PHYSICAL PARAMETERS The essential parameters that need to be determined are the parameters entering the constitutive models described in Section 3.2. In addition, the natural frequency of the soil profile proves to be very important for the analyses: it represents a good indicator for the validation of the site modelling (geometry, properties), at least in the linear range, and is useful to constrain the range of possible variation of the soils characteristics. The parameters entering the constitutive relationships depend on the adopted model for the soil. For viscoelastic models, elastic (small strain) characteristics and variation of these characteristics with shear strain are required. In view of the large uncertainties involved in soil-structure interaction problems, it is sufficiently accurate to consider an isotropic material, thereby reducing the numbers of moduli to 2: the shear and the bulk moduli, or equivalently the S-wave and velocities. Energy dissipation is represented by the loss coefficients (or damping ratios) associated to each modulus. Practically, due to the difficulty in damping measurements and to the scatter in the results, a single value of the loss coefficient is usually considered applicable to both moduli. These small strain characteristics depend mainly on the soil density and past and present state of stresses. The nonlinear shear strain-shear stress behaviour is characterized by the variation with shear strain of the secant shear modulus and loss coefficient (Figure 38); these curves are mainly influenced by the present state of stresses and the soil plasticity index. For 1D-nonlinear models, in addition to the previous parameters, the maximum shear strength that can be developed under simple shear loading is required (equation (3.12)); for dry soils or drained conditions, it can be computed from the knowledge of the strength parameters, friction angle ’ and cohesion c’, and of the at rest earth pressure coefficient K0. The latter parameter is the most difficult one to measure directly and is usually estimated from empirical correlation based on the friction angle and overconsolidation ratio of the soil. (3.12) For saturated soils under undrained conditions, the maximum shear strength is the cyclic undrained shear strength of the soil. For the 3D-nonlinear models the same parameters as for the 1D-nonlinear models are needed but, these models also involve a large number of additional parameters which do not all have a physical meaning; these parameters are “hidden” variables used to calibrate the constitutive P-
Mean and modal magnitude and distance The M–D deaggregation results provide the relative contribution to the site hazard of earthquakes of different sizes and at different distances. From these distributions, the mean and/or modal magnitudes and the mean and/or modal distances of earthquakes that contribute to the hazard can be determined. The mean and modal magnitudes and distances should be reported for each ground motion parameter and level for which the M–D deaggregated hazard results are given. Unless otherwise specified in the work plan, these results should be reported for response spectral frequencies of 1, 2.5, 5 and 10 Hz. Seismic source deaggregation The seismic hazard at a site is a combination of the hazard from individual seismic sources modelled in the probabilistic seismic hazard analysis. A deaggregation on the of seismic sources provides an insight into the possible location and type of future earthquake occurrences. The seismic source deaggregation should be reported for ground motion levels corresponding to each ground motion parameter considered in the probabilistic seismic hazard analysis. The deaggregation should be performed for the mean hazard and presented as a series of seismic hazard curves. Aggregated hazard curves In a probabilistic seismic hazard analysis, thousands to millions of hazard curves are generated to account for epistemic uncertainty. For use in certain applications (e.g. a seismic probabilistic safety assessment), a smaller, more manageable set of curves is required. Aggregation methods are used to combine like curves that preserve the diversity in shape of the original curves as well as the essential properties of the original set (e.g. the mean hazard). A of aggregated discrete hazard curves, each with an assigned probability should be reported in tabular as well as graphic format. Earthquake time histories For the purposes of engineering analysis, time histories may be required that are consistent with the results of the probabilistic seismic hazard analysis. The criteria for selecting and/or generating a time history may be specified in the work plan. Example criteria include the selection of time histories that are consistent with the mean and modal magnitudes and distances for a specified ground motion or annual frequency of exceedance. The format for presenting earthquake time histories will generally be defined in the work plan. Figure 41 in the PSHA Process
Uncertain Site (Soil). Once such uncertain seismic motions reach surface layers (soil), they propagate through uncertain soil (, ; , ). Uncertain soil adds additional uncertainty to seismic motions response. Soil material properties can exhibit significant uncertainties and need to be carefully evaluated (, ,; , ; , )
FIG. Figure 6.20: Comparison between (a) case 3 (top, Vs = 1000 m/s, 15 Hz, element size = 10m) and (b) case 9 (bottom, Vs = 1000 m/s, 15 Hz, element size = 20m) APPROACH 3, JJJ - Draft A. Preparatory work: 1. Site profile: a. Develop one or more alternative models of the site soil profile from hard rock to TOG and other locations in the soil column; these are denoted base cases. b. Identify physical parameters of the soil profile that are to be treated probabilistically, i.e., uncertain parameters; candidates are depth to bedrock, soil layer thickness, low strain shear moduli or shear wave velocity, low strain material damping, and others; use site specific field data to the extent possible (Chapter 3); multiple degradation curves; c. Identify soil layer properties to be used in equivalent linear analyses, i.e., shear moduli degradation relationships and material damping values for increasing shear strain levels (Chapter 3); use site specific field and laboratory data to the extent possible; SPID says use EPRI curves; 2. Seismic hazard: a. For each annual frequency of occurrence (AFO) (AFO is derived from AFE values and is a function of the assumed increment of AFE in the site response calculation) and each spectral frequency (for some approaches, these frequencies are referred to as “conditioning frequencies”) at which the seismic hazard was calculated, the seismic hazard is deaggregated into source contributors defined by magnitude and distance. b. From recorded motion data individual events corresponding to these magnitude and distance pairs are identified. The ground motion response spectra are assembled to be used in the representation of the candidate events. In addition, for RVT approaches