وهاب سرفرازی

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.

The mechanical behaviour of transversely isotropic elastic rocks can be numerically simulated by the discrete element method. The successive bedding layers in these rocks may have different mechanical properties. The aim of this research work is to investigate numerically the effect of anisotropy on the tensile behaviour of transversely isotropic rocks. Therefore, the numerical simulation procedure should be well-calibrated by using the conventional laboratory tests, i.e. tensile (Brazilian), uniaxial, and triaxial compression tests. In this study, two transversely isotropic layers were considered in 72 circular models. These models were prepared with the diameter of 54 mm to investigate the anisotropic effects of the bedding layers on the mechanical behaviour of brittle geo-materials. All these layers were mutually perpendicular in the simulated models, which contained three pairs of thicknesses 5 mm/10 mm, 10 mm/10 mm, and 20 mm/10 mm. Three different diameters for models were chosen, i.e. 5 cm, 10 cm, and 15 cm. These samples were subjected under two different loading rates, i.e. 0.01 mm/min and 10 mm/min. The results gained from these numerically simulated models showed that in the weak layers, the shear cracks with the inclination angles 0° to 90° were developed (considering 15° increment). Also there was no change in the number of shear cracks as the layer thickness was increased. Some tensile cracks were also induced in the intact material of the models. There was no failure in the interface plane toward the layer of higher strength in this research work. The branching was increased by increasing the loading rate. Also the model strength was decreased by increasing the model scale.

In this paper, the effect of variations in the number and area of the rock bridges on the non-persistent discontinuities is investigated. In this regard, blocks containing rock bridges and joints with dimensions of 15 cm * 15 cm * 15 cm are prepared from plaster. The available rock bridges that have occupied 0.2, 0.4, and 0.6  of the shear surface show latitudinal extension along the shear surface. There are variations in the number and extension of the rock bridges in the fixed area. For each of the samples, tests are performed on three blocks of the same material, by putting it under various direct normal stresses. Normal stresses were 3.33, 5.55, 7.77 kg/cm2. Also the obtained shear strength by laboratory tests was compared with the outputs of Jenning's criterion and Guo and Qi's criterion to determine the accuracy of these criteria for predicting the shear strength of non-persistent joints. The results show that the tensile crack started in the rock bridge under normal stress of 3.33 kg/cm2. Mixed-mode tensile shear cracks were propagated in the rock bridge under a normal stress of 5.55 kg/cm2, while a pure shear crack developed in the rock bridge under a normal stress of 7.77 kg/cm2. With the increase of normal stress, the number of microfractures increased. The variance in the number of rock bridges in the fixed area of the rock bridge does not affect the friction angle along the shear surface. Furthermore, the cohesion along the shear surface shows a small decrease with the increasing number of rock bridges. Also by the increase in the area of rock bridges, the friction angle along the shear surface remains constant, while at the same time, there is an almost linear increase in cohesion. Guo and Qi's criterion predicts the shear strength of the non-persistent joint exactly close to the shear strength of the physical samples.

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.

The tensile strengths of geomaterials such as rocks, ceramics, concretes, gypsum, and mortars are obtained based on the direct and indirect tensile strength tests. In this research work, the Brazilian tensile strength tests are used to study the effects of length and inclination angle of T-shaped non-persistent joints on the mechanical and tensile behaviors of the geomaterial specimens prepared from concrete. These specimens have a thickness of 40 mm and a diameter of 100 mm, and are prepared in the laboratory. Two T-shaped non-persistent joints are made within each Brazilian disc specimen. The Brazilian disc specimens with T-shaped non-persistent joints are tested experimentally in the laboratory under axial compression. Then these tests are simulated in the two-dimensional particle flow code (PFC2D) considering various notch lengths of 6, 4, 3, 2, and 1 cm. However, different notch inclination angles of 0, 30, 60, 90, 120, and 150 degrees are also considered. In this research work, 12 specimens with different configurations are provided for the experimental tests, and 18 PFC2D models are made for the numerical studies of these tests. The loading rate is 0.016 mm/s. The results obtained from these experiments and their simulated models are compared, and it is concluded that the mechanical behavior and failure process of these geomaterial specimens are mainly governed by the inclination angles and lengths of the T-shape non-persistent joints presented in the samples. The fracture mechanism and failure behavior of the specimens are governed by the discontinuities, and the number of induced cracks when the joint inclination angles and joint lengths are increased.  For larger joints when the inclination angle of the T-shaped non-persistent joint is around 60 degrees, the tensile strength is minimum but as it is closed to 90 degrees, the compressive strengths are maximum. However, an increase in the notch length increase the overall tensile strength of the specimens. The strength of samples decreases by increasing the joint length. The strain at the failure point decreases by increasing the joint length. It is also observed that the strength and failure process of the two sets of specimens and the corresponding numerical simulations are consistence.

