STABILITY OF UNDERGROUND STRUCTURES IN ANISOTROPIC ROCK MASSES

Abstract

In recent years, the underground space is being increasingly utilized for avariety of purposes such as for hydropower projects, large storages and activities related to economic and strategic importance. It is essential to treat these excavations highly professionally and with great precision due to the complex process of analysis, design and construction and the high cost involved. The underground openings are sometimes located in regions with complex geological conditions such as presence of joints, weak shear zones, faults and other discontinuities. These geological discontinuities exert a dominant influence on the response of rock mass. Other factors such as rock mass strength, in-situ stress, shape and size of underground opening, sequence of excavation, saturation of rock mass and the nature of ground condition like elastic, in-elastic, squeezing or swelling, also influence the behaviour of underground structures. The cumulative effect of all these factors is to give rise to instability conditions. Jointed rock mass may be treated either as a continuum or a discontinuum. In the continuum approach, rock mass is treated as an equivalent anisotropic continuum whereas in the discontinuum approach, intact rock and the joints are explicitly modeled. When major discontinuities like faults and shear zones are present in the rock mass, it becomes essential to check the local stability of underground structures during the excavation process. Nonlinear analysis of structures in jointed rock masses is essential for obtaining their realistic response. There are two types of nonlinearities, namely, the geometrical nonlinearity and the material nonlinearity. Material nonlinearity has been considered for both the rock mass constituents, i.e. intact rock and the rock joints. The stress-strain behavior of rock is nonlinear and dependent on confining pressure. In addition, the joint stiffnesses are also stress dependent. Simulation of sequence of excavation is important in the analysis and design of supports during the excavation process. Many algorithms have been suggested for simulation of the excavation process. Some of these violate the uniqueness requirements. The instability of structures in jointed rock masses is initiated when water seeps through joints and other discontinuities. The effect of the flow of water is to reduce the effective stresses due to increase in joint water pressure as well as the softening of the in filling material. Various models have been proposed to simulate the flow of water through porous and fractured media. These models treat jointed rock either as a discontinuum or as a continuum. In addition, when underground excavations are constructed in jointed rock masses, the pattern offluid flow alters and water seeps towards the openings. Interaction between flow of water and the stress in jointed rock mass is one of the most important parameters which affects the stability ofstructures in jointed rock masses. The stress changes may affect the flow pattern in the fractured media and also the flow of water, in turn, may affect the deformation and stress pattern. Most of the earlier studies involved 2-D analysis of jointed rock masses. A comprehensive solution using 3-D analysis of stresses and deformations in jointed rock masses has become vital in rock engineering, especially in case of problems ofcaverns. The numerical techniques have proved to be very powerful tools to analyze the deformations and stresses around underground openings. One of the most appropriate numerical techniques is the finite element method, which is capable of simulating the complex rock masses. In the present study, the stability ofstructures founded on or excavated in anisotropic jointed rock masses has been examined under different boundary conditions of displacement and seepage. The analyses which have been carried out herein include linear analysis of underground structures in jointed rock masses, analysis of structures in rock u masses with major discontinuities, nonlinear analysis of structures in jointed rock masses, analysis of seepage through rock masses, and the coupled stress-flow analysis ofstructures in jointed rock masses. The powerhouse cavern of Nathpa-Jhakri hydropower project in India has been taken for the case study. To consider the influence of most of the parameters on the response and stability of underground structures, an anisotropic continuum approach has been proposed in this thesis for modeling of jointed rock masses. The constitutive relationships for anisotropic jointed rock masses have been formulated in which the compliance of rock mass equals the summation of compliances of intact rock and all the joint sets. Attempt has also been made to propose the constitutive relationships for a 3-D joint/interface element to represent the characteristics of interface between two fault surfaces or the interface between two different materials. The constitutive relations include the dilatant behavior of undulating joints, orientation, frequency and number of joint sets. A finite element software for linear elastic analysis has been developed and validated against the behavior of tunnel excavated in isotropic and anisotropic rock masses. Results for isotropic media compare well with those obtained from the