A model for thin shells in the combined finite-discrete element method

This thesis presents new numerical models for analysis of thin beam and arch structures and thin plate and shell structures based on the combined finite-discrete element method (FDEM). The new models perform quasistatic and dynamic analysis. The thesis also presents an overview of the established numerical tools for the analysis of arch and shell structures, together with their strengths and disadvantages. The bases of the combined finite-element method and its strengths are also presented. The main motivation was the development of precise, robust and computationally efficient numerical models. The model for the analysis of thin beam and arch structures uses straight two-noded rotation free finite elements, and takes into account linear-elastic material behaviour, finite displacement, finite rotations and small strains. The thesis describes axial and bending carrying mechanisms of a beam finite element in detail. The presented model is implemented into the open source FDEM package ‘Yfdem’. Performance of the new numerical model is demonstrated on simple benchmark tests by a comparison with known analytical and numerical results. Its application for the seismic analysis of arch structures is presented. This thesis also presents a new numerical model for analysis of thin plate and shell structures. The model uses three-noded triangular finite elements, and takes into account linear-elastic material behaviour, finite rotations, finite displacements and small strains. The thesis describes membrane and bending carrying mechanisms for triangular finite element in detail. The model is implemented into the open source FDEM package ‘Yfdem’. Performance of the new numerical model was demonstrated on simple benchmark tests by comparing it with the known analytical and numerical results. Its application in typical problems of stability of plate and shell structures is presented. Directions for further development and upgrade of the model in performing contact interaction and material nonlinearity are given.

Dynamic stability analysis of jointed rock slopes using the combined finite-discrete element method (FDEM)

Masonry arches are usually composed of individual blocks or voussoirs, which are highly discontinuous and nonlinear, and it is extremely difficult or even impossible to simulate their collapse behavior using finite element methods. Therefore, a combined finite–discrete element method (FDEM) is employed to simulate the collapse behavior of dry-joint masonry arches induced by spreading supports. With finite elements incorporated into discrete elements, both the deformation of arch voussoirs and the interaction between them such as contact can be predicted accurately. Moreover, a cohesive fracture model is implemented to simulate the potential rupture of masonry voussoirs. Based on them, several examples are validated with experiments, and the results indicate that the FDEM is able to simulate the collapse of masonry arches well. Furthermore, a parametric study is conducted on selected geometric and physical parameters to investigate the collapse of masonry arches due to support movements. The influences of friction and voussoir fracture where limited attention was paid to are also examined.

Node binding scheme based realization of extrinsic cohesive zone model (ECZM) to overcome the time discontinuity problem in 2D finite-discrete element method (FDEM)

In this paper, we present a three-dimensional (3D) grouting model based on the combined finite-discrete element method (FDEM). The 3D grouting model discretizes the problem domain into tetrahedral elements and joint elements, and the grout flows only in the broken joint elements, which satisfies the planar Poiseuille flow. By combining grout migration, FDEM mechanical cracking computation, and stress-induced fracture aperture variation in a graphics processing unit (GPU) parallel multiphysics FDEM software, called MultiFracS, the 3D grouting model can model rock cracking and the effect of hydromechanical (HM) coupling. First, a grouting example with analytical solutions is presented to validate the 3D grouting model. Then, we investigate the influence of several key parameters on grout penetration in fractured rock masses. The results reveal that the 3D grouting model can model grout migration, pressure distribution, grout–rock mass interaction, rock deformation, and crack initiation and propagation. Finally, the evolution of fracture geometry induced by grouting under different in situ stresses is studied. The numerical results present high coincidence with the in situ experimental results, demonstrating that the 3D grouting model is effective in dealing with fracture grouting.

The combined finite–discrete element method (FDEM) is an advanced numerical calculation method that is highly suitable for simulating the entire rock blasting process. Considering that rock mass contains many joints, the present study introduces a rock joint constitutive model to capture the transmission and reflection phenomena of blasting stress waves when they reach the joint. At the same time, based on the original FDEM code, an optimized blasting calculation model is proposed. This model considers the effect of explosive gas and accurately describes the physical relationship between the explosive gas pressure and the change in the blasting chamber area caused by crack propagation. To overcome the limitation of previous blasting models that only apply the pressure of the explosive gas to the borehole wall, the present study optimizes the determination conditions for crack penetration and the calculation method for the blasting chamber area as well as further considered the influence of the embedding effect of explosive gas on crack propagation. Finally, through three examples, the transmission and reflection laws of stress waves at the joints and the entire process of rock mass throw blasting are simulated. The results illustrate that this model can capture the propagation of stress waves, the gas wedge effect of explosive gas, and the entire process of crack initiation, propagation, and penetration in the rock mass during the explosion, demonstrating the potential of FDEM in blasting simulation.

