Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

A hybrid contact approach for modeling soil-structure interaction using the material point method

The grid-based multi-velocity field technique has become increasingly popular for simulating the Material Point Method(MPM)in contact problems.However,this traditional technique has some shortcomings,such as(1)early contact and contact penetration can occur when the contact conditions are unsuitable,and(2)the method is not available for contact problems involving rigid-nonrigid materials,which can cause numerical instability.This study presents a new hybrid contact approach for the MPM to address these limitations to simulate the soil and structure interactions.The approach combines the advantages of point-point and point-segment contacts to implement contact detection,satisfying the impenetrability condition and smoothing the corner contact problem.The proposed approach is first validated through a disk test on an inclined slope.Then,several typical cases,such as granular collapse,bearing capacity,and deformation of a flexible retaining wall,are simulated to demonstrate the robustness of the proposed approach compared with FEM or analytical solutions.Finally,the proposed method is used to simulate the impact of sand flow on a deformable structure.The results show that the proposed contact approach can well describe the phenomenon of soil-structure interaction problems.

Mobility and dynamic erosion process of granular flow:insights from numerical investigation using material point method

In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility and dynamic erosion process of granular flow subjected to the complex settings,i.e.,the aspect ratio,granular mass,friction and dilatancy resistance,gravity and presence of water.A set of power scaling laws were proposed to describe the final deposit characteristics of granular flow by the relations of the normalized run-out distance and the normalized final height of granular flow against the aspect ratio,being greatly affected by the complex geological settings,e.g.,granular mass,the friction and dilatancy resistance of granular soil,and presence of water in granular flow.An index of the coefficient of friction of granular soil was defined as a ratio of the target coefficient of friction over the initial coefficient of friction to quantify the scaling extent of friction change(i.e.,friction strengthening or weakening).There is a characteristic aspect ratio of granular column corresponding to the maximum mobility of granular flow with the minimum index of the apparent coefficient of friction.The index of the repose coefficient of friction of granular flow decreased gradually with the increase in aspect ratio because higher potential energy of granular column at a larger aspect ratio causes a larger kinetic energy of granular soil to weaken the friction of granular soil as a kind of velocity-related friction weakening.An increase in granular mass reduces gradually the indexes of the apparent and repose coefficients of friction of granular soil to enhance the mobility of granular flow.The mobility of granular flow increases gradually with the decrease in friction angle or increase in dilatancy angle of granular soil.However,the increase of gravity accelerates granular flow but showing the same final deposit profile without any dependence on gravity.The mobility of granular flow increases gradually by lowering the indexes of the apparent and repose coefficients of friction of granular flow while changing the surroundings,in turn,the dry soil,submerged soil and saturated soil,implying a gradually increased excessive mobility of granular flow with the friction weakening of granular soil.Presence of water in granular flow may be a potential catalyzer to yield a long run-out granular flow,as revealed in comparison of water-absent and water-present granular flows.In addition,the dynamic erosion and entrainment of based soil induced by granular flow subjected to the complex geological settings,i.e.,the aspect ratio,granular mass,gravity,friction and dilatancy resistance,and presence of water,were comprehensively investigated as well.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

Modeling footing resting on anisotropic sand using material point method

Sand typically exhibits anisotropic internal structure which may significantly influence its mechanical behavior. The material point method (MPM) can eliminate mesh distortion and thus is suitable for investigating geotechnical problems with large deformation. In this study, an advanced anisotropic critical state theory (ACST)-based soil model is implemented in MPM to study the response of strip footing resting on anisotropic sand. The capability of the model is verified by simulating several element tests and strip footing tests with different soil densities and fabric bedding plane orientations. For the footing problem with a vertical load, as the fabric bedding plane orientation increases, the bearing capacity decreases and its corresponding settlement increases. The failure pattern becomes asymmetrical when the bedding plane orientation or the loading direction is inclined. A comparison between the simulation results predicted by the anisotropic and isotropic models is made, which demonstrates that neglecting the fabric anisotropy may lead to the overestimation of the bearing capacity.

