Journal of Engineering Geology

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In this study, seepage phenomena through the left abutment of Marun dam are investigated. The Marun dam is a 170 m high rock fill dam, which regulates the waters of the Marun River, serves power generation, and flood control and provides irrigation needs. The dam site lies in the Zagros Mountains of southwest Iran. This region presents continuous series of mainly karstic limestone, marl, shale and gypsum ranging in age from Cretaceous to Pliocene. The region has subsequently been folded and faulted. All underground excavations are sited in the left abutment. The spacing of the diversion tunnels and pressure tunnel is considered to be acceptable, meaning relatively short, thus requiring 2 row grouting curtain into both embankments. Prior the reservoir impoundment, the concrete plug was constructed into the middle section of second diversion tunnel. Upstream section of tunnel was not concreted. During the first reservoir impounding, the old karst channels along ‘Vuggy Zone’ cut by the second diversion tunnel were reactivated and leakage occurred. The total amount of water leakage through the left bank of Marun dam was about. The unlined second diversion tunnel had a key role in connecting reservoir with karst conduit system. On the basis of detailed engineering geological analysis, the concept of remedial works was carried out. The main points of this concept are one of row grout curtain extension up to the section with shaly interbeds declared as watertight Asmari sequence (close to the watertight Pabdeh formation) and plugging of accessible section of main karst channel by concrete. In order to determine the seepage direction and karstification pattern, solubility studies were done. Also pinhole, XRD and XRF tests were carried out. The major joint system and interbedding cracks have predominant role in karst evolution process. Hydrogeological role of joints, perpendicu-lar to geological structure, is not negligible. As a result of these studies, seepage paths have been identified in the karstic limestone in the left abutment of the dam.

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Schmidt hammer is used for calculation of joint compressive strength and elasticity modulus of rocks. Today, application of Schmidt hammer is a common method in evaluation of properties of rocks. This method is quick, inexpensive and non-destructive which are benefits of this method. In this regard, different experimental equations proposed by Barton & Choubey (1977), Deere (1960), Keadbinski (1980), Aufmuth (1973) and ISRM (1981) can be employed in order to calculate the Joint Compressive Strength (JCS) of rocks. Due to the importance of this research, new experimental equations are introduced. Using this equations show a very good results in comparison with the results of other researchers. It should be noted that this equations are achieved from 827 records of Schmidt Hammer results from different types of hard rocks such as granite, diorite and hornfels from the Ganjnameh-Shahrestaneh road in Hamedan province, west of Iran.

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In the karstic areas, detailed studies of phenomena such as seepage of water from hydraulic structures and land subsidence in the residential and quarry areas  is of  higher importance. In this study, the dissolution rate constant of gypsite samples of Gachsaran Formation, obtained from the Chamshir dam reservoir, were measured equal to 0.24×10^-3 cm/sec. Then, the changes of amounts of joint apertures using theoretical and experimental (by changes of joint water flowing and direct measurement) methods were calculated. The results showed that the predicted aperture for joints calculated through theoretical method is less consistent with the measured value of the changes of joint water flowing while the value measured by direct method (measured using a caliper) compliance is higher. Also based on research findings, if gypsites of the dam reservoir are exposed to the water flow, the amount of aperture of a joint with 0.5 cm initial opening will increase to 10 cm after about 278 days. This increase in joint aperture compared with the useful life of the dam draws for special attention to water tightening of dam reservoir.

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Discontinuities have properties such as orientation, number of set and frequency that can affect the rock strength. Rock specimens having one, two and three cross- sets of discontinuities, various frequencies and orientations of 0, 30, 45, 60 and 90 degrees were prepared. The numbers of rock pieces increased progressively with an increase of frequency and set of discontinuities. As specimens having three sets of discontinuities that one of their sets had four number of parallel discontinuities were consisted 20 rock pieces and they represented jointed rock mass. Joint factor, uniaxial compressive strength and friction angle along the discontinuity surface in direct shear were determined. The uniaxial compressive strength of specimens having one, two and three sets of discontinuities in horizontal and vertical direction was less than the uniaxial compressive strength of intact rock. The uniaxial compressive strength of specimens approached approximately to zero value particularly when the orientation of discontinuities was 60 degrees. This considerable decrease of strength was occurred also for specimens having two and three sets of discontinuities at orientation of 30 degrees. The analysis of results showed that the relationship between ratio of uniaxial compressive strength of jointed specimens to the uniaxial compressive strength of intact rock specimens (anisotropy factor) and joint factor of this research is considerably different with the suggested relationship by Ramamurthy. Properties of discontinuities have altogether essential role on the strength of rock mass.

