Development of an inverse analysis framework for extracting dynamic soil behavior and pore pressure response from downhole array measurements

Observations from earthquakes over the past several decades have highlighted the importance of local site conditions on propagated ground motions. Downhole arrays are deployed to measure motions at the ground surface and within the soil profile, and also to record the pore pressure response within the soft soil profiles during excitation. The degradation of soil stiffness as excess pore pressures are generated during earthquake events has also been observed. An inverse analysis framework is developed and demonstrated to directly extract soil material behavior including pore water pressure (PWP) generation from downhole array measurements that can then be readily used in 1D nonlinear site response analysis. The self‐learning simulations (SelfSim) inverse analysis framework, previously developed for total stress site response analysis, is extended to extract PWP generation behavior of the soil in addition to cyclic response during ground shaking. A Neural Network based constitutive model is introduced to represent PWP generation during cyclic loading. A new analysis scheme is introduced that can use data from co‐located piezometer and accelerometer sensors. The successful performance of the proposed framework is demonstrated using four synthetic vertical array recordings. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparison of two inverse analysis techniques for learning deep excavation response

Performance observation is a necessary part of the design and construction process in geotechnical engineering. For deep urban excavations, empirical and numerical methods are used to predict potential deformations and their impacts on surrounding structures. Two inverse analysis approaches are described and compared for an excavation project in downtown Chicago. The first approach is a parameter optimization approach based on genetic algorithm (GA). GA is a stochastic global search technique for optimizing an objective function with linear or non-linear constraints. The second approach, self-learning simulations (SelfSim), is an inverse analysis technique that combines finite element method, continuously evolving material models, and field measurements. The optimization based on genetic algorithm approach identifies material properties of an existing soil model, and SelfSim approach extracts the underlying soil behavior unconstrained by a specific assumption on soil constitutive behavior. The two inverse analysis approaches capture well lateral wall deflections and maximum surface settlements. The GA optimization approach tends to overpredict surface settlements at some distance from the excavation as it is constrained by a specific form of the material constitutive model (i.e. hardening soil model); while the surface settlements computed using SelfSim approach match the observed ones due to its ability to learn small strain non-linearity of soil implied in the measured settlements.     

Bifurcation modeling in geomaterials: From the second‐order work criterion to spectral analyses

The present paper investigates bifurcation analysis based on the second‐order work criterion, in the framework of rate‐independent constitutive models and rate‐independent boundary‐value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi‐static boundary‐value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculté des sciences de Toulouse 1907; 9 :203–274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207–220) and the plasticity limit criterion are revived in order to clarify the application field of the second‐order work criterion and to contrast these criteria. The first part of this paper analyses the second‐order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form (dσ = Mdε) or in the dual form (dε = Ndσ), is discussed. In the second part, the analysis is extended to the boundary‐value problems in quasi‐static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary‐value problem. Copyright © 2008 John Wiley & Sons, Ltd.     

Micromechanical viscoelasto‐plastic models and finite element implementation for rate‐independent and rate‐dependent permanent deformation of stone‐based materials

This paper presents parallel and serial viscoelasto‐plastic models to simulate the rate‐independent and the rate‐dependent permanent deformation of stone‐based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto‐plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement‐based incremental formulation for the viscoelastic part and an elastic predictor—plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto‐plastic model employed a viscoelastic predictor—plastic corrector algorithm. The stone‐based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto‐plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto‐plastic matrix models. The simulation results showed that the serial viscoelasto‐plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto‐plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate‐independent and rate‐dependent viscoelasto‐plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto‐plastic behaviors of the stone‐based materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Two‐dimensional finite element analysis of gravitational and lateral‐driven deformation in sedimentary basins

The paper deals with the modeling of some aspects, such as the formulation of constitutive equations for sediment material or finite element approach for basin analysis, related to mechanical compaction in sedimentary basins. In addition to compaction due to gravity forces and pore‐pressure dissipation, particular emphasis is given to the study of deformation induced by tectonic sequences. The numerical model relies upon the implementation of a comprehensive constitutive model for the sediment material formulated within the framework of finite poroplasticity. The theoretical model accounts for both hydromechanical and elasticity–plasticity coupling due to the effects of irreversible large strains. From the numerical viewpoint, a finite element procedure specifically devised for dealing with sedimentary basins as open systems allows to simulate within a two‐dimensional setting the process of sediment accretion or erosion. Several basin simulations are presented. The main objective is to analyze the behavior of a sedimentary basin during the different phases of its life cycle: accretion phase, pore‐pressure dissipation phase and compressive/extensional tectonic motions. Copyright © 2013 John Wiley & Sons, Ltd.     

Data assimilation using the particle filter for identifying the elasto‐plastic material properties of geomaterials

A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto‐plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto‐plastic problems from which the existing inverse analysis strategies have suffered. A soil–water coupled problem, which uses the elasto‐plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto‐plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto‐plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.     

