discrete element method

Unlike the mechanical properties of intact rock, which can be obtained on a laboratory scale, estimating the mechanical properties of the jointed rock mass is very difficult due to the presence of different joints and the complexity of the joints. Therefore, to calculate the mechanical parameters of the jointed rock mass and use the continuous media theory of the jointed rock mass, it is necessary to calculate the Representative Element Volume (REV) of the rock mass. In this study, the Discrete Element Method (DEM) and the mechanical index of strength were used to investigate the effect of persistent and non-persistent joint angles, as well as model size on the REV in x, y, and z directions. The numerical results showed that by changing the joint angles and side length, both the strength and the REV of the rock mass were affected. The maximum representative side length for the persistent joint in the x and z directions occurred at angles of 60° and 75°, respectively. The minimum strength was obtained for joints in the x and z directions at a 45° angle. Finally, the REV for persistent and non-persistent joints is calculated as 10*0.5*8m and 4*0.5*4m, respectively.

The mechanical behavior of rock-rock bolt interface considering the effects of indents’ shape and their number was numerically simulated based on discrete element method using the two-dimensional particle flow code. The conventional and standard uniaxial compressive and Brazilian tensile strengths tests were used to calibrate the modelled samples with 100 cm 100 cm in dimension. The numerical models were prepared such that different indent shape and number were inserted in the cable bolts arrangements during the rock reinforcement process. The effects of confining pressure 3.7 MPa and different shear failure loads were modeled for the punch shear test of the concrete specimens. The results of this study showed that the dominant failure mode of the rock-cable bolt interface was of tensile mode and the shape and number of cable indents significantly affected the strength and mechanical behavior of the modelled samples. It has also been showed that the indent dimensions and number affected the shear strength of the interfaces.

Around 70% of the world's hydrocarbon fields are situated in reservoirs containing low-strength rocks, such as sandstone. During the production of hydrocarbons from sandstone reservoirs, sand-sized particles may become dislodged from the formation and enter the hydrocarbon fluid flow. Sand production is a significant issue in the oil industry due to its potential to cause erosion of pipes and valves. Separating grains from oil is a costly process. Oil and gas companies are motivated to reduce sand production during petroleum extraction. Hydraulic fracturing is one of the parameters that can influence sand production. However, understanding the complex interactions between hydraulic fracturing mechanisms and sand production around wellbores is critical for optimizing reservoir recovery and ensuring the integrity of production wells. This article explores the integrated simulation approach to model hydraulic fracturing processes and assess their effects on sand production. Two-dimensional models were created using the discrete element method in PFC2D software for this research. The fractures' length in the models varies based on the well's radius. The angle between two fractures at 90 and 180 degrees to each other was also modeled. In the first case, the length of the fracture is less than the radius of the well, in the second case, the values are equal and finally, the fracture length is assumed to exceed the well radius. The calibrated and validated results demonstrate the change in sand production rate in comparison to the unbroken state.

This work presents the hollow center cracked disc (HCCD) test and the cracked straight through Brazilian disc (CSTBD) test of oil well cement sheath using the experimental test and Particle Flow Code in two-dimensions (PFC2D) in order to determine mode I fracture toughness of cement sheath. The tensile strength of cement sheath is 1.2 MPa. The cement sheath model is calibrated by outputs of the experimental test. Secondly, the numerical HCCD model and CSTBD model with diameter of 100 mm are prepared. The notch lengths are 10 mm, 20 mm, 30 mm, and 40 mm. The tests are performed by the loading rate of 0.018 mm/s. When the notch length in CSTBD is 40 mm, the external work is decreased 48%, related to the maximum external work of model with notch length of 10 mm (0.225 KN*mm decreased to 0.116 KN*mm). When the notch length in HCCD is 30 mm, the external work is decreased 33%, related to the maximum external work of model with notch length of 10 mm (0.06 KN*mm decreased to 0.04 KN*mm). The fracture energy is largely related to the joint length. The fracture energy is decreased by increasing the notch length. In constant to the notch length, the fracture energy of the CSTBD model is more than the HCCD model. Mode I fracture toughness is constant by increasing the notch length. The HCCD test and the CSTBD test yield a similar fracture toughness due to a similar tensile stress distribution on failure surface. The experimental outputs are in accordance to the numerical results.