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Evaluation of the excavation-induced ground movements is an important design aspect of supporting system in urban areas. This evaluation process is more critical to the old buildings or sensitive structures which exist in the excavation-affected zone. Frame distortion and crack generation are predictor, of building damage resulted from excavation-induced ground movements, which pose challenges to projects involving deep excavations. Geological and geotechnical conditions of excavation area have significant effects on excavation-induced ground movements and the related damages. In some cases, excavation area may be located in the jointed or weathered rocks. Under such conditions, the geological properties of supported ground become more noticeable due to the discontinuities and anisotropic effects. This paper is aimed to study the performance of excavation walls supported by nails in jointed rocks medium. The performance of nailed wall is investigated based on evaluating the excavation-induced ground movements and damage levels of structures in the excavation-affected zone. For this purpose, a set of calibrated 2D finite element models are developed by taking into account the nail-rock-structure interactions, the anisotropic properties of jointed rock, and the staged construction process using ABAQUS software. The results highlight the effects of different parameters such as joint inclinations, anisotropy of rocks and nail inclinations on deformation parameters of excavation wall supported by nails, and induced damage in the structures adjacent to the excavation area. The results also show the relationship between excavation-induced deformation and the level of damage in the adjacent structure.

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Introduction
The rock block volumes are formed due to the intersection of discontinuities in the jointed rock mass. The block dimensions affected by joint spacing, joint orientation, joint sets, are taken to be the most important parameters determining the rock mass behavior, strength parameters, and deformations. In the numerical modeling using distinct element method, the creation of the discontinuities can affect the final results very much. Using 3DEC software, it is possible to create joint sets in four conditions: regular and persistent, regular and non-persistent, non-regular and persistent, irregular and non-persistent. As an important point to consider, the major effect of block dimensions on rock mass behavior, strength parameters and deformation modulus can help to decide which one is most suitable to indicate the real conditions of rock mass. As explained in the previous studies, the use of persistent joints leads to the block dimensions being considered as small ones. In this way, due to the high strength of intact rock compared to the joints, the possibility of instability increases.
Material and methods
In this research, from quantitative point of view, Geological Strength Index (GSI) is calculated, based on block dimensions as an influential parameter, to consider the most appropriate case for creating joints in the numerical method. In this regard, according to valuable studies in Bakhtiari dam structure, the characteristics of discontinuities system and GSI of rock mass are utilized to come up with real conditions. Then, the modeling is done with different conditions of joints, block volume distribution, GSI for each case, and the results are compared with quantitative ones. And then the most suitable case for creation of joints in numerical modeling is suggested by using 3 DEC software, regarding the blocks volumes, type of distribution function, and GSI value. Also, the accuracy of this finding is investigated for other structures, independently of input parameters, by making changes in spacing, and joints persistence as two effective parameters in rock blocks dimensions. Owing to the difficulty in the accurate definition of joints persistence, which is related to dimensions of the location, the numerical models for joint persistence are done in an acceptable level in order to create blocks with high conformity in terms of the dimensions. Then, the comparison is made between block dimensions from perspectives of numerical models and GSI values, to choose the best ones showing high conformity with real conditions.
Results and discussion
The comparison of the modeling results using creation of joints in different cases with quantitative results obtained according to geological strength shows that the created block volumes are not properly distributed due to the creation of joints as irregular ones in the two cases of persistent and non-persistent. In this case, the blocks volume changes from a few centimeter to cubic meter, and as the block dimensions increase, the created blocks become bigger. Thus, according to the created blocks volume and the obtained GSI range, the creation of joints is not a suitable method as an irregular one. The creation of regular and persistent joints is not an appropriate method either, as the most created blocks are small, and blocks volume distributions do not comply with quantitative distribution. But with creation of joints as regular and persistent ones, the distribution function of blocks volume in numerical method and quantitative method is log normal. Therefore, according to the created blocks dimensions and GSI range using 3DEC software, the most suitable case is the creation of joints as regular and non-persistent ones. 
Conclusion
According to the obtained results in the four cases, when the joints are considered only as regular and non-persistent ones, the blocks volume range is more compatible with real conditions and follows log normal distribution. Thus it can be concluded that the suggested method for creation of joints in the numerical modeling using 3DEC software is more suitable than others considering the rock blocks dimensions and their distributions. This method can be utilized in any structure to accurately define the persistence of joints regarding created blocks dimension.