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic,viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Based on the continuum damage mechanics, a general and comprehensive thermodynamic‐based framework for coupling the temperature‐dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery‐type nonlinear viscoelasticity, Perzyna‐type viscoplasticity, and a viscodamage model analogous to the Perzyna‐type viscoplasticity. The resulting constitutive equations are implemented in the well‐known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep‐recovery, creep, uniaxial constant strain rate, and repeated creep‐recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulation of long‐term consolidation behavior of soft sensitive clay using an elasto‐viscoplastic constitutive model

The phenomenon of excess pore water pressure increase or stagnation and continuing large ground deformation in soft sensitive clay following the completion of construction of embankment is simulated for a case study at Saint Alban, Quebec, Canada. The present model employs an updated Lagrangian finite element framework and is combined with an automatic time increment selection scheme. The simulation based on an elasto‐viscoplastic constitutive model considers soil‐structure degradation effect. It is shown that without consideration for the microstructural degradation effect, it is not possible to reproduce the field responses of soft sensitive clay even during the construction of the embankment. When the soil‐structure degradation effect is considered, the present model can offer reasonably accurate prediction for the consolidation behavior of soft sensitive clay, including the so‐called anomalous pore water pressure generation and continuing large deformation even after the end of construction, which has been posing numerous uncertainties on the long‐term performance of earth structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Semi‐analytical far field model for three‐dimensional finite‐element analysis

A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.     

A combined neural network/gradient‐based approach for the identification of constitutive model parameters using self‐boring pressuremeter tests

This paper presents a numerical procedure of material parameter identification for the coupled hydro‐mechanical boundary value problem (BVP) of the self‐boring pressuremeter test (SBPT) in clay. First, the neural network (NN) technique is applied to obtain an initial estimate of model parameters, taking into account the possible drainage conditions during the expansion test. This technique is used to avoid potential pitfalls related to the conventional gradient‐based optimization techniques, considered here as a corrector that improves predicted parameters. Parameter identification based on measurements obtained through the pressuremeter expansion test and two types of holding tests is illustrated on the Modified Cam clay model. NNs are trained using a set of test samples, which are generated by means of finite element simulations of SBPT. The measurements obtained through expansion and consolidation tests are normalized so that NN predictors operate independently of the testing depth. Examples of parameter determination are demonstrated on both numerical and field data. The efficiency of the combined parameter identification in terms of accuracy, effectiveness and computational effort is also discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Strain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a micro‐crack‐based anisotropic damage model for rock‐like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well‐known mesh‐sensitivity problem in FEM. In the computation, elements with C₁ continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D‐non‐linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

A continuum mechanics‐based framework for boundary and finite element mesh optimization in two dimensions for application in excavation analysis

The determination of the optimum excavation sequences in mining and civil engineering using numerical stress analysis procedures requires repeated solution of large models. Often such models contain much more complexity and geometric detail than required to arrive at an accurate stress analysis solution, especially considering our limited knowledge of rock mass properties. This paper develops an automated framework for estimating the effects of excavations at a region of interest, and optimizing the geometry used for stress analysis. It eliminates or simplifies the excavations in a model while maintaining the accuracy of analysis results. The framework can equally be applied to two‐dimensional boundary and finite element models. The framework will have the largest impact for non‐linear finite element analysis. It can significantly reduce computational times for such analysis by simplifying models. Error estimators are used in the framework to assess accuracy. The advantages of applying the framework are demonstrated on an excavation‐sequencing scenario. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiscale insights into classical geomechanics problems

We pay a revisit to some classical geomechanics problems using a novel computational multiscale modelling approach. The multiscale approach employs a hierarchical coupling of the finite element method (FEM) and the discrete element method. It solves a boundary value problem at the continuum scale by FEM and derives the material point response from the discrete element method simulation attached to each Gauss point of the FEM mesh. The multiscale modelling framework not only helps successfully bypass phenomenological constitutive assumptions as required in conventional modelling approaches but also facilitates effective cross‐scale interpretation and understanding of soil behaviour. We examine the classical retaining wall and footing problems by this method and demonstrate that the simulating results can be well validated and verified by their analytical solutions. Furthermore, the study sheds novel multiscale insights into these classical problems and offers a new tool for geotechnical engineers to design and analyse geotechnical applications based directly upon particle‐level information of soils. Copyright © 2015 John Wiley & Sons, Ltd.     

