Model uncertainty of design tools to analyze block stability

Sammanfattning: Block failure is one of the most common failure modes in tunnels. Design tools have some simplifications and, therefore, they also have some model uncertainties. The purpose of this licentiate thesis is to assess the model uncertainty for different design tools in order to estimate block stability. Different approaches of kinematic limit equilibrium (KLE) including conventional KLE, limited joint length, limited joint length and stress field consideration and probabilistic KLE were compared to that of DFN-DEM. In this approach, the results of the calibrated DFN-DEM with field mapping were considered to be of true value. The results show that the conventional KLE is overdesign due to it’s over simplification. By considering fracture length and stress field, the volume of predicted unstable blocks is reduced. The probabilistic approach of KLE by considering finite joint length and stress field predicts the volume of unstable blocks to be lower than DFN-DEM approach. Therefore there is a great model uncertainty of our standard design tools for block stability analysis. The assumption made in this study is that the results from DEM were considered to have a true value; the results from analytical solution based on joint relaxation process were compared to those of DEM in a different condition of depth, K0, apical and friction angle, Kn and Ks value, and ratio of Kn/Ks. The comparison shows that for shallow depth with K0 less than 1, analytical solution leads to an overestimation of block stability. The analytical solution predicts that the block is stable, while the analyses from numerical solution show the block is unstable. The analyses show that by increasing K0, accuracy of analytical solution also increases. Moreover, for the cases with close value of friction angle to semi-apical angle, the use of analytical solution is not recommended. As the ratio of Kn/Ks increases, the accuracy of analytical solution decreases. Increasing the angle ratio (ratio between semi-apical angle to friction angle) is one source of increasing uncertainty in the model. The analytical solution is very uncertain in cases with a low value of K0, and a high value of stiffness ratio and angle ratio. On the other hand, the analytical solution is more certain in conditions with a high value of K0 and a low value of stiffness ratio and angle ratio. According to current information (K0, angle ratio, stiffness ratio), one can determine the value of model uncertainty by using the diagrams presented in Chapter 6 of the thesis. The analyses show that by having more information about the key parameters, the model uncertainty could be identified more precisely. However, having more information means spending more money, and this increase in cost must be compared to the cost of failure or delay in the project or overdesign.