closed form solution and those reported by Wang and Garga (1993). However, results of the anisotropic case have shown that the vertical deformation is higher than the horizontal deformation and the ratio of the two is influenced by the ratio of height to the width of opening. The stresses change both in magnitude and direction upon excavation of the opening, especially near the excavated region. In general, the predicted behavior has been found to bein good agreement with the results obtained byWittke (1990). Results from the analysis of underground structures excavated in rock media intersected by a shear zone indicate an increase in the displacements in the vicinity of shear zone. When the shear zone is located close to the cavern periphery, displacements of cavern have been found to increase upto 3 times. Maximum compressive stress has been recorded in near the toe of the cavern where the shear zone intersects the cavern. These results have been compared with those obtained byPfisterer et al. (1974). Anumerical procedure developed by Sharma et al. (2001) for simulating the sequence of excavation in a 2-D situation has been extended to a 3-D situation with multi-stage excavation in jointed rock masses. A3-D finite element software has been developed to accommodate the sequence of excavation in isotropic and anisotropic media. The stress dependent modulus ofdeformation (Janbu, 1963) and stress dependent normal joint stiffness, k„ (Bandis et al., 1983) have been incorporated in the model. Two approaches have been followed to evaluate the shear stiffness of joint upon the stress variation. First approach considers the ratio of normal stiffness to shear stiffness of the order of 10. The second approach suggested by Wang and his co-workers (Wang et al., 2003) considers the shear stiffness to be the function of the normal stress at the interface. The mobilization of roughness and dilatancy of joint surface during shearing have also been taken into account. All these features have been incorporated in the software developed for the purpose. Three problems have been considered to verify the proposed method. First problem is an open vertical excavation made in soil media. The most important findings have shown an increase in lateral deformation with the stages ofexcavation. The results compare well with the results presented by Sharma et al. (2001). In second problem, a square underground opening has been excavated in three stages in an isotropic rock. An increase in displacement at the roof of the opening has been observed with the excavation process. The maximum change in the displacement has been obtained at the first stage of the excavation. Good agreement has been obtained with the results presented earlier by Kumar (1997). Third problem includes an excavation ofa powerhouse cavern in an anisotropic rock mass having two joint sets. The results indicate, generally, a concentration of stresses and displacements near the cavern periphery at all excavation stages as the excavation progresses. Despite an increase in vertical IV displacement with the excavation process, the first stage gives the maximum changes in displacement which is quite logical also. The displacement contours are oriented towards the steepest joint set. In addition, the results show a concentration of stresses in the sidewall. The displacements and stresses obtained from the first approach are higher than those from the second approach but within acceptable limit. It is certain that the final stage is certainly not the critical one, however, the first and third stages appear to be so. The results have been found to match well with those obtained by Fairhurst and Pei (1990). Attempts have been made in this study to analyze the flow of water through the jointed rock mass. The analysis includes both confined and unconfined flow problems. Seepage through joints and other discontinuities has been represented by the parallel, undulating plates. An iterative method based on the residual flux approach has been adopted to locate the position ofthe phreatic surface. Acontinuum approach has been proposed for the hydraulic characteristics of anisotropic jointed rock mass. The constitutive laws for seepage through jointed rock masses have been derived. Finite element software has been developed and verified by suitable examples. Seven problems have been solved for seepage analysis with different media and different boundary conditions. First problem is related to one-dimensional flow in a confined aquifer. Results show a very good agreement with those reported by Yu and Singh (1994). In second problem, flow through a cubic rock mass model has been considered and a good agreement has been observed with the results given by Smith and Griffiths (1998). Seepage around a tunnel has been considered in the third problem in which a higher disturbance was noticed in the flow of water near the tunnel periphery. A good comparison has been achieved with the results reported by Ohkawa et al. (1986). Fourth problem analyzed is that ofconfined seepage through isotropic media below the dam. A maximum uplift pressure has been noticed at the heel of dam which reduces to zero at the toe. The results compare well with those obtained by Desai (1972). A jointed media stresses using the effective stress concept. A3-D software has been developed using the finite