Identifying parameters controlling soil delayed behaviour from laboratory and in situ pressuremeter testing

The aim of this paper is to present a methodology for identifying the soil parameters controlling the delayed behaviour from laboratory and in situ pressuremeter tests by using an elasto‐viscoplastic model (EVP‐MCC) based on Perzyna's overstress theory and on the elasto‐plastic Modified Cam Clay model. The influence of both the model parameters and the soil permeability was studied under the loading condition of pressuremeter tests by coupling the proposed model equations with Biot's consolidation theory. On the basis of the parametric study, a methodology for identifying model parameters and soil permeability by inverse analysis from three levels of constant strain rate pressuremeter tests was then proposed and applied on tests performed on natural Saint‐Herblain clay. The methodology was validated by comparing the optimized values of soil parameters and the values of the same parameters obtained from laboratory test results, and also by using the identified parameters to simulate other tests on the same samples. The analysis of the drainage condition and the strain rate effect during a pressuremeter test demonstrated the coupled influence of consolidation and viscous effects on the test results. The numerical results also showed that the inverse analysis procedure could successfully determine the parameters controlling the time‐dependent soil behaviour. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic Model of Fracture Normal Behaviour and Application to Prediction of Stress Wave Attenuation Across Fractures

Summary.  The purpose of this paper is to establish a dynamic constitutive model of fracture normal behaviour, based on laboratory tests of artificial fractures cast by cement mortar. A series of tests are systematically carried out under quasi-static (10⁻¹ MPa/s) up to highly dynamic (10³ MPa/s) monotonic loading conditions. The normal stress-fracture closure response is measured at different loading rates. Based on the measured curves, a nonlinear (hyperbolic) dynamic model of fracture normal behaviour, termed as dynamic BB model, is proposed. The dynamic model is modified from the existing BB model of static normal behaviour of fractures by taking into account the loading-rate effect. Two important dynamic parameters of fractures, FSC _d (dynamic fracture stiffness constant, which describes the incremental ratio of dynamic initial stiffness) and FCC _d (dynamic fracture closure constant, which describes the decremental ratio of dynamic maximum allowable closure), are identified. They indicate the quantitative degree of loading-rate effect on fracture normal behaviour subjected to dynamic loads. For practical application, the new model is incorporated into the Universal Distinct Element Code (UDEC) and subsequently, UDEC modelling of normally incident P-wave transmission across single fractures with the dynamic BB model is conducted. Wave transmission coefficient is obtained for various combinations of fracture dynamic parameters, as well as different wave amplitudes and frequencies. The numerical results show that wave transmission coefficient for a fracture with the dynamic BB model is greater than that for a fracture with the static BB model. In addition, a fracture with higher values of FSC _d and FCC _d leads to higher transmission (lower attenuation). Author’s address: J. Zhao, Ecole Polytechnique Federale de Lausanne (EPFL), Rock Mechanics Laboratory, 1015 Lausanne, Switzerland     

Experimental and numerical studies of rock salt strain hardening

The work presented in this paper comes as part of a research program dealing with the thermomechanical behaviour of rock salt. It aims to study laboratory and in-situ long-term behaviour by means of creep tests with deviator and temperature changes. The laboratory results, using a triaxial multi-stages creep tests, highlighted the strain hardening character of rock salt. Furthermore, the in-situ results, using a borehole dilatometer multi-step creep test, have shown that the drilling is carried out in a weakly stressed pillar. The interpretation of the laboratory results, using the J.LEMAITRE law, did not indicate full agreement with all the test results. As a result a ‘double’ J.LEMAITRE model, which takes into account a double strain hardening variable, has been put forward. The validation of this model on the laboratory creep tests is very satisfactory. Furthermore, the activation energy seems satisfactory to represent the influence of the temperature. The in-situ behaviour modelling is clearly more complex than the modelization based on laboratory tests. In fact, it seems that if the rock salt behaviour is maintained by J.LEMAITRE law, it is necessary to vary with the stress, at least, one of the parameters assumed constant in the basic law.     