One of the most important tasks in conducting a laboratory research work is how to make the samples. The purpose of this research work is to create heterogeneous rock-like samples containing non-persistent notches. Regarding that, the molds with dimensions of 250 mm x 200 mm x 50 mm are made. A mixture of plaster and water with different mixing percentages is used to make the heterogeneous samples. Various techniques are also employed to create non-persistent notches on the samples. One of the methods to create a notch is to insert an aluminum blade into the groove of the mold, and finally, remove it after the plaster slurry has hardened. Due to the displacement of the blade and its tilting during slurring, the notches are out of the vertical position. In addition to the mentioned method, other methods such as water jet, cutting by thread, cutting by diamond wire cutting, cutting by rotary saw, and using hand saw are applied. Finally, using a hand saw to create a notch on the samples is chosen as the best method.

In this work, the mechanical behavior of strata deformation due to drilling and surface loading is investigated using a 3D physical model. For this purpose, a scaled-down physical model is first designed. Then the tunnel drilling and support system are built. The subsidence experiments performed due to tunnel excavation and loading in a very dense and loose soil are performed. Soil is clayey sand (SC), and the percentages of its components are as sand (S = 1. 41%), gravel (G = 25%), and clay (C = 9.33%). Unstable tunnel support experiments are also carried out using physical simulation. Finally, deformations of soil surface and subsidence of strata are observed and recorded. In the tunnel with segmental support, 18.75% more load is applied than in the unsupported tunnel, and the total subsidence of the strata is reduced by 36.2%. The area of the deformed inner layers is decreased by 74.2%, and the length of the affected area in the largest layer is decreased by 48%. The depth of the cavity created at the surface is 46.66% less.

The interaction between an internal hole and two surrounded joints under a uniaxial compression are examined using the experimental and discrete element procedures. Inside the concrete sample, two notches and an internal hole are created. The joint angle change from 0° to 90° with an increment of 30°. The distances between the joint and the internal hole are 2 cm and 3 cm. Also the numerical models are provided. The joint angle change from  0° to 90° with an increment of 15°. The distances between the joint and the internal hole are 2 cm, 3 cm, and 4 cm. The compressive strength is 7.2 MPa. The rate of loading is 0.005 mm/s. The experiment indicates that the failure process is significantly dependent on the notch angle and the joint distance from the hole. The pattern of fracture and mechanism of failure of joints affect the shear strengths of the samples. The models with joint angles of 30° and 60° have a less compressive strength since the pure tensile failure occurs in these configurations. The model strength decreases with decrease in the join spacing. In fact, in the case that the joint spacing is 2 cm, the interaction between the hole and the neighboring joint is so strong. Consequently, the compressive strength is declined. In both approaches of the numerical simulation and experimental methods, the pattern and strength of failure are identical.

Particle Flow Code in Two Dimensions (PFC2D) was used in order to examine the influence of single tunnel and twin tunnel on the collapse pattern and maximum ground movement. Since first PFC was calibrated by the experiments, the results obtained were rendered by a uniaxial test. Further, a rectangular model with dimensions of 100 m ˟ 100 m containing both the central tunnel and twin tunnel was built. The center of the single tunnel was placed 25 m under the ground surface, and its diameter changed from 10 m to 35 m with an increment of 5 m. The center of the twin tunnel was situated 25 m under the ground surface, and its diameter was changed from 10 m to 30 m with an increment of 5 m. For measurement of the vertical displacement, one measuring circle with a 2 m diameter was opted on the ground surface above the tunnel roof. The average of the vertical movement of discs covered in these circles was determined as a ground settlement. A confining pressure of 0.01 MPa was applied on the model. The uniaxial compression strength was 0/09 MPa; the results obtained depicted that the tunnel diameter controlled the extension of the collapse zone. Also the vertical displacement at the roof of the tunnel declined by decreasing the tunnel diameter. The ground settlement increased by increasing the tunnel diameter.

In this investigation, the impact of confining pressure on the tensile strength obtained by point load test (PLT) is examined by particle flow code in two dimensions. In this regard, at first, a numerical model is calibrated using the Brazilian experimental test results. The tensile strength of the model material is equal to 2.5 MPa. Secondly, PLT is performed on the numerical models with dimension of 15 cm × 50 cm. The rectangular models are tested by PLT under the presence of the confining pressure. The loading rate is 0.001 mm/min, confining that the pressure is changed with the 13 different values of 0 MPa, 0.002 MPa, 1MPa, 1.5 MPa, 2 MPa, 2.5 MPa, 3MPa, 3.5 MPa, 4 MPa, 5MPa, 6 MPa, 9 MPa, and 11 MPa. The results obtained show that the vertical tensile crack develops through the model under a low confining pressure, while several shear bands are developed in the models under a high confining pressure. The number of shear cracks is augmented by augmenting the confining pressure. Is(50) is the augment by augmenting the confining pressure. Also a new criterion is rendered in order to determine Is(50) based on the confining pressure.

