•A system is proposed to obtain heterogeneous rocks with irregular inclusions.•Realistic inclusion geometry is obtained and controlled by combining the circular parameterization and Fourier ...transformation.•An unique overlapping detection algorithm based on level-set function is developed to allocate inclusions.•Hydraulic fracturing are captured by integrating cohesive pore pressure elements into traditional finite element model.•A systematic hybrid finite-discrete approach for investigating hydraulic fracturing of heterogeneous rocks is proposed and validated.
A systematic hybrid approach for modelling the hydraulic fracturing process of heterogeneous rocks with irregular inclusions is developed. This approach is based on a series of computational algorithms, including Fourier series transformation, level-set-based overlapping detection, and the finite-discrete element method. Three major steps are included: (1) circular parameterization and Fourier transformation are employed to reproduce realistic inclusion contours with arbitrary irregular shapes; (2) a novel overlapping detection method based on a level-set function is employed to allocate irregular inclusions effectively and efficiently; and (3) the finite-discrete element model is established by integrating cohesive elements with pore pressure nodes into the solid mesh to simulate the progressive hydraulic fracture and interface crack of heterogeneous rocks. To validate the proposed hybrid approach, modelling results by the established model are compared with numerical simulations in the literature. In addition, the influences of injection speed and interface strength on the mechanical and fracturing responses of heterogeneous rocks are discussed. The results demonstrate that the proposed hybrid approach is capable of simulating the hydraulic fracturing process of heterogeneous rocks.
This study introduces GeoTaichi, an open-source high-performance numerical simulator designed for addressing multiscale geophysical problems. By leveraging the power of the Taichi parallel language, ...GeoTaichi maximizes the utilization of modern computer resources on multicore CPU and GPU architectures. It offers robust and reliable modules for the discrete element method (DEM), material point method (MPM), and coupled material point-discrete element method (MPDEM). These modules enable efficient solving of large-scale problems while being implemented in pure Python. The design philosophy of GeoTaichi focuses on creating a framework that is readable, extensible, and user-friendly. This paper highlights the coupling procedure of MPDEM, the code structures, and the most important features of GeoTaichi. Rigorous benchmark tests have been conducted to verify the validity and robustness of GeoTaichi. Additionally, the performance of GeoTaichi is compared with similar software tools in the field, underscoring a notable improvement in both computational efficiency and memory savings when compared to existing alternatives.
Program title: GeoTaichi
CPC Library link to program files:https://doi.org/10.17632/858bmcf7j6.1
Developer's repository link:https://github.com/Yihao-Shi/GeoTaichi
Licensing provisions: GNU General Public License v3.0
Programming language: Python
Nature of problem: The simulations of large-deformation geophysical flows and their interaction with structures play a crucial role in the field of geophysics. To address the complexities of these nonlinear problems, the discrete element method (DEM), material point method (MPM), and their coupling (MPDEM) have proven to be highly suitable numerical schemes. However, these schemes impose substantial computational demands, necessitating the development of an efficient framework that can harness modern computer resources on multicore CPU and GPU architectures.
Solution method: The open-source code GeoTaichi implements the DEM, MPM, and coupled MPDEM, encompassing a range of constitutive models and contact laws for different geologic materials. The clump particle model is also introduced in DEM to solve granular mechanics involving complex-shaped particles. One significant advantage of GeoTaichi is its utilization of the Taichi parallel language, which is designed to be user-friendly and easily extensible for customized applications.
This paper presents a new, fully-coupled, hydro-mechanical (HM) formulation for a finite-discrete element method computer code. In the newly-developed, hydraulic solver, fluid flow is assumed to ...occur through the same triangular mesh used for the mechanical calculations. The flow of a viscous, compressible fluid is explicitly solved based on a cubic law approximation. The implementation is verified against closed-form solutions for several flow problems. The approach is then applied to a field-scale simulation of fluid injection in a jointed, porous rock mass. Results show that the proposed method can be used to obtain unique geomechanical insights into coupled HM phenomena.
Hydraulic fracturing has proven to be an efficient technique to enhance production in unconventional reservoirs. Since heterogeneity is commonplace in reservoir rocks, it is vital to investigate the ...influence of rock heterogeneity on hydraulic fracture propagation. Here, based on the combined finite-discrete element method (FDEM) and cohesive zone model, two series of numerical models with uniformly distributed and Weibull-distributed elastic modulus of rock are assembled, respectively. The comparison with the theoretical solution demonstrates the reliability of the simulation models in both the toughness-dominated regime (TDR) and viscosity-dominated regime (VDR). The parameter analysis demonstrates the rationality of parameters for cohesive elements. The results show that the previous theoretical equations can be used as a preliminary evaluation of simulation parameters. The effects of different parameters such as element size, Weibull distribution type, and far-field stress on hydraulic fracture length, fluid pressure, maximum fracture aperture, and the final fracture morphology are evaluated. The results demonstrate that the distribution type of rock elastic modulus has a significant impact on the hydraulic fracture propagation in both TDR and VDR. The “jump” phenomena have been observed in TDR caused by high fracture toughness. The displacement of fracture location and asymmetrically dynamic propagation are affected by the distribution of rock elastic modulus. Besides, the hydraulic fracture propagation in TDR is more susceptible to element size, the distribution of rock elastic modulus, and far-field stress than that in VDR. This research may shed light on the development of hydraulic fracturing technology in tight reservoirs.
