Large Deformation Problems Research Articles

Elasto-plastic simulation of hot shape rolling of steel by a meshless method

This paper describes the development of meshless simulation of thermomechanics of steel in a continuous hot rolling process using a novel meshless solution procedure. During the process, steel billets at high temperatures are transferred through multiple roll passes, each with a specific groove shape and roll gap. The major outcome of this simulation system is to design the rolling schedule and confirm whether the final shape is inside the acceptable range. For this purpose, a perpendicular 2D slice model approach is used to obtain fast and reasonably accurate simulation results. A return mapping algorithm solves the elasto-plastic material model with linear hardening to obtain displacements, strains and stresses. They are calculated by the local radial basis function collocation method (LRBFCM), which uses the local interpolation of the strong form of partial differential equations. The predefined slice positions are entered into the rolling system, and for each position, the slice contact line and amount of reduction are predicted and used as boundary conditions. Thermal and mechanical models are run sequentially, which is repeated until the final slice position reaches the exit from the last roll. The simulation system was validated with multiple rolling schedules provided by the industrial partner and was successfully used in the steel production plant afterwards. The meshless LRBFCM successfully solves a complex elasto-plastic large deformation problem of hot rolling for the first time.

Application of material point method in modeling soil-geosynthetics interactions-a literature survey

The material point method (MPM) has garnered significant attention in recent years owing to its advantages in solving soil–water-structure interaction problems involving large deformations in geotechnical engineering. The MPM combines the benefits of point-based and mesh-based approaches (finite element method) with both Eulerian computational mesh and continuum descriptions of materials. The successful integration of MPM in simulated landslides, internal erosion, and excavation has been frequently reported. However, solving the soil–geosynthetic interaction problem with the MPM has not been explored, although such problems often entail large deformations. The goal of this study is to collate studies on the simulation of geosynthetics and their interactions with soil using MPM. This paper first discusses the basics of MPM and the formation of thin membrane materials using MPM. It also includes limited applications of MPM in simulating soil–geosynthetic interactions. The applications demonstrate that the MPM is particularly effective in resolving large deformation problems associated with geosynthetics, including problems of landfill settlement, reinforced-slope stability, and geocontainer dropping.

3D SPH implementation to large deformation of granular mass using an advanced hypoplastic constitutive model

In this study, an advanced hypoplastic model incorporating the critical state is integrated into smoothed particle hydrodynamics (SPH) for the numerical investigation of geotechnical large-deformation problems. Moreover, a return mapping strategy is proposed to regulate the stress state to avoid calculation failure. Furthermore, a closed-form solution to predicting the failure surface implicitly incorporated in the hypoplastic model is derived. The proposed SPH method is examined with element tests such as the oedometer test and biaxial compression test to observe a good performance of the SPH model. Finally, the SPH model is applied to numerically reproducing sand column collapse to investigate the effect of the initial void ratio on the behavior of soil.

Method for Pressure Relief in Deep Coal Mine Roadways Using Borehole Groups and Its Application to Guqiao Coal Mine

Abstract With the increase in the mining depth of coal mines in China, the problem of large deformation of roadways owing to high-ground pressure has become prominent even under enhanced support systems. To reduce the high pressure on the surrounding rock, this study investigates a pressure-relief method for deep roadways using drilling borehole groups. Based on a deep roadway in the Huainan mining area of China, the influences of drilling parameters, such as borehole diameter, length, and arrangement were investigated. The results indicate that the fan-shaped arrangement of the borehole group can compensate for the dilatancy deformation of the surrounding rock. The peak stress of the surrounding rock is reduced and transferred to the inner part of the surrounding rock. Furthermore, a field experiment was conducted on an experimental roadway. The deformation of the roadway was monitored and compared with that of an adjacent roadway that did not apply the pressure-relief method. The monitoring results indicated that the deformation of the experimental roadway was significantly reduced.

Research on Active-passive Joint Support Technology for the Roadway of Thick Coal Seam Mining

The lower trench of 2301 working face of Anyang Main Coking Coal Mine has the problems of large deformation of surrounding rock and high difficulty of maintenance in the process of digging. According to the deformation characteristics of the surrounding rock, a "U-type steel + anchor cable" joint support technology is proposed to control the deformation. In this paper, the main parameters of joint support are studied through numerical simulation, and the effect of perimeter rock control is verified through on-site monitoring. The results show that: within a reasonable range of preload force, the larger the preload force of the anchor cable, the better the effect of controlling the deformation of the surrounding rock; when the bracket row spacing is 600-800mm, the stability of the surrounding rock of the roadway can be ensured; during the roadway excavation, the maximum deformation of the surrounding rock is 40mm, which realizes the control of the stability of the surrounding rock in the roadway of the top coal of the soft and thick coal seam.