Discrete numerical modelling of rockfill dams

The aim of this study is to obtain quantitative information on the behaviour of rockfill used in embankment dams, and particularly on the influence of block breakage on the displacement field, from a numerical analysis using the Distinct element method. A methodology is set up to define the resistance of the 2D particles so that the same probability of breaking blocks may be reproduced as in a 3D material. The model uses the discrete element code PFC^2D (Itasca Consulting Group Inc., PFC2D (Particle Flow Code in Two Dimensions), Version 3.0, 2002) and considers breakable clusters of 2D balls. The different parameters are determined from experimental data obtained from laboratory tests performed on rock blocks. The model is validated by comparing the results of the simulation of shearing tests with actual triaxial tests on rockfill material published in the literature. The numerical analysis of block crushing in an actual dam is proposed in the last part of this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Pull-out behaviour of steel grid soil reinforcement embedded in silty sand

This paper investigates the pull-out behaviour (particularly the bearing resistance) of a steel grid reinforcement embedded in silty sand using laboratory tests and numerical analyses. It is demonstrated that the various common analytical equations for calculating the bearing component of pull-out resistance give a wide range of calculated values, up to about 200% disparity. The disparity will increase further if the issue of whether to use the peak or critical state friction angle is brought in. Furthermore, these equations suggest that the bearing resistance factor, N_q, is only a function of soil friction angle which is not consistent with some design guidelines. In this investigation, a series of large scale laboratory pull-out tests under different test pressures were conducted. The test results unambiguously confirmed that the N_q factor is a function of test pressure. A modified equation for calculating N_q is also proposed. To have more in-depth understanding of the pull-out behaviour, the tests were modelled numerically. The input parameters for the numerical analysis were obtained from laboratory triaxial tests. The analysis results were compared with the experimental results. Good agreement between experimental and numerical results was achieved if the strain-softening behaviour from peak strength to critical state condition was captured by the soil model used.     

Visco‐elastic load transfer models for axially loaded piles

Viscoelastic or creep behaviour can have a significant influence on the load transfer (t–z) response at the pile–soil interface, and thus on the pile load settlement relationship. Many experimental and theoretical models for pile load transfer behaviour have been presented. However, none of these has led to a closed‐form expression which captures both non‐linearity and viscoelastic behaviour of the soil. In this paper, non‐linear viscoelastic shaft and base load transfer (t–z) models are presented, based on integration of a generalized viscoelastic stress–strain model for the soil. The resulting shaft model is verified through published field and laboratory test data. With these models, the previous closed‐form solutions evolved for a pile in a non‐homogeneous media have been readily extended to account for visco‐elastic response. For 1‐step loading case, the closed‐form predictions have been verified extensively with previous more rigorous numerical analysis, and with the new GASPILE program analysis. Parametric studies on two kinds of commonly encountered loading: step loading, ramp (linear increase followed by sustained) loading have been performed. Two examples of the prediction of the effects of creep on the load settlement relationship by the solutions and the program GASPILE, have been presented. Copyright © 2000 John Wiley & Sons, Ltd.     

复杂应力路径下流体饱和砂岩本构模型

高孔隙率砂岩在不同围压及被不同流体（水及油）饱和时表现出不同的应力-应变特性及不同的破坏过程。复杂应力路径下油和水饱和砂岩的力学试验表明,存在某一临界围压,随着围压的增加,饱和砂岩从以压剪破坏为主,逐渐转变为以孔隙坍塌破坏为主的破坏机制。通过力学试验结果的分析,以两种破坏理论对油和水饱和砂岩的破坏特征进行了力学解释,并应用经典塑性力学的盖帽模型建立了相应的本构模型,应用非线性有限元法进行了数值验证,研究结果表明,提出的模型与试验资料吻合良好,能较好地模拟复杂应力路径下油和水饱和砂岩的破坏机制及模拟注水采油引起的砂岩附加沉降。     

A semi‐empirical method for the liquefaction analysis of offshore foundations

This paper presents a relatively simple method for three‐dimensional liquefaction analysis of granular soil under offshore foundations. In this method, the Mohr–Coulomb model, which defines the elasto–plastic stress–strain relationship under monotonic loading, is modified to accommodate the plastic strains generated by cyclic loading. The effects of cyclic loading, evaluated from the results of laboratory tests on saturated samples of soil, are incorporated into the model. The method is implemented in an efficient finite element program for analyses of three‐dimensional consolidating soil. The practicability of the model is demonstrated by analysis of a typical offshore foundation, and the predictions of the numerical analysis are compared with the observed behaviour of the foundation. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical modelling of soil nails in loose fill slope under surcharge loading