A driving technical concern for the automobile industry is their assurance that developed windshield products meet Federal safety standards. Besides conducting innumerable glass breakage experiments, product developers also have the option of utilizing numerical approaches that can provide further insight into glass impact breakage, fracture, and fragmentation. The combined finite-discrete element method (FDEM) is one such tool and was used in this study to investigate 3D impact glass fracture processes. To enable this analysis, a generalized traction-separation model, which defines the constitutive relationship between the traction and separation in FDEM cohesive zone models, was introduced. The mechanical responses of a laminated glass and a glass plate under impact were then analyzed. For laminated glass, an impact fracture process was investigated and results were compared against corresponding experiments. Correspondingly, two glass plate impact fracture patterns, i.e., concentric fractures and radial fractures, were simulated. The results show that for both cases, FDEM simulated fracture processes and fracture patterns are in good agreement with the experimental observations. The work demonstrates that FDEM is an effective tool for modeling of fracture and fragmentation in glass.

Numerical investigation of mechanical responses and failure features of coal measure strata using combined finite-discrete element method

The combined finite–discrete-element method (FDEM) is an advanced and relatively new numerical modeling technique that combines the features of the FEM with those of the discrete-element method. It simulates the transition of brittle geomaterials from continua to discontinua through fracture growth, coalescence, and propagation. With FDEM, it is possible to simulate landslides from triggering to runout and carry out landslide scenario analyses, the results of which can be successively adopted for cost-effective early warning systems. The purpose of this paper is to describe the results of the FDEM simulations of the triggering mechanism and the evolution scenarios of the Torgiovannetto di Assisi rockslide (central Italy), a depleted limestone quarry face where a rock wedge with an approximate volume of 182,000 m3 lies in limit equilibrium conditions, posing relevant issues in terms of civil protection. The results obtained demonstrate that the FDEM is able to realistically simulate the different p...

This paper numerically investigates the seismic response of the filled joint under high amplitude stress waves using the combined finite-discrete element method (FDEM). A thin layer of independent polygonal particles are used to simulate the joint fillings. Each particle is meshed using the Delaunay triangulation scheme and can be crushed when the load exceeds its strength. The propagation of the 1D longitude wave through a single filled joint is studied, considering the influences of the joint thickness and the characteristics of the incident wave, such as the amplitude and frequency. The results show that the filled particles under high amplitude stress waves mainly experience three deformation stages: (i) initial compaction stage; (ii) crushing stage; and (iii) crushing and compaction stage. In the initial compaction stage and crushing and compaction stage, compaction dominates the mechanical behavior of the joint, and the particle area distribution curve varies little. In these stages, the transmission coefficient increases with the increase of the amplitude, i.e., peak particle velocity (PPV), of the incident wave. On the other hand, in the crushing stage, particle crushing plays the dominant role. The particle size distribution curve changes abruptly with the PPV due to the fragments created by the crushing process. This process consumes part of wave energy and reduces the stiffness of the filled joint. The transmission coefficient decreases with increasing PPV in this stage because of the increased amount of energy consumed by crushing. Moreover, with the increase of the frequency of the incident wave, the transmission coefficient decreases and fewer particles can be crushed. Under the same incident wave, the transmission coefficient decreases when the filled thickness increases and the filled particles become more difficult to be crushed.

In this study, a three-dimensional (3D) combined finite-discrete element method (FDEM) based simulator, which enables the robust simulation of full-scale triaxial Hopkinson bar (Tri-HB) testing system, including the capture of fracture and fragmentation processes of rock specimens as well as the detection and analysis of generated rock fragments, is developed for investigating the dynamic responses of rocks subjected to multiaxial coupled static and dynamic loads. An innovative two-step approach is proposed to first efficiently achieve the static stress state in the entire Tri-HB system and then apply dynamic loading to the system. The proposed approach with the schemes of mass scaling and local damping can significantly reduce the run time for static computation involving cohesive elements and complex contact mechanics in the framework of explicit time-integration. The developed program is well validated by achieving dynamic stress equilibrium in the Tri-HB system and comparing the simulated stress wave profiles with those from laboratory experiments. Then, the progressive dynamic fracture and fragmentation processes of rocks under different static stress conditions in a full-scale Tri-HB system are investigated, which vividly exhibit the confinement dependence of the dynamic behaviours of rocks in the testing system. It is found that, even with the same loading rate, separate input parameter sets for rock need to be established in FDEM for different confinement conditions to capture the actual rate dependent behaviour of rock. Further studies are also conducted to investigate the effect of interfacial friction on the fracture behaviour, and the results indicate that higher interfacial frictions significantly disturb the dynamic stress variations and the true rock behaviour in the system. Through high performance computing of 3D FDEM, this study is expected to contribute to the understanding of dynamic responses of rocks subjected to multiaxial coupled static and dynamic loads in deep underground engineering.