Liquefaction-induced large deformation method with automatic time-step mapping and interfacial interpolation improvement: Case study of the San Fernando dam

This study constructed the u-p equation for saturated soil in the meshfree global weak form within the arbitrary Lagrangian-Eulerian (ALE) framework to solve the problem of liquefaction-induced large deformation induced by strong seismic loading. The interpolation improvement in the near-interface zone was achieved using domain truncation optimization and the local nodal refinement algorithm, and the relative error of the shape function was proposed as the judgment criterion for radial basis function (RBF) field variable mapping. Finally, a high precision meshfree liquefaction-induced large deformation method (MFLLDM) with automatic time step mapping and interfacial zone interpolation improvement was established. The MFLLDM achieved the efficient dynamic updating of soil stress state and pore pressure information in space during the deformation process and more accurately depicted the localized large shear deformation characteristics of the soil in the near-interface zone. The proposed method was integrated into a custom-built large-scale finite element method (FEM) computing system (GEODYNA), based on object-oriented and super element program design technology. This enabled the efficient coupled analysis of MFLLDM in the liquefied-induced large deformation zone and FEM in the small deformation zone. Numerical consolidation examples were used to validate the accuracy, convergence, and applicability of the soil elasto-plastic model for MFLLDM. The method was then used to simulate the liquefaction damage of the San Fernando dam, which reproduced the development process of large slip deformation and high-water pressure ratio for the upstream dam slope.

A parallel multi-resolution Smoothed Particle Hydrodynamics model with local time stepping

Smoothed Particle Hydrodynamics (SPH) model has exhibited remarkable efficacy in addressing strongly nonlinear large deformation problems. However, the expensive computational cost could limit its application. To address this, we propose a novel parallel multi-resolution SPH model with a local time step strategy. This model integrates the multi-resolution model with a Message Passing Interface-based parallelization framework, wherein subdomains discretize the computational domain at varying resolutions. Meanwhile, a local fourth-order Runge-Kutta time integration scheme is introduced, enabling different subdomains to use different time steps. Subdomains of varying resolutions are devoid of overlapping regions, and changes in particle resolution at interfaces are achieved through a dynamic strategy involving particle merging and splitting. Besides that, we conducted a comparative analysis of different SPH discretization formats concerning their impact on the accuracy of multi-resolution particle discretization. Finally, several numerical tests were conducted to validate the accuracy and efficiency of the present multi-resolution SPH model.

A stabilized two-phase material point method for hydromechanically coupled large deformation problems

A stabilized two-phase material point method for hydromechanically coupled large deformation problems

Mapped material point method for large deformation problems with sharp gradients and its application to soil‐structure interactions

AbstractThe material point method (MPM) is often applied to large deformation problems that involve sharp gradients in the solution field. Representative examples in geomechanics are interactions between soils and various “structures” such as foundations, penetrometers, and machines, where the displacement fields exhibit sharp gradients around the soil‐structure interfaces. Such sharp gradients should be captured properly in the MPM discretization to ensure that the numerical solution is sufficiently accurate. In the MPM literature, several types of locally refined discretizations have been developed and used for this purpose. However, these local refinement schemes are not only quite complicated but also restricted to certain types of basis functions or update schemes. In this work, we propose a new MPM formulation, called the mapped MPM, that can efficiently capture sharp gradients with a uniform background grid compatible with every standard MPM basis function and scheme. The mapped MPM is built on the method of auxiliary mapping that reparameterizes the given problem in a different domain whereby sharp gradients become much smoother. Because the reparameterized problem is free of undesirably sharp gradients, it can be well solved with the standard MPM ingredients including a uniform background grid. We verify and demonstrate the mapped MPM through several numerical examples, with particular attention to soil‐structure interaction problems.

Pressure-relief joints of initial support structural system used in tunnels with high-stress surrounding rock.