A plane–strain numerical model has been developed to mimic a nailed loose fill slope under surcharge loading. The model has been used to back-analyse a field test that was conducted to examine the behaviour of soil nails in loose fill slopes under surcharge loading. Incremental elasto-plastic analyses coupled with pore water diffusion have been performed to study the internal deformation, water content redistribution in the soil, and the performance of the soil nails during and after the application of surcharge loading. The model parameters describing the mechanical and hydraulic properties of the nailed slope were obtained from field or laboratory tests. Different modelling techniques and boundary conditions for mimicking soil–nail interaction in loose fill material have been examined. Comparisons between numerical predictions and field measurements demonstrate that a new interfacial model, denoted as the embedded bond–slip interface model, is more suitable for mimicking the interfacial behaviour. Despite the simplicity of the numerical model, the predicted responses are in close agreement with the field test results, in particular the mobilisation and distribution of nail forces in response to surcharge loading. Both the numerical and the field test results suggest that soil nails are capable of increasing the overall stability of a loose fill slope for the loading conditions considered in this study. The increase in confining stress along the soil nails near the surcharge area is central to the overall stabilising mechanism. On the contrary, the nail forces mobilised near the nail heads are much smaller, indicating that the beneficial effect of having a structural grillage system at the slope face is limited for the range of surcharge pressures considered in this study.     

Laboratory testing and numerical simulation of properties and thermal-induced cracking of Eibenstock granite at elevated temperatures

The knowledge about thermo-mechanical properties of granite is still limited to some extent. Individual measurements are necessary to obtain reliable properties for specific granite types. A reliable numerical model of thermal cracking behaviours of granite exposed to extreme high temperatures (e.g. 800–1000 °C) is missing. In this study, the impact of temperature up to 1000 °C on physical, mechanical, and thermal properties as well as thermo-mechanical coupled behaviour of Eibenstock granite was investigated by laboratory testing and numerical simulations. The physical properties including mineral composition, density, P-wave velocity, and open porosity are measured to be temperature dependent. Uniaxial compression and Brazilian tests were carried out to measure uniaxial compressive strength (UCS), Young’s modulus, stress–strain relationship, and tensile strength of Eibenstock granite before and after thermal treatment, respectively. Thermal properties including specific heat, thermal conductivity, thermal diffusivity, and linear thermal expansion coefficient are also measured and found to be temperature dependent, especially the expansion coefficient which shows a steep increase around 573 °C as well as at 870 °C. The numerical simulation code FLAC^3D was used to develop a numerical scheme to simulate the thermal-induced damage of granite at high temperatures. Statistical methods combined with real mineral composition were used to characterize the heterogeneity of granite. The numerical model is featured with reliable temperature-dependent parameters obtained from laboratory tests. It can well reproduce the laboratory results in form of thermal-induced micro- and macrocracks, as well as the stress–strain behaviour and the final failure pattern of Eibenstock granite after elevated temperatures up to 1000 °C. The simulation results also reveal that the thermal-induced microcracks are randomly distributed across the whole sample. Although most thermal-induced damages are tensile failures, shear failure begins to develop quickly after 500 °C. The obvious UCS reduction in granite due to heating is mainly caused by the increase in shear failure. The simulation also shows that the dominant impact of α–β quartz transition is widening pre-existing cracks rather than the formation of new microcracks.