This work presents the Semi-Circular Bend (SCB) test and Notched Brazilian Disc (NBD) test of shotcrete using experimental test and Particle Flow Code in two-dimensions (PFC2D) in order to determine a relation between mode I fracture toughness and the tensile strength of shotcrete. Firstly, the micro-parameters of flat joint model are calibrated using the results of shotcrete experimental test (uniaxial compressive strength and splitting tensile test). Secondly, numerical models with edge notch (SCB model) and internal notch (NBD model) with diameter of 150 mm are prepared. Notch lengths are 20 mm, 30 mm, and 40 mm.  The tests are performed by the loading rate of 0.016 mm/s. Tensile strength of shotcrete is 3.25 MPa. The results obtained show that by using the flat joint model, it is possible to determine the crack growth path and crack initiation stress similar to the experimental one. Mode I fracture toughness is constant by increasing the notch length. Mode I fracture toughness and tensile strength of shotcrete can be related to each other by the equation, σt = 6.78 KIC. The SCB test yields the lowest fracture toughness due to pure tensile stress distribution on failure surface.

One of the important cost items in mechanized tunneling is the cost of repairing or replacing the disc cutters that have suffered from normal wear during the boring of the hard abrasive rocks. For inspecting the health of the disc cutters, the boring operation shall be stopped, and after checking, the worn disc cutters may be replaced. In this work, the dynamic process of the TBM boring in the jointed rocks is simulated using a real-scale numerical analysis based on the rock fracturing factor using the discrete element method (DEM). The stress distributions induced within the disc cutters as well as the development of the plastic zones in the rock are investigated and compared with the actual results recorded in the Kerman water conveyance tunnel (KWCT). The numerical results indicate that the increase in the rock fracturing causes a decrease in the induced stresses and an increase in the size of the plastic zone. In other words, a higher penetration rate as well as more lifetime for disc cutters can be achieved in highly fractured rocks. Moreover, the average von Misses stress in the disc cutters in the highly fractured rocks is predicted about 16-23% less than stress induced in the slightly fractured rocks. Due to the TBM tunneling, the volume of the plastic zone as well as the actual penetration depth in the highly fracturing rocks are also about 40% and 42% higher than in the slightly fractured rocks under applying the same TBM parameters, respectively.

Split Hopkinson Pressure Bars (SHPB) test is widely used among the various methods for investigating the dynamic behavior of rocks at high strain rates. Various factors affect the waveform and the results of this test. In this study, the aim was to investigate the effect of geometrical parameters of strikers including the effect of shape, length, and impact cross-section width (ICSW) on the waveform induced in the SHPB test using numerical modeling. For this purpose, in the first stage, the required information including geometrical properties and the required micro-parameters have been collected from two laboratory and numerical modeling studies. Then, the initial model was constructed using the discrete element numerical method (DEM), and its results were compared with laboratory and numerical results. Evaluation of the effect of striker shape demonstrated that SS strikers have induced a semi-sinusoidal wave and CS strikers have induced a quasi-rectangular wave. Among the waveform properties, the wavelength was strongly related to the geometric properties of the strikers in both CS and SS types in a way that was directly related to the striker’s length and inversely related to the ICSW. On the other hand, the maximum amplitude is directly related to the striker’s length and ICSW in both CS and SS types. According to the results, the use of SS strikers is more appropriate according to the waveform, and its geometric properties can be determined according to the problem requirement, using numerical modeling results.