Modeling pipe-soil interaction under vertical downward relative offset using B-spline material point method

To analyze the pipeline response under permanent ground deformation,the evolution of resistance acting on the pipe during the vertical downward offset is an essential ingredient.However,the efficient simulation of pipe penetration into soil is challenging for the conventional finite element(FE)method due to the large deformation of the surrounding soils.In this study,the B-spline material point method(MPM)is employed to investigate the pipe-soil interaction during the downward movement of rigid pipes buried in medium and dense sand.To describe the density-and stress-dependent behaviors of sand,the J2-deformation type model with state-dependent dilatancy is adopted.The effectiveness of the model is demonstrated by element tests and biaxial compression tests.Afterwards,the pipe penetration process is simulated,and the numerical outcomes are compared with the physical model tests.The effects of pipe size and burial depth are investigated with an emphasis on the mobilization of the soil resistance and the failure mechanisms.The simulation results indicate that the bearing capacity formulas given in the guidelines can provide essentially reasonable estimates for the ultimate force acting on buried pipes,and the recommended value of yield displacement may be underestimated to a certain extent.

Coseismic site response and slope instability using periodic boundary conditions in the material point method

This paper proposed the explicit generalized-a time scheme and periodic boundary conditions in the material point method(MPM)for the simulation of coseismic site response.The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh.The explicit generalized-a time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations.Firstly,the MPM was verified against finite element method(FEM).Secondly,ability of the MPM in capturing the analytical transfer function was investigated.Thirdly,a symmetric embankment was adopted to investigate the effects of ground motion arias intensity(I_(a)),geometry dimensions,and constitutive models.The results show that the larger the model size,the higher the crest runout and settlement for the same ground motion.When using a Mohr-Coulomb model,the crest runout increases with increasing I_(a).However,if the strain-softening law is activated,the results are less influenced by the ground motion.Finally,the MPM results were compared with the Newmark sliding block solution.The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications,the importance of geometry characterization,and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

Physical and numerical investigations of target stratum selection for ground hydraulic fracturing of multiple hard roofs

Ground hydraulic fracturing plays a crucial role in controlling the far-field hard roof,making it imperative to identify the most suitable target stratum for effective control.Physical experiments are conducted based on engineering properties to simulate the gradual collapse of the roof during longwall top coal caving(LTCC).A numerical model is established using the material point method(MPM)and the strain-softening damage constitutive model according to the structure of the physical model.Numerical simulations are conducted to analyze the LTCC process under different hard roofs for ground hydraulic fracturing.The results show that ground hydraulic fracturing releases the energy and stress of the target stratum,resulting in a substantial lag in the fracturing of the overburden before collapse occurs in the hydraulic fracturing stratum.Ground hydraulic fracturing of a low hard roof reduces the lag effect of hydraulic fractures,dissipates the energy consumed by the fracture of the hard roof,and reduces the abutment stress.Therefore,it is advisable to prioritize the selection of the lower hard roof as the target stratum.

Joint Beam Scheduling and Power Optimization for Beam Hopping LEO Satellite Systems

Low earth orbit(LEO) satellite communications can provide ubiquitous and reliable services,making it an essential part of the Internet of Everything network. Beam hopping(BH) is an emerging technology for effectively addressing the issue of low resource utilization caused by the non-uniform spatio-temporal distribution of traffic demands. However, how to allocate multi-dimensional resources in a timely and efficient way for the highly dynamic LEO satellite systems remains a challenge. This paper proposes a joint beam scheduling and power optimization beam hopping(JBSPO-BH) algorithm considering the differences in the geographic distribution of sink nodes. The JBSPO-BH algorithm decouples the original problem into two sub-problems. The beam scheduling problem is modelled as a potential game,and the Nash equilibrium(NE) point is obtained as the beam scheduling strategy. Moreover, the penalty function interior point method is applied to optimize the power allocation. Simulation results show that the JBSPO-BH algorithm has low time complexity and fast convergence and achieves better performance both in throughput and fairness. Compared with greedybased BH, greedy-based BH with the power optimization, round-robin BH, Max-SINR BH and satellite resource allocation algorithm, the throughput of the proposed algorithm is improved by 44.99%, 20.79%,156.06%, 15.39% and 8.17%, respectively.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

