Numerical optimization applying trust-region reflective least squares algorithm with constraints to optimize the non-linear creep parameters of soft soil

Determination of the creep model parameters is a challenging task particularly when a non-linear elastic visco-plastic (EVP) model is adopted, mainly due to the limited test duration as well as the assumption of the reference time. Therefore, this paper presents an innovative numerical solution to find the EVP model parameters applying the trust-region reflective least square optimization algorithm. The developed approach involves several available laboratory consolidation test results in the optimization procedure with the adopted commencing time to creep as a unit of time. In this paper, the laboratory results of Ottawa clay were employed to demonstrate the limitation of the recent method to obtain model parameters. Furthermore, the developed method is verified against Skå-Edeby clay in the laboratory conditions. The EVP model parameters are obtained by applying the developed method to the available laboratory consolidation results of clay samples. The analysis results of vertical strains and excess pore water pressures demonstrate that the developed method can be a feasible tool to estimate the settlement properties of clays.     

System reliability analysis of slope stability using generalized Subset Simulation

Slope failure mechanisms (e.g., why and where slope failure occurs) are usually unknown prior to slope stability analysis. Several possible failure scenarios (e.g., slope sliding along different slip surfaces) can be assumed, leading to a number of scenario failure events of slope stability. How to account rationally for various scenario failure events in slope stability reliability analysis and how to identify key failure events that have significant contributions to slope failure are critical questions in slope engineering. In this study, these questions are resolved by developing an efficient computer-based simulation method for slope system reliability analysis. The proposed approach decomposes a slope system failure event into a series of scenario failure events representing possible failure scenarios and calculates their occurrence probabilities by a single run of an advanced Monte Carlo simulation (MCS) method, called generalized Subset Simulation (GSS). Using GSS results, representative failure events (RFEs) that are considered relatively independent are identified from scenario failure events using probabilistic network evaluation technique. Their relative contributions are assessed quantitatively, based on which key failure events are determined. The proposed approach is illustrated using a soil slope example and a rock slope example. It is shown that the proposed approach provides proper estimates of occurrence probabilities of slope system failure event and scenario failure events by a single GSS run, which avoids repeatedly performing simulations for each failure event. Compared with direct MCS, the proposed approach significantly improves computational efficiency, particularly for failure events with small failure probabilities. Key failure events of slope stability are determined among scenario failure events in a cost-effective manner. Such information is valuable in making slope design decisions and remedial measures.     

A two-dimensional artificial viscosity technique for modelling discontinuity in shallow water flows

In this study, a two-dimensional cell-centred finite volume scheme is used to simulate discontinuity in shallow water flows. Instead of using a Riemann solver, an artificial viscosity technique is developed to minimise unphysical oscillations. This is constructed from a combination of a Laplacian and a biharmonic operator using a maximum eigenvalue of the Jacobian matrix. In order to achieve high-order accuracy in time, we use the fourth-order Runge–Kutta method. A hybrid formulation is then proposed to reduce computational time, in which the artificial viscosity technique is only performed once per time step. The convective flux of the shallow water equations is still re-evaluated four times, but only by averaging left and right states, thus making the computation much cheaper. A comparison of analytical and laboratory results shows that this method is highly accurate for dealing with discontinuous flows. As such, this artificial viscosity technique could become a promising method for solving the shallow water equations.     

Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.     

某软土深基坑工程时间效应有限元分析

软土地区的深基坑因土体的固结作用和流变性而具有了时间效应。本文以Biot固结有限元法为基础,用三元件模型中的第一个线性弹簧模拟固结作用,弹性模量考虑了开挖应力路径和应力历史的影响;另外一部分(KELVIN模型)来模拟土体的流变性,以实际变形的反演来得到两个参数的大致取值,再对基坑的变形情况以及进一步开挖进行分析。假定为正常固结饱和粘土,平面应变问题。通过对某饱和软粘土地基深基坑开挖工程实例的分析,得到的挡墙水平位移曲线与实测曲线很吻合,表明程序较好地反映出基坑的时间效应。     

A thermodynamics based damage mechanics model for particulate composites

A micro-mechanical damage model is proposed to predict the overall viscoplastic behavior and damage evolution in a particle filled polymer matrix composite. Particulate composite consists of polymer matrix, particle fillers, and an interfacial transition interphase around the filler particles. Yet the composite is treated as a two distinct phase material, namely the matrix and the equivalent particle-interface assembly. The CTE mismatch between the matrix and the filler particles is introduced into the model. A damage evolution function based on irreversible thermodynamics is also introduced into the constitutive model to describe the degradation of the composite. The efficient general return-mapping algorithm is exploited to implement the proposed unified damage coupled viscoplastic model into finite element formulation. Furthermore, the model predictions for uniaxial loading conditions are compared with the experimental data.     

Interaction between a rigid inclusion and a line crack under uniform heat flux

The thermoelastic displacement boundary value problem for a rigid inclusion interacting with a line crack in an infinite plane subjected to a uniform heat flux is studied, in which the rigid body rotation of the inclusion is considered. To solve the prescribed problem, we use the principle of superposition to decompose it into two groups of problems, which are further reduced to several basic subproblems including Green’s functions of edge dislocation and heat source couple, as well as the problem of a plane containing the inclusion under uniform heat flux and the problem of the inclusion subjected to a small rotation. The problems are solved using the complex variable method along with the rational mapping function technique. The variations of the stress intensity factors at the crack tips and the rigid body rotation angles with various crack lengths and heat flux angles are shown. The effects of the inclusion shape and size are also investigated.     

Thermal fatigue crack networks parameters and stability: an experimental study

A thermal fatigue device––called SPLASH––similar to the facility developed by Marsh [Fatigue crack initiation and propagation in stainless steels subjected to thermal cycling, International Conference on Mechanical Behaviour and Nuclear Applications of Stainless Steels at Elevated Temperature, 1981] has been built in CEA/SRMA in 1985. Since then, it was used mostly on austenitic stainless steels to assess the initiation and growth of thermal fatigue crack networks. In 1998, a leak appeared in an auxiliary loop of the primary circuit of a pressurized water nuclear plant in Civaux (France). Thermal fatigue was suspected and studies began on AISI 304 L type austenitic stainless steel. They were eventually compared to results obtained earlier on AISI 316 L(N). First, the initiation conditions were determined and the damage before initiation was qualitatively observed. Then, some crack networks parameters were chosen and quantitatively determined by image analysis. This part of the study was done at the surface, during crack growth, and at the end of the tests, in depth. Finally, the stability of the crack networks obtained by thermal fatigue was tested under isothermal load controlled four point bending fatigue test, and some conclusions were drawn on the mechanisms of propagating crack selection.     

Hyperbolicity and one-dimensional waves in compressible two-phase flow models

Hyperbolic models for compressible two-phase flows including a conservative symmetric hyperbolic model are reviewed. The basis for a theory of shock waves is developed within the framework of the latter. The analysis of small amplitude discontinuities allows us to conclude that in general there are two types of shocks corresponding to two sound waves. The problem of transition between a pure phase and a mixture (the phase vacuum problem) is analysed. It is proved that for some models the smooth centred wave solution can not provide such a transition. Within the framework of our conservative model there is the possibility of constructing discontinuous solutions which can resolve the phase vacuum problem.PACS: 47.55Kf, 47.40.-xE. Romenski: On leave from Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk 630090, Russia