     

Numerical simulation of the seismic response of tunnels in sand with an elastoplastic model

The number of larger tunnels in seismic regions has grown significantly over the last decades. The behaviour of tunnels under seismic actions may be assessed using simplified or more complex approaches. Plane–strain centrifuge tests with dynamic loading on a model tunnel are used as experimental benchmark on the seismic behaviour of tunnels, with the ultimate aim of calibrating numerical and analytical design methods. Two models with dry uniform fine sand were prepared at two different densities, in which an aluminium-alloy tube was installed. This paper describes the numerical simulation of these tests with an elastoplastic model. The tunnel response recorded in the centrifuge tests is compared with the numerical prediction, showing the evolution of accelerations and internal forces along the tunnel lining during the model earthquakes. In general, the numerical simulation diverges from the recorded at the centrifuge tests. The numerical simulation largely amplifies the motion at the fundamental frequency of the soil deposit, while this effect is not significant in the centrifuge tests. It is shown that the peak increments in lining forces during dynamic loading measured in the centrifuge test disagree with the values from the numerical simulation and from the Wang’s elastic solution. The divergence observed between simulation and centrifuge tests may result mainly from the real initial stiffness of the sand in the centrifuge tests which are lower than those measured in laboratory tests and to the insufficient knowledge of all relevant stress paths to be imposed to soil for the calibration of model parameters.     

Modelling the settlement behaviour of a strip footing on sloping sandy fill under cyclic loading conditions

This paper investigates the settlement behaviour of a strip footing seating on the crest of an embankment and subjected to cyclic loading. The embankment fill is a dense sand and the issue is the gradual accumulation of settlement over a large number of load repetitions. Cyclic triaxial tests were first conducted to develop a consistent but simple material model for numerical implementation. Particular emphasis was placed on linking the stress-strain behaviour of an unload-reload cycle to the accumulation of permanent strain, with only five input parameters required to model the cyclic behaviour. The material model was implemented in a numerical analysis to compute the settlement behaviour obtained from model tests conducted by another researcher. It is pertinent to highlight that the same soil, compacted to same density at same moisture content, was used for both the cyclic triaxial tests and model tests. Reasonable to good agreement between the experimental and numerical results was achieved.     

An Example of Realistic Modelling of Rock Dynamics Problems: FEM/DEM Simulation of Dynamic Brazilian Test on Barre Granite

The scope of this study is to numerically simulate the behaviour of Brazilian disc specimens as observed in laboratory during dynamic, high-strain rate, indirect tensile tests using an innovative combined finite-discrete element method (FEM/DEM) research code. Laboratory experiments using a split Hopkinson pressure bar (SHPB) apparatus were conducted by the authors and the measured indirect tensile strength values were used to verify the FEM/DEM models. In the models the applied boundary conditions, related to the loading rate of the specimen, were matched with the experimental observations. The results of the numerical simulations, including tensile strength and failure time, are in agreement with the laboratory findings. The main failure mechanisms, i.e. tensile splitting along loading axis and shear failure close to loading platens are captured by the numerical model. A linear relationship between tensile strength and loading rate is found for the range of dynamic strain rates tested and simulated. The simulation results are in good agreement with laboratory observations and demonstrate the potential for using FEM/DEM to realistically model dynamic response of rocks.     

A 1D Hypoplastic constitutive model for expansive soils

This paper presents a simple hypoplastic constitutive model that describes the essential features of the material behaviour of partially saturated clayey soils observed in oedometric compression tests. The model is formulated in terms of net stress and degree of saturation. The total strain rate is decomposed into a portion related to the changes in saturation and a portion for the evolution of net stress. However, no distinction is made between plastic and elastic strains. With this strain rate decomposition, the maximum swelling strain/stress are obtained by simulating wetting processes under constant stress/strain conditions. In addition to the void ratio, the model includes two scalar variables to track the loading history (preloading). The calibration of the model constants using common laboratory tests is discussed. Confined and unconfined swelling tests under oedometric conditions with subsequent loading and unloading phases carried out on three different materials were satisfactorily simulated by the model. Its promising results call for an extension to a 3D formulation.

     

Constitutive modelling of granular materials using a contact normal-based fabric tensor

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

     

Experimental and numerical study of soil-reinforcement effects on the low-strain stiffness and bearing capacity of shallow foundations

This paper presents results of meticulous laboratory testing and numerical simulations on the effect of reinforcement on the low-strain stiffness and bearing capacity of shallow foundations on dry sand. The effect of the location and the number of reinforcement layers is studied in the laboratory, whereas numerical simulations are used to study the reinforcement-foundation interaction. Laboratory tests show an increase of 100, 200, and 275% not only in bearing capacity but also in low-strain stiffness (linear load–displacement behaviour) of a square foundation when one, two, and three layers of reinforcement are used, respectively. The specimen preparation technique is found to be crucial for the repeatability and reliability of the laboratory results (less than 5% variability). Numerical simulations demonstrate that if reinforcements are placed up to a depth of one footing width (B) below the foundation, better re-distribution of the load to deeper layers is achieved, thus reducing the stresses and strains underneath the foundation. Numerical simulations and experimental results clearly identify a critical zone between 0.3 and 0.5B, where maximum benefits not only on the bearing capacity but also on the low-strain stiffness of the foundation are obtained. Therefore, soil reinforcement can also be used to reduce low-strain vibrations of foundations.     