A novel DPSS filter optimization scheme to reduce the intrinsic interference of FBMC-QAM systems

In order to reduce the intrinsic interference of the filter bank multicarrier-quadrature amplitude modulation(FBMC-QAM)system,a novel filter optimization scheme based on discrete prolate spheroidal sequences(DPSS)is proposed.Firstly,a prototype filter function based on DPSS is designed,since the eigenvalue can be used as an indicator of the energy concentration of DPSS,so a threshold is set,and the sequence with the most concentrated energy is selected under the threshold,that is,the sequence with the eigenvalue higher than the threshold,and the prototype filter function is rewritten as a weighted sum function of multiple eigenvectors.Under the energy constraints of the filter,the relationship between the eigenvectors and the intrinsic interference function is established,and the function problem is transformed into an optimization problem for the weighted coefficients.Through the interior point method,the most suitable weight is found to obtain the minimum intrinsic interference result.Theoretical analysis and simulation results show that compared with the prototype filters such as Type1 and CaseC,the DPSS filter applying the proposed optimization algorithm can effectively suppress the intrinsic interference of the system and obtain a better bit error rate(BER)performance.

耦合拉格朗日-欧拉方法及其在海洋工程中的应用

Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

A novel PID controller tuning method based on optimization technique

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was proposed.SQP/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM solver.The task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control systems.To assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) method.The results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

Coupled GIMP and CPDI material point method in modelling blast-induced three-dimensional rock fracture

Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challenging task.Some inherent weaknesses can be overcome by coupling the generalized interpolation material point(GIMP)and the convected particle domain interpolation technique(CPDI).For the media in the borehole,unchanged GIMP-type particles are used to guarantee a homogenous blast pressure.CPDITetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material.A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions.A good agreement was achieved between the simulation and experimental results.Moreover,the mechanism of three-dimensional rock fracture was analyzed.It was concluded that rock particle size and material parameters play an important role in rock damage.The reflected tensile waves cause severe damage in the lower part of the model.Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.

An ideal point method adopting grey relational entropy to estimate life cycle cost with effectiveness of torpedo

To making the decision of the developing blue prints,ideal point method was selected to estimate the life cycle cost with effectiveness of torpedo.At the same time,the concept of grey relational entropy of the grey system theory was adopted to compute the distance between each blue print and the ideal point(or negative ideal point).The blue print,nearest to the ideal point and farthest to the negative ideal point,is the best one.As an example,four blue prints of torpedo were estimated.The result indicates the practical value of this method.

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.

A Flux Based Approximation to Simulate Coupled Hydromechanical Problems for Mines with Heterogeneous Rock Types Using the Material Point Method

Advances in numerical simulation techniques play an important role in helpingmining engineers understand those parts of the rock mass that cannot be readily observed.The Material Point Method(MPM)is an example of such a tool that is gaining popularity for studying geotechnical problems.In recent years,the original formulation of MPM has been extended to not only account for simulating the mechanical behaviour of rock under different loading conditions,but also to describe the coupled interaction of pore water and solid phases in materials.These methods assume that the permeability of mediums is homogeneous,and we show that these MPM techniques fail to accurately capture the correct behaviour of the fluid phase if the permeability of the material is heterogeneous.In this work,we propose a novel implementation of the coupled MPM to address this problem.We employ an approach commonly used in coupled Finite Volume Methods,known as the Two Point Flux Approximation(TPFA).Our new method is benchmarked against two well-known analytical expressions(a one-dimensional geostatic consolidation and the so-called Mandel-Cryer effect).Its performance is compared to existing coupled MPM approaches for homogeneous materials.In order to gauge the possible effectiveness of our technique in the field,we apply ourmethod to a case study relating to a mine known to experience severe problems with pore water.