NGI‐ADP: Anisotropic shear strength model for clay

Many geotechnical problems involve undrained behavior of clay and the capacity in undrained loading. Most constitutive models used today are effective stress based and only indirectly obtain values for the undrained shear strength. To match the design profiles of undrained shear strengths, in active (A), direct simple shear (D) and passive (P) modes of loading are complicated. This paper presents the elastoplastic constitutive model NGI‐ADP which is based on the undrained shear strength approach with direct input of shear strengths. Consequently, exact match with design undrained shear strengths profiles is obtained and the well‐known anisotropy of undrained shear strength and stiffness is accounted for in the constitutive model. A non‐linear stress path‐dependent hardening relationship is used, defined from direct input of failure strains in the three directions of shearing represented by triaxial compression, direct simple shear and triaxial extension. With its clear input parameters the model has significant advantages for design analysis of undrained problems. The constitutive model is implemented, into finite element codes, with an implicit integration scheme. Its performance is demonstrated by a finite element analysis of a bearing capacity problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive finite element analysis of mode I fracture in cement‐based materials

Microscopic studies using advanced experimental techniques have provided better insight into the fracture mechanisms in cement‐based materials. A clear understanding of fracture mechanisms is critical for the development of rigorous computational models for analysing fracture. Fracture analysis is usually carried out by finite element method. Accuracy of FE analysis depends upon the choice of mesh and for the predictions to be reliable, discretization errors are to be minimized. In cohesive crack approach, the non‐linearity is limited to the boundary conditions along the geometric discontinuity while the bulk of the material retains its elastic nature. The paper presents a mesh‐adaptive strategy based on ZZ error estimator to model discrete crack propagation in cement‐based materials. Examples of simulations have demonstrated the potential of the mesh‐adaptive technique in modelling the evolution of the localized strain profiles as well as failure of concrete test specimen. Copyright © 2001 John Wiley & Sons, Ltd.     

A computational framework to predict the water‐leakage pressure of segmental joints in underwater shield tunnels using an advanced finite element method

The construction of shield tunnels under riverbeds and seabeds has considerably increased over the past decades. Due to the ultra‐high water head, water leakage through tunnel joints is a major concern during a tunnel's service life. One practical solution to prevent groundwater penetration is to implement ethylene‐propylene‐diene‐monomer gaskets at the segmental joints. However, numerical simulation of fluid pressure penetration into rubber materials remains a challenging problem in computational mechanics. Severe mesh distortions can occur due to large deformation. Consequently, a convergent solution is difficult to achieve. This paper presents an Abaqus‐based numerical framework to solve the previously mentioned problem using the implicit finite element solver. The key aspects of this framework are twofold: (1) a remesh and re‐map algorithm to overcome the excessive mesh distortion, and (2) simulation of fluid penetration into the contact interface of the gaskets to reproduce the water‐leakage process at the tunnel joints. The proposed framework is first tested to simulate the gasket‐in‐groove mechanical behavior and is then validated using experimental data and the solution produced by an explicit finite element solver. The developed framework is then adopted to predict the water‐leakage pressure at gasketed tunnel joints to illustrate the practical applications. Finally, the numerical results are compared with experimental data to demonstrate the accuracy and robustness of the proposed method and confirm its superiority and effectiveness over existing methods. This novel method can be used by tunnel designers to analyze and estimate the waterproof behavior of gasketed joints in shield tunnels without performing extensive experimental testing works.     

Hybrid FE‐DQ for dynamic analysis of multilayered half‐space subjected to concentrated point impulsive loading

A hybrid finite element method and differential quadrature method (DQM) is developed to estimate the dynamic response of two‐dimensional multilayered half‐spaces subjected to impulsive point loading. Nonreflecting absorbing boundary conditions consist of appropriate springs, and dampers are considered. The capabilities of the finite element method for solving boundary value problems with general domain, loading and systematic boundary treatment are combined with accurate and stable time marching capabilities of the DQM to develop an accurate and efficient numerical technique. The capability, efficiency, robustness and convergence of the DQM for solving the dynamic problem are demonstrated through numerical simulations of various half‐spaces with different time increments and layer arrangement. Also, comparison study when using Newmark's time integration scheme for the same problem is done. It can be concluded that the DQM as an unconditionally stable method is suitable for solving such a problem. Also, parametric study is performed to show the effect of the absorbing boundary conditions on the dynamic response. Copyright © 2012 John Wiley & Sons, Ltd.     

Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method

The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.     

Simplified numerical modelling of pile penetration – the press‐replace technique

This paper presents a simplified finite element analysis technique, the ‘Press‐Replace’ technique, to model pile penetration problems in geotechnical engineering, particularly, pile jacking. The method is employed in standard finite element analysis software. The method involves a straining and a consequent geometry update phase. First, a cone penetration test in (undrained) clay is modelled and compared with the results of analytical, semi‐analytical and more advanced finite element techniques. The model sensitivity for the step size and mesh is investigated using a hypoplastic constitutive model. An optimum way of modelling based on the numerical performance is shown. Copyright © 2015 John Wiley & Sons, Ltd.