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Introduction
Safety and sustainability of infrastructures which were placed in or on rock mass mainly control by geometrically size distribution and physical and mechanical characteristics of rock blocks that is created by intersection of discontinuities. hence identification of rock blocks has a key role in mechanical analysis and hydraulic behaviour of jointed rock mass. Detection process of blocks have many applications in rock mechanic which could be referred to their use in the numerical methods like discrete element method or in analysis of continuous deformation of discontinuities. As pioneer researchers, Goodman and Shi, Warburton and Heliot could be known as leaders in the field of diagnosis of rock mass blocks. Warburton provides a method based on geometric parameters of rock mass and developed a software based on it. Warburton in his work assumed discontinuities as parallel and infinite. In the earlier works, discontinuities were considered as infinite panes. So, just convex blocks were distinguishable. Concave blocks were diagnosis in more detailed researches that is created by finite discontinuities. Basically, methods based on finite planes was classified into two branches. Aforementioned branches were based on blocks detection based on topology concepts and assemble of block elements. Lin at al. presented detection method that assumed discontinuities as finite planes and worked based on topology theory. This method could realize convex and concave blocks of rock mass. Ikegawa and Hudson, Jing presented the similar methods using more accurate process. Sharma et al. presented an equation for calculating the volume of rock blocks in their work. Ferreira provided a method based on graph theory which is better than other method considering time and complicity. Based on this method, firstly vertices were detected in two dimensions and then created a graph based in vertices and edges which in next step constitute polygons that are form in two-dimension blocks. In the present research, it is developed high-speed algorithms to identify the blocks. New method was developed in MATLAB software that by assuming infinite discontinuities and inclusion of a set of joints. we have identified created blocks and calculated their volume and at last block volume histogram were draw that paves the way to obtain their distribution function.
Material and methods
Infinite planes are used to simulate of discontinuities.in this study, each discontinuity is represented by a plane in a three-dimensional Euclidean space. To identify the block, a certain volume of rock mass space should be considered as study region. The studied volume is called domain. By the intersection of discontinuity planes in space, rocky blocks are created in the domain. First, vertices should be recognized at first as first step in block detection. Then, edges are diagnoses and after that it's time to specify the polygons and finally, polyhedron or blocks are obtained by joining edges together. Each vertex in space is created by the intersection of three nonparallel planes. In fact, the vertex is the interface of three planes in the Euclidean space. The next element in the block metric process is the diagnosis of the edges or the blocks' edges. All edges are sections on the lines which created by the intersection of the planes in space. first the parallel vector of all the lines resulting from the intersection of the pair of planes is obtained.
After detection of edges, it’s time to identify polygons that form key element of blocks. Each polygon of a block is formed from their constituent unit. In this step, polygons belong to each discontinuity plane is identified separately. Some edges are determined that are start from the end of selected edge between other edges. In this state, if there is just one edge, that edge is record as the next edge of first polygon. If there is more than one edge from the edge of the selected edges, the angle is calculated between each possible of end edge with the selected edge.
In the next step, it’s time to diagnosis polyhedrons that have created by discontinuities intersection. In the previous step, possible polygons were obtained for each discontinuity. In this stage, it is used the principle which is designed this algorithm that two polygons that formed a block have a common edge. So, the first polygon of first discontinuity is consider as first polygon of first block to recognize block.
Results and discussion
According to the developed algorithm, MATLAB software was used to model the discontinuities. The computational and graphic capabilities of this software have created a lot of attractions for most researchers to use its potential. The strengths of this software are high computing power with its graphical accuracy. The code developed in MATLAB is called RockBlock2 that is designed using a graphical user interface (GUI) to make it easy to use. To illustrate how the program works, there are 29 discontinuities given to the program. The program first takes the dip and dip direction of discontinuities along with the desired point on it and calculates the parameters that make up the equation of discontinuity planes.
