastic plane frames including soil-structure interaction

In this paper the analysis of linear elastic plane frames interacting with an elastic Winkler foundation, consisting of rafts and piles, is studied with respect to the stability of the entire structure. The theory is based on small deformation beam theory with second order effects included. The differential equation describing the behavior of each element of the frame is solved exactly and, thus, no discretization errors occur. A new exact finite element is presented for a beam on elastic foundation according to second order theory. This new exact element gives a significant reduction in calculation effort compared to standard elements used in commercial computer codes. Stiff areas, hinges and rollers are defined by a general formulation of the coupled boundary value problem. The problem becomes non-linear in axial force parameters and is solved with a secant iteration procedure. Soil-structure interaction is idealized by using uncoupled load transfer functions in both lateral and axial directions, when perfectly elastic soil properties are assumed. In order to demonstrate the accuracy and the efficiency obtained when exact solutions are used a few numerical examples are included. Firstly, the exact solution to a compressed beam on Winkler foundation is given, and secondly, the elastic stability of one single pile is studied. Finally, the elastic stability of a multi-storey frame resting on a piled/raft foundation is studied with respect to the relative stiffness between the structure and the soil medium.

Seismic Refraction Survey For Continuously Nonhomogeneous Soils

The analysis of seismic refraction is presented for uniformly deposited soil strata of constant density and Poisson's ratio and stiffness increasing continuously with depth due to differential compaction effects. Analytical expressions for the surface-to-surface travel time as well as for the depth to maximum penetration are presented for realistic functions of the variation of the soil stiffness with depth. Approximate formulas are also given for practical use in nondestructive subsoil investigation. The results may be used either to determine in-situ elastic soil properties directly from refraction surveys or to support and verify conventional surface wave vibration tests. INTRODUCTION Although dispersion measurements have gained in popularity during the last decade, seismic refraction surveys still offer an attractive adjunct to the determination of in situ stiffness parameters. In civil engineering the method is mainly applied to determine wave propagation velocities and layer thicknesses in a soil stratum. The theory and exploration techniques are well known as described e.g. by Dobrin* or Woods. Even for a non-layered soil, however, the assumption of a constant wave velocity is no longer valid due to the dependence of soil stiffness on overburden pressure. This effect has to be taken into account in order to properly interpret the experimental time-distance curves. Because of its simplicity a linear depth-function has been widely used to represent the variation of wave velocity in sedimentary strata, e.g. Abbiss For an approximately constant mass density -which is a reasonable assumption for this type of stratumthis function leads to a quadratic depth-variation of Transactions on the Built Environment vol 3, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509