An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities

This paper presents an advanced constitutive model for unsaturated soils, using Bishop’s effective stress (σ′) and the effective degree of saturation (S_e) as two fundamental constitutive variables in the proposed constitutive model. A sub-loading surface and a unified hardening parameter (H) are introduced into the σ′–S_e modelling framework to interpret the effects of initial density on coupled hydro-mechanical behaviour of compacted soils. Compared with existing models in the literature, the main advantage of the proposed model that it is capable of modelling hydro-mechanical behaviour of unsaturated soils compacted to different initial densities, such as the dependence of loading–collapse volume on initial void ratio and density effect on the shearing-induced saturation change. The proposed model requires 13 material parameters, all of which can be calibrated through conventional laboratory tests. Numerical studies are conducted to assess the performance of the model for a hypothetical soil under two typical hydro-mechanical loading scenarios. The proposed advanced unsaturated soil model is then validated against a number of experimental results for both isotropic and triaxial conditions reported in the literature.     

Three‐dimensional analysis of the seismic behaviour of micropiles used in the reinforcement of saturated soil

This paper includes a numerical study of the behaviour of micropiles used for the reinforcement of saturated soil. Analysis is carried out using the (u–p) formulation (displacement for the solid phase and pore‐pressure for the fluid phase) implemented in a three‐dimensional finite element program. The soil behaviour is described by means of a cyclic elastoplastic constitutive relation which was developed within the framework of the bounding surface concept. The paper is composed of three parts. The first one is concerned with a presentation of the numerical model; the second includes analysis of the seismic behaviour of a single micropile; the last part deals with the group effect under seismic loading. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical study of group effects for pile groups in sands

The OpenSees finite element framework was used to simulate the response of 3×3 and 4×3 pile groups founded in loose and medium dense sands. Several numerical static pushover tests were conducted to investigate the interaction effects for pile groups. The results were then compared with those from centrifuge study. It is shown that our simulations can predict the behaviour of pile groups with good accuracy. Special attention was given to the three dimensional distribution of bending moment. It was found that bending moment develops in the plane perpendicular to the loading direction. In addition, bending moment data from simulations was used to derive p–y curves for individual piles, which were used to illustrate different behaviour of individual piles in the same group. Copyright © 2003 John Wiley & Sons, Ltd.     

Experimental study and constitutive modelling of elasto‐plastic damage in heat‐treated mortar

This study investigates the effect of a heat‐treatment upon the thermo‐mechanical behaviour of a model cement‐based material, i.e. a normalized mortar, with a (w/c) ratio of 0.5. First, a whole set of varied experimental results is provided, in order to either identify or validate a thermo‐mechanical constitutive model, presented in the second paper part. Experimental responses of both hydraulic and mechanical behaviour are given after different heating/cooling cycling levels (105, 200, 300, 400^°C). The reference state, used for comparison purposes, is taken after mass stabilization at 60^°C. Typical uniaxial compression tests are provided, and original triaxial deviatoric compressive test responses are also given. Hydraulic behaviour is identified simultaneously to triaxial deviatoric compressive loading through gas permeability K_gas assessment. K_gas is well correlated with volumetric strain evolution: gas permeability increases hugely when ε_v testifies of a dilatant material behaviour, instead of contractile from the test start. Finally, the thermo‐mechanical model, based on a thermodynamics approach, is identified using the experimental results on uniaxial and triaxial deviatoric compression. It is also positively validated at residual state for triaxial deviatoric compression, but also by using a different stress path in lateral extension, which is at the origin of noticeable plasticity. Copyright © 2009 John Wiley & Sons, Ltd.