The propagation mechanism of cracks emanating from two holes within the concrete specimens is studied by considering the effects of different lateral compressive stresses. The experimental part of this research work is carried out on some specially prepared pre-cracked specimens with two neighbouring holes under only a uniaxial compression in the laboratory. The numerical modeling part is performed under both the uniaxial compresion and the lateral confinment by the 2D particle flow code (PFC2D). It is shown that the lateral confinement may change the path of crack propagation in a specimen compared to that of the uniaxially-loaded one. Various senarios of the mixed mode radial crack propagation around the holes are obtained, and both the wing (induced tensile) cracks and secondary (shear) cracks are produced and propagated in various paths due to a change in the confining pressure. The fracturing pattern changes from a single tensile crack to that of the several shear bands by increasing the confining pressure. Also the number of shear cracks is increased by increasing the lateral confinement.On the other hand, as the confining pressure increases, the wing cracks start their growth from the walls and reach the center of the cracks under high confinements.

In this work, we investigate the interaction between tunnel and surface foundation in two dimensions by the particle flow code. At the first stage, the PFC calibration is conducted using the experimental test results rendered by a biaxial test. Then the simulation of a biaxial test is performed by confining a rectangular sample inside four walls. The walls are located at the top and bottom simulated loading plates and the adjacent walls are located at the left and right simulated sample side confinement. The velocities of the top and bottom walls are determined, and they are used for loading the sample in a strain-controlled mode. The respond of the material is evaluated by following the diverse stress and strain quantities. The axial deviatoric stress versus the axial strain for biaxial test on the bonded granular material is drawn, and then the Mohr's circle is drawn in order to reach the failure envelope of laboratory. Secondly, a rectangular model with dimensions of 10 m 10 m containing a central tunnel and a surface foundation is built. The tunnel is situated in sixteen different positions below the foundation. The foundation moves downward with a velocity of 0.016 mm/s. The results obtained show the position of the tunnel controlling the failure volume. Also the vertical displacement at the roof of the tunnel decreases by increasing the vertical spacing between tunnel and foundation. The settlement beneath the foundation increases by reducing the vertical spacing between the tunnel and the foundation. The settlement beneath the foundation decreases by augmenting the horizontal spacing between the tunnel and the foundation.

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 tensile strength of the anisotropic rock-like material specimens is meastred directly in the laboratory using a new device converting the compressive loading to that of the tensile before the rock breakage. The specially prepared concrete slabs of dimensions 19 cm * 15 cm * 15 cm with a central hole of 7.5 cm in diameter are tested experimentaly. The specimens are located in the compressive-to-tensile load converting device, and tested under a compressive loading rate of 0.02 MPa/s by the universal testing machine. The cubic slab samples are made in three different configurations to have the directions of  0°, 45°, and -45° with respect to the applied loading direction. In order to compare the direct tensile strength of the concrete samples with that of the indirect measuring tests, some Brazilian tests are also carried out on the concrete disc specimens prepared in the laboratory. By comparing the direct and indirect testing results of the concrete tensile strength, it can be concluded that the direct tensile strength values are somewhat lower than those of the indirect ones. The tensile strength values for the three different configurations of the concrete specimens are nearly the same.

The experimental and numerical methods were used to investigate the effects of joint number and joint angle on the failure behaviour of rock pillars under a uniaxial compressive test. The gypsum samples with dimensions of 200 mm × 200 mm × 50 mm were prepared. The compressive strength of the intact sample was 7.2 MPa. The imbeded joint was placed inside the specimen. The joint length was 6 cm in a constant joint length. There were several numbers of cracks including one, two, and three cracks. In the experimental tests, the angles of the diagonal plane with respect to the horizontal axis were 0, 30, 60, and 90 degrees. The axial load was applied to the model with a rate of 0.01 mm/s. In the fracture analysis code, the angles of the diagonal plane with respect to the horizontal axis were 0, 15, 30, 45, 60, 75, and 90 degrees. A constant axial load of 135 MPa was applied to the model. The results obtained showed that the failure process was mostly dependent on the angle and number of the non-persistent joint. The compressive strength of the samples was dependent on the fracture pattern and the failure mechanism of the discontinuities. It was shown that the tensile cracks were developed whithin the model. The strength of the specimens increased by increasing both the joint angle and joint number. The joint angle of 45°  KI had the maximum quantity. The stress intensity factor was decreased by increasing the joint number. The failure pattern and failure strength were analogous in both methods, i.e. the experimental testing and the numerical simulation methods.