A combined experimental and numerical approach is proposed in this study for the characterisation of the mechanical behaviour of foamed geopolymer concretes. Advanced experimental techniques ...employing X-Ray CT give both microstructures and mechanical responses of a range of geopolymer concretes with varying densities. In parallel with this, a numerical modelling technique based on the discrete element method (DEM) is developed for explicit descriptions of air-void distribution, while the mortar binder is described at the micro/meso scale with cohesive behaviour. The calibrated and validated DEM model is then used to systematically study the effects of air-void content, air-void distribution and microstructural parameters, including particle size and porosity on the compressive strength of foamed concretes. A non-linear relationship between the compressive strength and porosity of foamed concretes is found from DEM simulations, which are consistent with our experimental findings and existing strength-porosity models. Furthermore, it is found that the air-void distribution has a significant influence on the compressive strength of foamed concretes, while the micro-void structure has less effect on the loading bearing capacity of the material. The proposed combined approach demonstrates the tight correlations between experimental and numerical techniques in characterising the mechanical behaviour of foamed concretes for practical design purposes.
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•A combined experimental-numerical approach can further the characterisation of foamed concretes with varying densities.•Porosity and types of air voids in a foamed concrete can have a profound effect on its mechanical properties.•DEM analyses indicate that local pore collapse and macro shear failure compete to govern the response of foamed concrete.•DEM simulations could provide consistent numerical data for the development of a better strength-porosity model.
•A 2D fully coupled hydro-mechanical finite-discrete element model with real pore seepage is proposed.•The model can simulate the deformation and fracture of rock with an arbitrary complex fracture ...network driven by fluid pressure.•The proposed method can capture crack initiation and propagation, the interaction of hydraulic fractures and natural fractures, and the fluid pressure distribution in the rock mass.
Based on the finite-discrete element method (FDEM), a 2D fully coupled model with real pore seepage is proposed. This model can solve the problem of the deformation and fracture of porous medium driven by fluid. In this model, the fluid flow in the fracture is expressed by the cubic law, while the fluid flow in the rock matrix is characterized by Darcy's law and solved by the finite volume method. The interaction between pore seepage and fracture seepage is realized at the fracture. Three analytical solutions are presented to verify the correctness of the proposed model. The results show that the numerical solutions agree well with the analytical solutions. In addition, a hydraulic fracturing problem with a complex fracture network is studied using this model. The simulation results show that the model can capture the fracture initiation, propagation, and intersection, the interaction of natural fractures and newly generated fractures, and the evolution of fluid pressure during hydraulic fracturing. The model can be used not only to simulate hydraulic fracturing in shale gas and geothermal mining but also to solve a series of geomechanical problems related to the effect of fluid. Thus, this model has broad application prospects.
This paper describes the implementation and advantages of grain based modelling (GBM) in the combined finite-discrete element method (FDEM) to study the mechanical behaviour of crystalline rocks. GBM ...in FDEM honours grain petrological properties and explicitly models grain boundaries. The simulation results demonstrated that GBM in FDEM predicted more realistic microscopic and macroscopic response of rocks than conventional FDEM models. The explicit modelling of crack boundaries captured microscopic failure transition from along grain boundaries to coalescence along the shear band, dominated by intraphase cracks. This novel framework presents a gateway into further understanding the behaviour of crystalline rocks and granular minerals.
The coupling between fluid and granular materials is commonly encountered in nature and engineering practice. Moreover, the shape of granular materials in practical applications is normally ...non-spherical. Therefore, investigating the particle-fluid systems containing non-spherical particles for a deeper understanding of their underlying mechanisms and then for improving the performance of the related industrial processes should be an urgent necessity for practical needs. For investigating the intricate flow behaviors of particle-fluid systems, the numerical simulation method of coupling DEM (Discrete Element Method) with CFD (Computational Fluid Dynamics) has been widely recognized as a promising tool, and many efforts have been devoted to the CFD-DEM investigations of non-spherical particles in recent years. This paper aims to review development of the CFD-DEM investigations for non-spherical particles from theoretical models to applications in recent six years. It primarily represents three principal aspects: the theoretical foundations of DEM for modeling non-spherical particles, the coupling methodologies between CFD and DEM and the use of the non-spherical CFD-DEM coupling model in different applications involving particle-fluid flows. In the end, the conclusions and the outlooks for future investigations are given.
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This paper presents a novel implementation of a hydro-mechanically coupled, finite-discrete element method (FDEM) optimized to exploit the computing parallelism of graphics processing units (GPUs). A ...co-processing approach is adopted with the control loop of FDEM executed serially on the CPU and compute-intensive tasks off-loaded to the GPU. A benchmarking study indicates speedups of up to 100× compared to sequential CPU execution. The implementation is validated by comparing 3D laboratory-scale rock fracturing simulations with experimental results. The effectiveness of the approach for practical rock engineering applications is demonstrated through the back analysis of a slope in a fractured rock mass.
Discrete element method (DEM) is widely used in industrial and environmental applications for numerical modelling of mixing and transport of lumpy materials. However, it is computationally expensive ...for a large number of particles. To reduce this cost, we have implemented a revision approach for traditional coarse graining as proposed by Bierwisch et al. J. Mech. Phys. and Solids, 57, 31, 2009. We introduce the use of variable coarse grain ratio instead of the uniform one to provide faster computation compare to the traditional coarse graining giving more flexibility to reduce the number of particles. To overcome the problem of violation of geometrical similarity derived from this method, we implement a correction parameter to measure overlap distance between parcels containing small and large particles. The results show fairly good agreement between the revision model, reference DEM simulations and the experimental data of W. Sui et al. Nature Sci. Reports, 7, 8, 2017.
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•Introducing a faster alternative tool for poly disperse granular flow simulation.•The simulation results are validated with respect to experimental data.•Better accuracy in particle distribution compare to traditional coarse graining.•Providing a prediction method for the revision parameter.
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