To address the problem of large deformations in weak surrounding rock tunnels under high ground stress, which cause damage to initial support structures, this study proposes a novel type of circumferential pressure-relief joint based on the concept of relieving deformation pressure of the surrounding rock. Key parameters of the pressure-relief joint, such as initial bearing capacity peak, constant bearing capacity, and allowable pressure-relief displacement, were obtained through numerical simulations and laboratory experiments. A comparison was made between the mechanical characteristics of rigid joints and the new type of pressure-relief joint. The applicability of the pressure-relief joint was verified through field tests, monitoring the surrounding rock pressure, internal forces in the steel frames, and the convergence displacement of the support structure. The results show that: (1) In the elastic stage, the stiffness of the new pressure-relief joint is similar to that of rigid joints. In the plastic stage, rigid joints fail directly, whereas the pressure-relief joint can control deformation and effectively release the deformation pressure of the surrounding rock while providing a constant bearing capacity. (2) The right arch foot in the experiment had poor rock quality, leading to high stress in the steel frame and significant horizontal displacement. After the deformation of the pressure-relief joint, the stress in the surrounding rock and steel frame significantly reduced, and the rate of horizontal deformation of the support structure slowed down. (3) The vertical and horizontal final displacements of the pressure-relief joint in the experiment were 61mm and 15mm, respectively, which did not exceed the allowable deformation values. The components of the support structure remained intact, ensuring safety. However, this study has limitations: the design of the new pressure-relief joint only allows for a vertical deformation of 150mm and a horizontal deformation of 50mm, limiting the range of pressure-relief deformation.

Study on the Influence of Mining Stress on the Sustainable Utilization of Floor Roadway in Qinan Coal Mine

Aiming at the problem of large deformations and difficult maintenance of cross-mining floor roadways, taking the track transportation roadway of the cross-mining east wing floor in Qinan Coal Mine as the engineering background, the stress field distribution of mining stress in floor strata and surrounding rock of floor roadway during the cross-mining process of the working face is studied by combining theoretical analysis with numerical simulation. The results show that the influence of mining stress on the vertical stress of floor strata is reflected in the stress-increasing area in front of the coal wall and the stress-decreasing area in the rear of the coal wall. With the increase in the depth of the floor strata, the peak value of the vertical stress gradually decreases, and the distance from the peak value of the vertical stress to the coal wall and the influence range of the vertical stress gradually increases. When the width of the coal pillar is greater than the influence range of advance abutment pressure of the working face, the development speed of the plastic zone is slow. When the roadway is located in the influence range of advance abutment pressure, the plastic zone of the roadway’s surrounding rock develops rapidly. When the working face crosses the floor roadway more than 10 m, the depth of the plastic zone of the surrounding rock of the roadway is no longer increased; the siltstone above the roadway is the key layer of fracturing, and the deformation of the roadway has been effectively improved after hydraulic fracturing. Through the analysis of numerical simulation results, the fracturing scheme has a significant effect on the stability control of the surrounding rock of the cross-mining floor roadway. This study has certain guiding significance for the maintenance and sustainable utilization of floor roadways in the cross-mining process, which is conducive to ensuring the sustainable mining of underground coal and the safety of personnel and equipment and is of great significance to the sustainable development of the coal mining industry.

An explicit material point and finite volume sequentially coupled method for simulating large deformation problems in saturated soil

An explicit material point and finite volume sequentially coupled method (MPM-FVM) is developed using u-p form coupling formulations for the simulation of large deformations in saturated soil. In MPM-FVM, the momentum conservation equation is solved by MPM under the updated Lagrange framework, and the mass conservation equations are solved by FVM under the Euler framework. The numerical implementation of an explicit sequentially coupled algorithm is developed considering the tradeoffs between computational cost and numerical stability. The critical time step of u-p form governing equations is derived using the Von Neumann method, which is found to be much greater than the u-U form explicit MPM at low permeability, allowing for high numerical stability. Three numerical cases are presented to demonstrate the stability, efficiency, and effectiveness of the developed MPM-FVM method. The simulation of a saturated one-dimensional soil column subjected to quasi-static and dynamic loads validates the method, and highlights its greater efficiency and accuracy compared to standard solid–fluid coupled MPM methods. The large deformation simulation capability of the method is exhibited via simulation of a saturated slumping block. In real-world application, simulation results obtained using method achieves excellent agreement with the experiment measurements and observations of the Selborne landslide experiment.

Stabilizing nodal integration in dynamic smoothed particle finite element method: A simple and efficient algorithm

The Smoothed Particle Finite Element Method (SPFEM) is a powerful numerical tool for the modelling of large deformation problems in the field of geomechanics. However, the standard SPFEM with nodal integration suffers from the rank deficiency problem due to under-integration. In this study, an hourglass-control based stabilization scheme is presented to overcome the rank deficiency in standard SPFEM with nodal integration. By introducing the hourglass-control based correction forces, the spurious low-energy models in standard SPFEM with nodal integration can be effectively suppressed. The presented stabilization scheme is simple and computationally efficient compared to the existing strain gradient-based stabilization approaches in SPFEM. The proposed hourglass-control based stabilized SPFEM is firstly validated by means of three benchmark examples and the results show that the stabilization scheme based on the hourglass-control can eliminate the rank deficiency instability in standard SPFEM and free of volumetric locking. Finally, two numerical examples related to the cohesive soil flow and the progressive failure of sensitive clay slopes are studied to highlight the robustness of the proposed stabilized SPFEM in solving large deformation geotechnical problems.