In this work, the effect of rock bolt angle on the shear behavior of Rock Bridges is investigated using the particle flow code in two dimensions (PFC2D) for three different Rock Bridge lengths. Firstly, the calibration of PF2D is performed to reproduce the gypsum sample. Then the numerical models with the dimensions of 100 mm * 100 mm are prepared. The Rock Bridge is created in the middle of the model by removal of the narrow bands of discs from it. The uniaxial compressive strength of the Rock Bridge is 7.4 MPa. The Rock Bridge lengths are 30 mm, 50 mm, and 70 mm. The rock bolt is calibrated by a parallel bond. The tensile strength of the simulated rock bolt is 360 MPa.One rock bolt is implemented in the Rock Bridge. The rock bolt angles related to the horizontal axis are the changes from 0 to 75 degrees. Totally, 18 models are prepared. The shear test condition is added to the models. The normal stress is fixed at 2 MPa, and the shear load is added to the model till failure occurs. The results obtained show that in a fixed rock bolt angle, the tensile crack initiates from the joint tip and propagates parallel to the shear loading axis till coalescence to rock bolt. In a constant Rock Bridge length, the shear strength decreases with increase in the rock bolt angle. The highest shear strength occurs when the rock bolt angle is 0°.

In this work, the interaction between the semi-circular space and the neighboring joint with and without the presence of rock bolts was investigated using the particle flow code (PFC) approach. For this purpose, firstly, the calibration of PFC was performed using both the Brazilian experimental test and the uniaxial compression test. Secondly, a numerical model with the dimension of 100 mm * 100 mm was prepared. A semi-circular space with a radius of 25 mm was situated below the model. A joint with a length of 40 mm was situated above the space. The joint opening was 2 mm. The joint angles related to the horizontal direction were 0°, 15°, 30°, 45°, 60°, and 75°. Totally, 6 different configurations of the semi-circular space and neighboring joint were prepared. These models were tested with and without the presence of vertical rock bolts by the biaxial test. The rock bolt length was 50 mm. The value of the lateral force was fixed at 2 MPa. An axial force was applied to the model till the final failure occurred. The results obtained showed that the presence of rock bolts changed the failure pattern of the numerical model. In the absence of rock bolts, two tensile wing cracks initiated from the joint tip and propagated diagonally till coalescence from the model boundary. Also several shear bands were initiated in the left and right sides of the tunnel. In the presence of rock bolts, several shear bands were initiated in the left and right sides of the tunnel. The compressive strength with the presence of rock bolts was more than that without the presence of rock bolts. The failure stress had a minimum value when the joint angle was 45°.

The aim of this study is analyzing the failure modes of sandstones related to Markazi Province using compressive strength changes. For this purpose, the fracture modes of five different types of sandstones with different compressive strength values have been studied experimentally and numerically. Also, The effect of failure modes on uniaxial compressive strength was quantified. block samples were collected from different sandstone formations located in northern part of Markazi province. These sandstones were divided into five types based on the textural and mineralogical characteristics. These samples were subjected to uniaxial compressive strength testing. Examination of the fracture modes showed that simple shear mode occurred at low values of strength and it changes to multiple extension mode with increasing the compressive strength. The dominant failure mode for types 1, 2 and 4 is simple shear and for types 3 and 5 is multiple extension. Investigation of failure modes in different strength ranges showed that the dominant failure modes up to 140 and over 140 MPa are simple shear and multiple extension, respectively. Therefore, strength of 140 MPa was considered as the transisson point. Also, in this study, the failure modes of the experimental samples were numerically simulated using PFC2D software. The results of numerical modeling showed a good agreement with the experimental results.

The dimension of underground structure is a key factor in its stability. Rock blotting has important effect in rock mechanic projects. It increases the stability of rock blocks. The performance of rock bolt is depending on the quality of its set up. Quality of its set up is determined by pull out test method. Numerical simulation is other method for determination of rock blotting behavior. In this paper, the effect of tensile loading on the “Y” shape joint is determined using FRANC2D. The angularity of large joint tail (β) changes from 0° to 90° with increment of 45°. The angularity of small joint tail related to large joint tail (α) changes from 20° to 160° with increment of 20°. The spacing between joint and loading place change from 2a to 4a with increment of “a” which “a” is the length of large joint tail. Totally 52 model were simulated. In the case of horizontal joint the crack growth length is maximum and vertical joint has minimum effect on the crack growth. When the angularity of large joint tail related to horizontal was 45°, the maximum of crack growth was occurred. The maximum of crack growth from small joint tail was occurred when it is in horizontal configuration. The maximum number of small joint tail growth occurred when its angularities related to horizontal axis was 45°.