Journal of Engineering Geology

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Various types of numerical analyses such as   Finite Element Method, Boundary Element Method and Distinct Element Method, are used in rock mechanics and in engineering practices for designing rock structures such as tunnels, underground caverns, slopes, dam foundations and so on. In this paper, the results of back analysis of Koohin tunnel which is located in the first section of Qazvin-Rasht railway have been presented. The main purpose of this paper is to perform the back analysis of the mentioned tunnel with the use of numerical models. For modeling the tunnel, two different sections of 30+150 km and 30+900 km are analyzed with FLAC 2D software.  To perform back analysis the suitable interval of geomechanical parameters according to the tests which were performed on the core drillings has been determined. With the use of direct method in back analysis, the errors of models have been corrected in several steps and finally the geomechanical parameters in 30+150 km station (Elastic Modulus = 0.3 GPa, Cohesion = 0.21 MPa and Internal Angle of Friction = 34^°) and in 30+900 km station (Elastic Modulus = 0.3 GPa, Cohesion = 0.21 MPa and Internal Angle of Friction = 35°) have been achieved. The geomechanical parameters which obtained from back analysis are completely in the chosen interval and compliance with the results of tests which performed on core drillings. On the basis of  geomechanical parameters obtained from back analysis with the parameters which used in the design of the tunnel, the tunnel design and the structure method were confirmed.  

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Introduction
Rock mass deformation modulus is one of  the major parameters has to be considered in the design phase of arch dams. Due to filling and discharging of reservoir and corresponding loading and unloading on the dam abutments, irreversible deformation takes place within the rock mass and consequently, increases the potential of creating a separation between dam body and abutments. Therefore, the rock mass modulus must be more than an alowable value in order to prevent arch dam failure. Regarding small core samples and lack of joints and other similar discontinuities in samples, the determined modulus through performing laboratory tests is higher than those obtained through in-situ tests. The available technique to estimate the rock mass deformation modulus is divided into two classes as direct and indirect methods. In direct methods, the rock mass deformation modulus is measured via performing in-situ tests such as plate loading test while it is estimated through empirical equations using rock mass classification and laboratory test results in indirect methods. These equations are developed based on regression analysis between the rock mass modulus calculated via in-situ tests, the rock mass classification and laboratory test results. Although application of these equations is simple and cost-effective, the results are doubtful and cannot be used in the design phase of arch dam due to the heterogeneous nature of rock mass and rock type variability. The numbers of micro-cracks which are developed after gallery excavation using drilling and blasting technique are more close to the loading plate. Thus, calculated modulus in these points is lower than reality. The displacement in the points far from loading plate was near to zero while the transmitted load which is calculated applying ASTM D4394 standard is more than reality in small galleries. Consequently, the calculated modulus was extremely larger than real values and sometimes even more than intact value. The empirical equations are site dependent and they are just applicable in sites with similar geotechnical condition. It is obvious that in-situ tests, such as plate loading, are the appropriate method in order to determine the modulus of deformation, however, due to some simplification in the data processing such as semi-infinite boundary condition, the application of numerical simulation as a data processing tool is more appropriate. In this research, the Beheshtabad dam was introduced and the geology characteristics of dam site were investigated. Applying direct and indirect methods, the rock mass modulus of dam abutments is calculated.
Material and Methods
The dam site is placed approximately at a distance of 2.7 km from the intersection of Koohrange and Beheshtabad river. In accordance with geological studies, the rocks in the site could be categorized in four units combined of Dolomite, Dolomitic Limestone, Limestone, Marl and Marly Limestone. Applying empirical equation the rock mass modulus of dam abutments is evaluated based on the laboratory test results and rock mass engineering classification systems. In addition, ASTM D4394 is applied to investigate the results of ten plate loading tests which are executed in the right and left abutments. To interpret the plate loading test results in the right abutment, a three-dimensional Fast Lagrange Analysis of Continuum (FLAC3D) model is developed.
Result and Discussion
To process the numerical simulation results, back analysis as a data processing tool is used. In this approach, the input parameters of numerical model will be changed in the way that the measured quantities by extensometers at the monitoring points are almost equal with the computed ones via numerical model at the corresponding points. Based on the sensitivity analysis carried out on the Mohr-Coulomb failure criterion parameters, the friction coefficient and cohesion variation do not affect the displacements calculated via numerical simulation as the more portion of gallery displacements are elastic. The error function is minimum when the rock mass modulus is 12 GPa and the horizontal to vertical stress ratio (K0) is equal to 0.5. The evaluated rock mass modulus based on the numerical simulation is two times lower than corresponding one evaluated applying empirical equation as a result of empirical equation uncertainty. Consideration of stress decrement under loading plate shows lower level of stress decrement under loading plate in ASTM D4394 compared to numerical simulation. This is why, the rock mass modulus, calculated based on ASTM D4394, increases dramatically by getting distance from the loading plate. 
Conclusion
The empirical methods estimating the modulus of deformation based on rock mass classification systems tend to evaluate large value of modulus especially for the weak massive rocks.
As a result of galleries dimensions and semi-infinite boundary condition assumed in ASTM D4394, the calculated rock mass modulus increases dramatically by getting distance from loading plate. Therefore, the numerical simulation was applied to process the plate loading test results. A new normalized error function was developed based on measured displacements and the rock mass modulus in the right abutment was determined 12 GPa which is very lower than the calculated value using ASTM D 4394. Also, as a result of numerical simulation, the rock mass is uniform. The stress increment perpendicular to the loading plate was calculated applying numerical simulation which is 0-90 percent lower than those suggested by ASTM D 4394.