Input data is stored in a separate Excel file that was previously introduced to the program. In the next step, the program attempts to identify the vertices. The program stores the coordinates of each corner, with the assignment of a number to it, in the matrix of the corners, which is in fact the Excel file that was previously introduced to the program to use in the next steps, after recognizing vertices on the area.
Identifying the edges is the next step that the program done. At this stage, the program begins to identify each single edge using the data from the previous step that means the coordinates of the corners and the algorithm defined.
The coordinates of the beginning and end of each edge along with its number are stored and maintained in the edge matrix in the Excel file format. In the stage of identifying the polygons, the polygons are formed by joining the edges together. This matrix is a special matrix that its matrix matrices are matrix itself. The matrix of polygons is a row matrix; whose number is the number of discontinuities. Because, as it mentioned in the chapter of the algorithm, the polygons are found by separation of discontinuities. Therefore, each column of the polygons matrix is consisting of faces that are on a certain discontinuity.
The next step begins the process of identifying the blocks, or the same polygons by the program. At this step, the program starts the identification process using the features found in the previous step and the algorithm defined for it. At this stage, the identified blocks are stored in the blocks matrix. By identifying blocks, the program calculates the volume of each block and finally draw its volume histogram. In fact, a volume histogram is presented to illustrate how the block volume is distributed. Obtaining the distribution of blocks or, in other words, achieving a block probability distribution function is an essential step in the behavior of rock mass. Because one of the most important consequences of the presence of discontinuities is the fragmentation of the rock material under the block intervals. By having the block distribution function, it is possible to produce a blockbuster method using random methods, such as Monte Carlo, and to analyze it in various and arbitrary modes.
Conclusion
To identify and study the rocky blocks created by discontinuities, a hierarchical algorithm was designed and developed in MATLAB software. This algorithm identifies and records blocks, consisting of blocks, edges, and facets of the blocks forming components, including stone blocks. This algorithm, which is written for user-friendly ease with the use of graphical coding capabilities, shows a very fast performance using the parallel computing power of MATLAB software. The developed code calculates the dip and dip direction of discontinuities using the geometric properties, and calculates the blocks created in three dimensions and calculates their volume. This histogram code displays the calculated volumes.
The results show that the developed code with its fast performance, while identifying the blocks, calculates and records their volumes without errors. The ability to display the step-by-step process of identifying blocks is one of the clear features of this code. Information about edge is also records and is available for auxiliary applications. Histogram of block volume is one of the most important results of the developed code, which can have different applications.
Identification of created rocky blocks is used both in the stability analysis and rock mass simulations such as Discrete Fracture Network modeling. Determination of block volume distribution function which is done using histogram is one of the most important uncertainties in three-dimensional rock masses behavior that can play a key role in optimizing the design of structures involved in rock mass. Therefore, considering the key role of blocks volume, identifying and calculating block volumes and, consequently, plotting their histogram and determining the distribution function governing them, has a key role in the static and dynamic analysis of rock base structures. ./files/site1/files/123/1Extended_Abstract.pdf

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A jointed rock mass presents a more complex design problem than the other rock masses. The complexity arises from the number (greater than two) of joint sets which define the degree of discontinuity of medium.  The condition that arises in these types of rock masses is the generation of discrete rock blocks, of various geometries. They defined by the natural fracture surfaces and the excavation surface. Stability problems in blocky jointed rock are generally associated with gravity falls of blocks from the roof and sidewalls. Whereas for block defined in the crown of tunnel,the requirement is to examine the potential for displacement of each block under the influence of the surface tractions arising from the local stress field and the gravitational load, in this paper various types of wedge formation in the crown of tunnel due to intersection of joint sets with various dip were examined. The state of stability of the wedge was then assessed through the factor of safety against roof failure. Following that the formed wedges in New York city and Washington D.C tunnels crown were investigated with limiting equilibrium analytical method and by use of Hoek and Brown failure criterion. The obtained results from analytical method corresponded with field observation.