Page - 854 - in Book of Full Papers - Symposium Hydro Engineering

stiffness of the layers equal to 30 cm and an estimated value of 13 for Kn, we will have Ev= 0.3 * Ei and Eh= Ei. 2- A wide range of studies have been done on finding the relationship between the intact modulus (Ei) and the mass modulus (Em) in rock mechanics [4], most of which apply a reduction factor to Ei in order to obtain Em. A simple equation proposed by Bieniawski [5] relates the two moduli using RQD as follows: Another method is to relate the reduction factor to RMR [4], which could be rewritten in terms of RQD in layered dam bodies. The RQDs of Hardfill cores are variable along the dam body, not perfectly precise and containing uncertainties, which makes a probabilistic approach necessary. Exerting RQD distribution of cores will enable us to calculate the modulus of the Hardfill using the relations above. The application of these probabilistic distributions of E to the finite element method will be discussed in the next section. Whereas the stress results in the dam body and foundation are directly dependent on the “modulus ratio” of Hardfill to rock and independent from the single values of E, it is clear that utilizing the same method and data to estimate E in both rock mechanics and dam analysis will result in a better estimation of stress values in the dam body. 5. CHARACTERISTIC COMPRESSIVE STRENGTH More “variations” occur in the compressive strength and the modulus of elasticity of Hardfill compared to RCC projects, which results in unknown stress distribution in the structure. Determining the characteristic compressive strength for Hardfill dams is of great importance since it plays the main role in the total cement usage of the project. Therefore, a probabilistic approach to determine the optimum compressive strength is proposed in this paper. All of the stresses in the dam body must be compared to allowable stresses considering various load combinations. A new stress distribution with respect to the load combination is obtained as shown in Fig. 8 (middle) for each value of E(c) or E(Hardfill). By performing finite element analysis for different values of E(Hardfill) and finding the highest compressive stress generated in the structure (and transforming tensile stresses into equivalent compressive stresses), a fitted curve for input E(Hardfill) against the maximum compressive strengths is resulted according to Fig. 8 (left). It is inferred from the figure that each f’c of the Hardfill material will produce an initially unknown E(Hardfill). Assuming that this relationship is characterized as curve R in Fig. 8 (left), it is clear that the intersection of these two curves may be the desired f’c, considering the safety factors for the stresses. It is worth noting that 854