ABSTRACT: The finely bedded structure of shale makes its mechanical behavior highly anisotropic both in terms of deformation and strength. The variations in the bedding plane thickness originates from different sedimentation processes occurred during the formation of the shale. It is well known that these features act as weakness planes in the rock matrix and thus studying the mechanical behavior of shale should incorporate the influence of bedding planes. Numerous investigations have been conducted so far to understand the influence of bedding plane orientation on the deformation and strength of shale. However, there exist only a few investigations which studied the influence that bedding plane thickness and friction might have on the mechanical response and cracking pattern of the rock. The present study discusses the results of a series of unconfined compressive test simulations conducted on shale samples with different bedding plane thickness and friction values using the combined Finite-Discrete Element Method (FDEM). The bedding planes have been discretely modeled as a distribution of preferentially oriented defects inside the rock matrix. Experimental results from the shaly facies of the Opalinus Clay at the Mont Terri Underground Research Laboratory (URL) have been used as input parameters to calibrate the numerical model. Simulation results show a difference in cracking pattern and strength of the rock owing to different bedding plane thicknesses but almost no effect due to different bedding plane frictions. 1. INTRODUCTION Shale formations play an integral role in many civil, petroleum, and environmental engineering projects. Shales not only act as an unconventional reservoir for extracting hydrocarbon resources, but also as a potential host rock for underground geological storage of nuclear wastes and as caprock for Carbon Capture and Sequestration (CCS) operations. Shale is formed through the sedimentation and subsequent hardening of fine sediments and thus it features a finely laminated and bedded structure. Platy particles tend to deposit in distinct orientations during the sedimentation of the shale causing an anisotropic texture at the macroscopic scale (Wenk et al., 2008). The layered structure of the shale makes its deformation and strength characteristics highly anisotropic at different scales, for example, at a larger scale it is attributed to the presence of bedding planes (Saroglou and Tsiambaos, 2008). The temporal variations in the sediment supply and flow velocity causes the thickness and properties of the bedding planes to differ along the deposition axis (O’Brien, 1996). These bedding planes act as weakness planes inside the rock matrix and thus understanding the shale mechanical behavior should incorporate the influence of bedding planes (Woo et al., 2021). In addition, the existence of physical discontinuities in the rock such as natural fractures or tectonic features contributes to the anisotropy at the rock mass scale.

Recent years have seen an increase in demand for the demolition of obsolete and potentially hazardous structures, including reinforced concrete (RC) structures, using blasting techniques. However, because the risk of failure is significantly higher when applying blasting to demolish RC structures than mechanical dismantling, it is critical to achieve the optimal demolition design and conditions using blasting by taking into account the major factors affecting a structure’s demolition. To this end, numerical analysis techniques have frequently been used to simulate the progressive failure resulting in the collapse of structures. In this study, the three-dimensional (3D) combined finite discrete element method (FDEM), which is accelerated by a parallel computation technique incorporating a general-purpose graphics processing unit (GPGPU), was coupled with the one-dimensional (1D) reinforcing bar (rebar) model as a numerical simulation tool for simulating the process of RC structure demolition by blasting. Three-point bending tests on the RC beams were simulated to validate the developed 3D FDEM code, including the calibration of 3D FDEM input parameters to simulate the concrete fracture in the RC beam accurately. The effect of the elements size for the concrete part on the RC beam’s fracture process was also discussed. Then, the developed 3D FDEM code was used to model the blasting demolition of a small-scale RC structure. The numerical simulation results for the progressive collapse of the RC structure were compared to the actual experimental results and found to be highly consistent.

A novel joint element parameter calibration procedure for the combined finite-discrete element method

Purpose In order to avoid the problem of volumetric locking often encountered when using constant strain tetrahedral finite elements, the purpose of this paper is to present a new composite tetrahedron element which is especially designed for the combined finite-discrete element method (FDEM). Design/methodology/approach A ten-noded composite tetrahedral (COMPTet) finite element, composed of eight four-noded low order tetrahedrons, has been implemented based on Munjiza’s multiplicative decomposition approach. This approach naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. The problem of volumetric locking is avoided via a selective integration approach that allows for different constitutive components to be evaluated at different integration points. Findings A number of validation cases considering different loading and boundary conditions and different materials for the proposed element are presented. A practical application of the use of the COMPTet finite element is presented by quantitative comparison of numerical model results against simple theoretical estimates and results from acrylic fracturing experiments. All of these examples clearly show the capability of the composite element in eliminating volumetric locking. Originality/value For this tetrahedral element, the combination of “composite” and “low order sub-element” properties are good choices for FDEM dynamic fracture propagation simulations: in order to eliminate the volumetric locking, only the information from the sub-elements of the composite element are needed which is especially convenient for cases where re-meshing is necessary, and the low order sub-elements will enable robust contact interaction algorithms, which maintains both relatively high computational efficiency and accuracy.