An ANS/ATFs‐based unsymmetric solid‐shell finite element algorithm for high‐quality finite deformation analysis of hyper‐elastic shell

AbstractAn effective updated Lagrangian (UL) algorithm is designed for extending the recent distortion‐tolerant unsymmetric 8‐node, 24‐DOF hexahedral solid‐shell element, US‐ATFHS8, to finite deformation analysis of hyper‐elastic shell structures. The distinguishing feature of this unsymmetric element is that two different interpolation schemes are employed for virtual displacement and real stress calculations, respectively. The assumed natural strain (ANS) method with shell assumptions, referring to the current configuration, is introduced to modify the strain tensors derived from the assumed virtual displacement fields in terms of isoparametric coordinates, thereby mitigating shear locking and trapezoidal locking. On the other hand, the analytical trial functions (ATFs) derived from the general solutions of homogenous governing equations for linear elasticity are updated in each increment step to obtain the incremental deformation gradient, which is then utilized for calculating the real stresses for curing the numerical difficulties in large deformation problems. Numerical examples show that the proposed algorithm enables the hyper‐elastic solid‐shell element US‐ATFHS8 to exhibit excellent performance in both regular and distorted meshes and yield considerable results even when other models cannot work.

An implicit Updated Lagrangian Fragile Points Method with a support domain refinement scheme for solving large deformation problems

AbstractEngineering structures may undergo large deformations, but simulating is still challenging for existing numerical methods, for example, the element‐based methods struggle from the mesh distortion and the strong form particle‐based methods exhibit tensile instability. This article aims on presenting a novel numerical method for large deformation simulations, which is named the implicit Updated Lagrangian Fragile Points Method (ULFPM). The point‐based nature of the proposed method ensures immunity to mesh distortion, and its stability is guaranteed by its foundation on weak form formulations. For verifications, the proposed implicit ULFPM has been applied to several large deformation problems. For all the examples, the proposed method is able to provide reliable results with a good agreement with the reference results. Moreover, the implicit ULFPM performs better than the Finite Element Method to some extent for extremely large deformation problems. It is also discussed that the accuracy of the implicit ULFPM is improved significantly by using the support domain refinement scheme. The examples indicate that the proposed method can serve as a reliable tool for predicting the large deformations of structures in engineering practices.

Research on intrusion and large arch bulge in lining structure for highway’s mudstone tunnel

During the construction of a highway in northwest China, large deformation of mudstone caused severe deformation of and damage to side walls, initial support, and secondary lining to various extents. To reveal the causes of mudstone’s large deformation in the tunnels of this highway, a comprehensive study was conducted by using engineering geological survey, on-site monitoring and measurement, indoor rock mechanics test, numerical simulation, and macroscopic analysis. For the problem of large deformation of this highway’s tunnel section from YK209 + 500 m to YK210 + 030 m, the 3D finite difference method FLAC3D was used to simulate the large deformation of the wall rock and compare the deformation of the tunnel and the mechanical characteristics of the lining structure under different conditions by means of inverse analysis of the rheological characteristics of the mudstone and simulation of the softening of the mudstone in water. The research results provide a reference and basis for the construction design of similar mudstone tunnel projects. For the management of tunnel deformation, it is recommended to enhance the tunnel’s drainage measures, thereby mitigating the intensification of mudstone softening when exposed to water.

Study on dynamic response of cushion layer-reinforced concrete slab under rockfall impact based on smoothed particle hydrodynamics and finite-element method coupling

