هادی حائری

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.

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.

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 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.

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 discontinuities are formed in different levels of concrete as a result of various curing processes. There are only few cases where cause and location of failure of a concrete structure are limited to a single discontinuity. Usually several discontinuities of limited size interact and eventually form a combined shear plane where failure takes place. So, besides the discontinuities themselves, the regions between adjacent discontinuities, which consist of strong concrete and are called concrete bridges, are of utmost importance for the shear strength of the compound failure plane. Also, the coalescence of non-persistent joints is important factors in controlling the mechanical behavior of brittle rocks and can be caused concrete failure in slopes, foundations and tunnels. Therefore, a comprehensive study on the shear behavior of non-persistent joint can provide a good understanding of both local and general concrete instabilities, leading to an improved design for concrete engineering projects. From last decade, direct shear test have been used to study shear behavior of echelon joint. Whereas, only one horizontal shear failure surface can be formed within the shear box therefore, it’s not possible to perform shear test on the echelon non-persistent joint. This paper introduces the modified shear box so the shear test can be performed on the both of the overlapped and non-overlapped echelon joint.

The presence of openings in concrete structure has destructive effect on the lifetime. In this paper, the interaction between two openings has been investigated using particle flow code. For this purpose, after calibration of model, one small opening has been situated in various distances and various angularities from big pore opening. The radius of smaller opening is 0.2 of radios of big opening.  This complex is situated in a concrete slab with uniaxial strength of 7 MPa. This slab is under principal stress of 2MPa and 6 MPa. The results show that spacing and angularity of small opening has important effect on the stress distribution and failure pattern around the big opening. The critical position for small opening is when it situated at 0.0 degree. Also the spacing between two openings is less, the failure volume is more.

Investigation of behavior of non-persistent joint is important in rock structure stability. This leads to improvement in rock engineering project design. Rock bridges in non-persistent joint increase shear strength of failure surface. For investigation of shear behavior of rock bridge, 24 gypsum samples with dimension of 10 cm × 10 cm × 5 cm were prepared. The joint lengths in various samples are different but in the one sample the joint length are similar. Joint lengths change from 1 cm to 4 cm. in each joint length, joint angularity was 0, 15, 30, 45, 60, 75 degrees. These samples were tested under uniaxial compression test. The results show that failure pattern was affected by joint length, joint angularity and rock bridge length while failure load was controlled by failure pattern. Concurrent with experimental test, numerical simulation was performed using PFC2D software. The joint lengths in numerical model change from 1cm to 4 cm with increment of 1cm. In each joint length, the joint angularity is 0° and 45°. Failure pattern in numerical model was similar to experimental sample while failure load in numerical model was more than experimental outputs.

In this paper, a compressive to tensile load convertor (CTC) device has been introduced which can be used for induction of tensile failure in specimen. This devise was consisted of 7 different parts. Parts number 1 and 2 which have U shape and П shape section have been made from stainless steel. Parts number 3 and 4 were made from two semi-cylindrical stainless steels with dimension of 10mm × 75mm × 60mm. Parts number 5 and 6 were made from two stainless steels with dimension of 190mm × 10mm × 20 mm. The concrete specimens used in this test have rectangle shape with internal pore. This geometry was gained from FRANC2D simulation outputs. The concrete samples has been prepared by mixing water, fine sand and cement by the ratio of 40%, 30% and 30%. The CTC device and sample were inserted in uniaxial test machine. The tensile test was performed by conversion of compression load to tensile load using CTC test. The tensile failure pattern occurred in the sample. For validation of experimental results, numerical simulations have been done using FRANC2D and high order displacement discontinuity method. The good accordance between failure pattern in numerical simulations and experimental test shows the validation of introduced device in induction of tensile failure in specimens.

In this paper, a simultaneous experimental and numerical analysis of opening mode toughness in The Pre-joined Brazilian disc using Brazilian tests are carried out. These numerical results are compared with the existing experimental results. For this purpose, two concrete disc specimens of 54 mm diameter and 27 mm thick were prepared. These specimens have a central joint of 20 mm in length and an opening in mm 1. Specimens are made from a mixture of water, fine sand, and cement with a ratio of 1-5 / 0-1. The same specimens are numerically simulated by a two-dimensional particle flow code (PFC).The results indicate that the crack formed from the tip of the joint and grows parallel to the load and connects to the edge of the specimen. The Fracture toughness obtained from the numerical method is in good agreement with experimental results.

The rocks with pre-existing cracks are normally under compression. Study of the propagation mechanism of these pre-existing cracks is important in the design of rock structures. In the present paper، a coupled numerical-experimental analysis of crack propagation، cracks coalescence and breakage process of brittle solids such as rocks and rock-like specimens are studied. The pre-cracked cylindrical specimens of rock-like materials (using specially made rock-like specimens from Portland Pozzolana Cement (PPC)، fine sand and water) tested under compressive loading. Several tests accomplished on the rock-like specimens containing two cracks to evaluate the final breakage path in these samples. The effect of the orientations of these two cracks with a constant spacing on the crack propagation paths and cracks coalescence have been experimentally investigate. These results show that the changing in the orientation of the second crack affect the crack growth and coalescence paths. The same specimens simulated numerically by an indirect boundary element method known as displacement discontinuity method. The numerical and experimental results obtained from the tested specimens compared with each other and showing good agreements between the corresponding values. The accuracy، validity and effectiveness of these approaches are quite evident by comparing these experimental and numerical results.