Investigating the crack propagation mechanism is of paramount importance in analyzing the failure process of most materials. This process may be exposed during each kind of loading on the materials. In this work, the cracking mechanism in rock-like materials is studied using the numerical methods and compared with the experimental test results. However, the mechanism of crack growth in brittle materials such as rocks is influenced by different parameters. This research work focuses on the effect of the initial crack angles on the crack growth paths of these materials. Some cubic samples containing pre-existing cracks are tested in compression by considering different flaw orientations. The specimens are made of cement, water, and sand. Moreover, the mentioned process is numerically simulated using three different methods the finite difference method for discontinuous bodies or discrete element method, the displacement discontinuity method, and the versatile finite element method. The micro-parameters for simulation are gained by the trial-and-error procedure for the discrete element method. Eventually, the crack growth paths observed in the experiments are compared with the numerically simulated models. The results obtained show that these central cracks propagate in two ways, which are dependent on their initial angle. By increasing the initial crack angle to greater than 30° (α > 30°), the wing crack path moves further away from the initial crack, and by decreasing α to smaller than 30° (α < 30°), only the shear cracks are initiated. Therefore, the validity and accuracy of the results are manifested by comparing all the corresponding results obtained by different methods. Based on these results, it can generally be concluded that the strength of the cubic (rock material) specimens increases with increase in the crack angles with respect to the applied loading direction.

The explosion process of explosives in a borehole applies a very high pressure on its surrounding rock media. This process can initiate and propagate rock fractures, and finally, may result in the rock fragmentation. Rock fragmentation is mainly caused by the propagation of inherent pre-existing fractures of the rock mass and also from the extension of the newly formed cracks within the intact rock due to the explosion. In this work, the process of extension of blast-induced fractures in rock masses is simulated using the discrete element method. It should be noted that, in this work, fracture propagation from both the rock mass inherent fractures and newly induced cracks are considered. The rock mass inherent fractures are generated using the discrete fracture network technique. In order to provide the possibility of fracture extension in the intact rock blocks, they are divided into secondary blocks using the Voronoi tessellation technique. When the modeling is completed, the fracture extension processes in the radial and longitudinal sections of a borehole are specified. Then a blast hole in an assumed rock slope is modeled and the effect of pre-splitting at the back of the blast hole (controlled blasting) on the fracture extension process in the blast area is investigated as an application of the proposed approach. The modeling results obtained show that the deployed procedure is capable of modeling the explosion process and different fracture propagations and fragmentation processes in the rock masses such as controlled blasting.

Due to existence of uncertainties in input geometrical properties of fractures, there is not any unique solution for assessing the stability of slopes in jointed rock masses. Therefore, the necessity of applying probabilistic analysis in these cases is inevitable. In this study a probabilistic analysis procedure together with relevant algorithms are developed using Discrete Fracture Network-Distinct Element Method (DFN-DEM) approach. In the right abutment of Karun 4 dam and downstream of the dam body, five joint sets and one major joint have been identified. According to the geometrical properties of fractures in Karun river valley, instability situations are probable in this abutment. In order to evaluate the stability of the rock slope, different combinations of joint set geometrical parameters are selected, and a series of numerical DEM simulations are performed on generated and validated DFN models in DFN-DEM approach to measure minimum required support patterns in dry and saturated conditions. Results indicate that the distribution of required bolt length is well fitted with a lognormal distribution in both circumstances. In dry conditions, the calculated mean value is 1125.3 m, and more than 80 percent of models need only 1614.99 m of bolts which is a bolt pattern with 2 m spacing and 12 m length. However, as for the slopes with saturated condition, the calculated mean value is 1821.8 m, and more than 80 percent of models need only 2653.49 m of bolts which is equivalent to a bolt pattern with 15 m length and 1.5 m spacing. Comparison between obtained results with numerical and empirical method show that investigation of a slope stability with different DFN realizations which conducted in different block patterns is more efficient than the empirical methods.