Approximate Estimation of Critical Bedrock Depth to be Implemented in Preliminary Seismic Design of Underground Structures

In seismic design of engineering structures, usually bedrock acceleration-displacement response spectra are within hand. The crucial issue in seismic design of underground structures is the serious need for the geotechnical logs to be used in numerical simulations. However, large dimensions of typical sub-surface structures like tunnels, subways and sewage water transporting routes, require considerable logging efforts based on notable budgets. As such structures would lay several ten meters under the ground surface, the mentioned efforts and budgets expand with respect to that of required for over ground systems. Hence, any approximate estimation on critical bedrock depth can help to draw reasonable engineering design judgments. Providing such information, regardless of precise log information, guide the designer to implement conservative assumptions and reach upper bound estimations on seismic demands. To approach this goal, here, an investigation is conducted to find such critical depth parametrically. The structures are considered as box shaped long embedded systems for which 2D rectangular cross sections are studied linearly and a simple procedure for fast and conservative seismic design is proposed. To this end, the article constitutes of two parts. At first, the approximate relation between maximum bedrock displacement (DB) and maximum internal drift of the soil layer over the bedrock (DL) is explored. It is notable that in underground soil-structure interaction, the soil deformation field surrounds the structure and through an interaction procedure, both soil and structure converge to an equilibrium state. So, maximum internal deformation of the soil layer, in which the structure is embedded, plays an important role in seismic demands of subsurface structures. In this part, a set of 20 real bedrock records is utilized to reach the approximate DB-DL relation through a linear well-known closed form equation for single layer transfer function. The bedrock histories were all selected from the sites with shear wave velocity, Vs, over 700 m/s. The results of this part show that the average value of DL, for the selected set of records, is approximately close to the value of DB. In the second part, various Finite Element (FE) models were developed in ABAQUS software including different structures. Then, the resulted DL from previous step was applied to the boundaries of FE models, in first-mode-shape of each layer. It is supposed that the total layer deformation comes from its first mode shape. Next, the uppermost flexural, shear and axial strains are tabulated and sketched against the parameter H/Vs, where H is the soil layer depth. This process was repeated for structures with different values of flexibility ratio, FR, and aspect ratio, AS. The effect of h/H ratio is also reviewed where h is the structure vertical dimension. The depth of the structure from ground surface is set to a constant value and just a single layer over the bedrock is taken into account. The trends of strain demands and critical layer depths are the explored and discussed. It is shown that, as the distant of the structure and the bedrock diminishes, the strain demands increase. This happens as the maximum gradient of soil deformation occurs near the bedrock surface. This makes clear that, in the absence of enough information on soil layers, it is suggested that the minimum stratum laye5r depth to be considered for a conservative analysis. Such depth, which can be assumed as the overburden depth plus structural vertical height, is expected to produce the upper most seismic demands for preliminary design of underground structures. It should be noted that this research is based on linear analysis and complementary investigations, considering different types of nonlinearities, are required to reach more precise conclusions with more reasonable safety factors.