element method. The software has been used to solve some problems for which the results are available in literature. For coupled stress-flow analysis, four problems with different geometry and boundary conditions have been considered. Firstproblem refers to the coupled stress-flow around a tunnel in jointed rock mass with one vertical joint set (Wei and Hudson, 1990). The hydraulic head has been found changing in the region near the tunnel periphery due to high stress redistribution. An increase inpore water pressure has been observed due to the closure ofjoints which results from stress redistribution upon excavation. Avery small increase in displacement has been found due to the flow ofwater through jointed media. This phenomenon is more pronounced near the tunnel periphery. The groundwater level has been found to rise with stress changes. In the second problem, a tunnel excavated in submerged jointed rock mass having horizontal and vertical joint sets has been analyzed (Kim et al., 1999). With the rise in water level above the tunnel roof, the pore water pressure increases and this in turn leads to higher displacements. An increase in the roof settlement by 2.7 times has been found when the water level rises from 0 mto 500 m. In contrast, the heave at the invert of tunnel reduces due to the rising water level. In the sidewalls, displacements have been found to increase by 2.5 times. Although the pattern of stress distribution remains unchanged with the rise of water level, effective horizontal stress has been found to reduce and the effective vertical stress increases. Coupled stress-flow analysis of square excavation in jointed rock mass with two joint sets has been carried out in the third problem with drained and undrained conditions having been imposed on the excavation boundary. Different pattern ofthe pore water pressure has been obtained depending upon the boundary conditions imposed. No change in displacements was noticed upon seepage under drained condition while, in contrast, the undrained condition has shown a reduction in displacements due to seepage. The stresses also change according to the pore pressure distribution pattern. Results vn have been found to agree well with those already presented by Yoshida et al. (1999). Fourth problem considered is that of a coupled stress-flowthroughjointed rock mass foundation of a dam. The rock media is intersected by two joint sets having different attitudes. A change in equipotential lines has been observed due to redistribution of stresses. The equipotential lines are offset (compressed) towards the downstream in accordance with the stress pattern. Both horizontal and vertical displacements have been found to increase due to seepage by about 10%and 7% respectively under the heel of the dam. A good agreement has been found with the results presented earlier by Bargui et al. (1998). The results of various problems with a wide range of boundary conditions have shown the applicability of the proposed method. Finally, a case-study of Nathpa-Jhakri hydropower project in India has been selected for a comprehensive study. A large powerhouse cavern, which is located in jointedrock mass with three joint sets, has been considered to be excavated in 27 stages. The displacements are concentrated at the corner of the cavern. Linear analysis has resulted in a maximum horizontal displacement of about 46.7mm in the sidewall of the cavern. The vertical displacements at the crown and the invert are of the order of 31.8mm downward and 37.1mm upward respectively. In nonlinear analysis, the horizontal displacement was found to increase by 5.7 times in the sidewalls of the cavern at the end of stage-6 of the excavation process. Subsequently, this increase gradually reduces as the excavation proceeds till it is only about 1.1 times as the end of the last stage of excavation. Vertical displacement also shows similar trend and shows an increase of about 4.1 times at the crown after completion of excavation stage-6. This value reduces to about 1.3 times at the end of the final stage. The maximum horizontal displacement inthe sidewall is oforder of40.8mm as found in nonlinear analysis. On the other hand, coupled analysis yields a maximum horizontal displacement in the sidewall of about 47.8 mm. The stresses in the linear analysis show concentration near the edges of the cavern. At crown and invert, a maximum average horizontal stress of about * viu 9.28 MPa and 9.60 MPa has been found. Amaximum intermediate stress ofabout 6.70 MPa has been found in the sidewall of the cavern. On the other hand, maximum average horizontal stress obtained from nonlinear analysis at crown and invert has been found to increase by about 1.2 and 1.5 times from stage-1 to stage-27. The vertical stresses have been found to increase due to the excavation process, the maximum compressive stress being of the order of 19.0 MPa near the corner of the cavern. Stresses from the coupled analysis have been found to be similar to the nonlinear analysis. All stresses have been found to be compressive in nature and are concentrated near the crown of the cavern. Higher disturbance in hydraulic head has been found near the periphery ofcavern in all stages ofexcavation. Pattern ofthe pore water pressure was found to have changed especially in the vicinity of cavern where the concentration is high. IX