Abstract In the rockfall prevention and control project, the reinforced concrete (RC) slab and sand (gravel soil) soil cushion layer are commonly used to form the protection structure, thereby resisting the rockfall impact. Considering that the oversized deformation of the cushion layer under impact load using the finite element simulation cannot converge, this article establishes a numerical calculation model using smoothed particle hydrodynamics–finite-element method coupling (SPH–FEM). First, the standard Lagrange finite-element mesh is established for the whole model using ABAQUS, and then the finite-element mesh of the soil cushion layer is converted to SPH particle at the initial moment of the calculation, and finally the calculation results are solved and outputted. The results indicate that, compared with the results of the outdoor rockfall impact test, the relative errors of the rockfall impact force and the displacement of the RC slab are within 10%, which proves the rationality of the coupling algorithm; moreover, in terms of the numerical simulation, the SPH–FEM coupling algorithm is more practical than the finite element for reproducing the mobility of the rockfall impacting the sand and soil particles. In addition, at an impact speed of less than 12 m·s−1, the cushion layer is able to absorb more than 85% of the impact energy, which effectively ensures that the RC slab is in an elastic working state under small impact energy and does not undergo destructive damage under large impact energy; the peak impact force of the rockfall is approximately linear with the velocity, and the simulated value of the peak impact force is basically the same as that of the theoretical value of Hertz theory; the numerical simulation is good for reproducing the damage process of the RC slab in accordance with the actual situation. The SPH–FEM coupling algorithm is more justified than the FEM in simulating the large deformation problem, and it can provide a new calculation method for the design and calculation of the rockfall protection structure.

A hydro-mechanical coupled contact method for two-phase geotechnical large deformation problems within the SNS-PFEM framework

This paper proposes a novel numerical algorithm to solve frictional contact problems in two-phase porous media, accounting for the large deformation and interface fluid flow, within the framework of the Stable Node-based Smoothed Particle Finite Element Method (SNS-PFEM). The proposed approach builds on our previous work that was only designed for single-phase large deformation contact problems. Within this work, the hydro-mechanical coupling system is discretized using equal-order interpolation, with a polynomial pressure projection method to eliminate the pore pressure instability. Surface-to-surface discretization is then applied to formulate the contact constraint of the two-phase porous medium. Using the dual Lagrange multiplier approach, a coordinate transformation is introduced to enforce the contact constraint of the solid phase. This transformation is subsequently utilized to develop a new interface fluid element, which serves as a tool to model the fluid exchange behaviour between porous media and contact gaps. Different from existing interface fluid elements, the proposed element is constructed based on the contact algorithm, thereby enabling it to handle non-conforming interfaces and tackle challenges associated with large sliding problems. Furthermore, the proposed method can maintain a well-conditioned system matrix throughout the computation process. These distinctive attributes significantly enhance the flexibility of numerical modelling. Finally, the accuracy and performance of our method are verified through four numerical examples. The results show that the proposed method can effectively simulate various geotechnical problems, including multi-layer soil consolidation, fluid-soil-structure interaction, and geological interface-controlled slope failure.

Time-dependent behavior of reinforcement rock unit anchored by energy-absorbing bolt for large deformation control in tunneling

The energy-absorbing bolt is designed to counteract both burst-prone and squeezing rock conditions in rock excavation. In this paper, the mechanical contribution of energy-absorbing bolts installed systematically around tunnels excavated in rock masses was investigated based on the assumptions of the reinforced rock unit (RRU) model. The time-dependent behavior of rock with a large deformation problem was simulated using a Nishihara model, while that of an energy-absorbing bolt was simplified by a rheological model connecting a Hookean elastic element and a Saint-Venant element in series. The mechanical model of RRU anchored by an energy-absorbing bolt was established by connecting the rock mass model and the energy-absorbing bolt model in a parallel combination. The closed-form solution presented the time-dependent behavior of RRU under an instantaneously applied tension stress and an linearly increasing load, respectively. The results showed the reinforcement could reduce the time-dependent deformation of the reinforced region of tunnels significantly. A preliminary estimate of NPR-bolt reinforcement for large-deformation controls in the Muzhailing tunnel was carried out using the proposed model. The results showed that the NPR cables could have critical effects in controlling the large deformation of the tunnel.

Damage creep model and application for sandy mudstone considering the effect of immersion deterioration

Abstract Aiming at the problem of performance degradation and large deformation of sandy mudstone after immersion in water, the compression test is carried out. The damage and deterioration law of strength and elastic modulus of immersed rock mass is analyzed, and the function relationship between rock damage variable and soaking time is obtained by fitting. Combined with the Hoek-Brown criterion and Mohr-Coulomb criterion, the calculation method of instantaneous cohesion and instantaneous internal friction angle of damaged rock mass is derived based on the tangent method, and the equivalent Mohr-Coulomb criterion which can effectively characterize the nonlinear strength characteristics of damaged rock mass is given. Based on the built-in creep model Cvisc of Flac3D, a damage creep model is given by introducing the damage factor and nonlinear strength criterion of immersed rock mass, which is more suitable for describing the creep characteristics of immersed sandy mudstone. The validity of the model is verified by comparing with the measured results.