Shear wave propagation along infinite slopes: A theoretically based numerical study

In this paper, the seismic response of ‘infinitely’ long slopes is numerically analysed via the formulation of a 1D analytical/numerical model, in which the soil mechanical behaviour is assumed to be elasto‐perfectly viscoplastic and simple shear (SS) kinematical constraints are imposed. In order to simplify the problem, a theoretically based procedure to set up a fully 1D shear constitutive model is defined, within which the mechanical response of a multiaxial relationship is condensed. The use of a 1D shear constitutive model is aimed at reducing the number of unknowns and, therefore, the computational costs. In particular, the case of the Mohr–Coulomb yield criterion is considered, while an enhanced Taylor–Galerkin finite element algorithm is employed to simulate the seismic wave propagation within the soil stratum. The proposed ‘condensation’/calibration procedure captures both the ‘pseudo’‐hardening pre‐failure behaviour and the influence of dilation on the occurrence of strain‐localization, which characterize, under SS conditions, the static response of virgin perfectly plastic soils. The effectiveness of the conceived method is shown with reference to freshly deposited deposits, while, in the case of highly overconsolidated strata, some difficulties arise because of the brittle behaviour induced both by unloading and non‐associativeness. Copyright © 2011 John Wiley & Sons, Ltd.     

Asteroid Mean Elements: Higher Order and Iterative Theories

Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation; they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step, used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory, resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete, fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements, incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain. This revised version was published online in July 2006 with corrections to the Cover Date.     

A mathematical and numerical model for reactive fluid flow systems

We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the time integration are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable sized rectangular grids we choose limited κ= related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code. This revised version was published online in July 2006 with corrections to the Cover Date.     

Automatic substepping integration of the subloading tij model with stress path dependent hardening

This paper discusses the numerical integration of the subloading tij model. This is an elastoplastic model with stress path dependent hardening, which can predict the behaviour of normally consolidated clays or loose sands, as well as of over-consolidated clays or dense sands, with a small number of material parameters. Three features distinguish the subloading tij model from the conventional ones: (a) the use of a modified stress space given by tensor t_ij; (b) the split of the plastic strain increments in two components leading to a stress path dependent hardening; and (c) the use of two yield surfaces (subloading yield surface and normal yield surface). This last feature is based on the concept of sub-yielding stress states and adds an extra internal strain-like hardening variable, related to the relative density state, which demands its own evolution law. The three characteristics above greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam clay model, at the cost of only two additional parameters. Nonetheless, the numerical integration of the constitutive equations of subloading tij model is a bit challenging, mainly due to the stress path dependent hardening. In order to integrate the equations of subloading tij model in the same way as for any conventional model, the authors reformulated its equations in a simpler and direct manner. Here, these equations are integrated using multi-step explicit schemes, such as modified-Euler and Runge–Kutta–Dormand–Price, with automatic error control. Simple forward-Euler scheme is also used for the sake of comparison. The results show that the modified-Euler scheme is more accurate as well as faster than the other schemes analysed over a wide range of error tolerance. Besides, the automatic feature of these schemes is a great convenience for the users of numerical codes.     

Particle swarm optimization of TMD by non‐stationary base excitation during earthquake

There are many traditional methods to find the optimum parameters of a tuned mass damper (TMD) subject to stationary base excitations. It is very difficult to obtain the optimum parameters of a TMD subject to non‐stationary base excitations using these traditional optimization techniques. In this paper, by applying particle swarm optimization (PSO) algorithm as a novel evolutionary algorithm, the optimum parameters including the optimum mass ratio, damper damping and tuning frequency of the TMD system attached to a viscously damped single‐degree‐of‐freedom main system subject to non‐stationary excitation can be obtained when taking either the displacement or the acceleration mean square response, as well as their combination, as the cost function. For simplicity of presentation, the non‐stationary excitation is modeled by an evolutionary stationary process in the paper. By means of three numerical examples for different types of non‐stationary ground acceleration models, the results indicate that PSO can be used to find the optimum mass ratio, damper damping and tuning frequency of the non‐stationary TMD system, and it is quite easy to be programmed for practical engineering applications. Copyright © 2008 John Wiley & Sons, Ltd.     

A Runge–Kutta,Taylor–Galerkin scheme for hyperbolic systems with source terms. Application to shock wave propagation in viscoplastic geomaterials

This paper presents an alternative formulation of Solid Dynamics problems based on (i) a mathematical model consisting of a system of hyperbolic PDEs where the source term is originated by the viscoplastic strain rate and (ii) a splitting scheme where the two‐step Taylor–Galerkin is used for the advective part of the PDE operator while the sources are integrated using a fourth‐order Runge–Kutta. Use of the splitting scheme results in a higher accuracy than that of the original two‐step Taylor–Galerkin. The scheme performs well when used with linear triangle or tetrahedra for (i) bending‐dominated situations (ii) localized failure under dynamic conditions and keeps the advantages of the two‐step Taylor–Galerkin concerning numerical dispersion and damping of short wavelengths. Copyright © 2006 John Wiley & Sons, Ltd.     

Analytical modelling of a large‐scale dynamic testing facility

An analytical model, which aims at reproducing the response of a large‐scale dynamic testing facility, that is a system composed of the specimen/shaking table/reaction‐mass/airbags/dampers/soil is developed. The Lagrangian of the system is derived, under the assumption of large displacements and rotations. A set of four nonlinear differential equations is obtained and solved with numerical methods. Preliminary verifications of the derived model are carried out by reproducing both well‐known results in the literature as well as those of a lumped model employed in the design of an existing dynamic testing facility. The case‐study for validating the nonlinear equations of motion is the shaking table of the EUCENTRE Laboratory. Copyright © 2011 John Wiley & Sons, Ltd.     

A new solution of transient confined–unconfined flow driven by a pumping well

A new solution of transient confined–unconfined flow driven by a pumping well is developed and compared to previous approximate solutions of Moench and Prickett [Moench AF, Prickett TA. Radial flow in an infinite aquifer undergoing conversion from artesian to water table conditions. Water Resour Res 1972;8:494–9] and Hu and Chen [Hu L, Chen C. Analytical methods for transient flow to a well in a confined–unconfined aquifer. Ground Water 2008;46(4):642–6]. The problem is rewritten in dimensionless form with the Boltzmann transform. The nonlinear equation for flow in the unconfined zone is solved with the Runge–Kutta method. Position of the conversion interface is determined with an iteration scheme. This study shows that the confined–unconfined flow depends on three dimensionless parameters that represent the confined–unconfined storativity ratio (a_D), the ratio of the initial hydraulic head over the aquifer thickness (f_i), and the dimensionless pumping rate (q_D). The rate of expansion of the unconfined zone increases with q_D, but decreases with a_D and f_i. Differences between the two previous approximate solutions and the new solution of this study are observable in the estimated position of the conversion interface and the drawdown–time curves. The new solution can be applied to estimate the time for confined–unconfined conversion to occur (critical conversion time), and the time when the pumping well becomes dry (critical drying time). The critical conversion time is found to be very sensitive to the initial hydraulic head. The critical drying time is often much larger than the critical conversion time and may never be observed during a finite pumping period.