Damping formulation for nonlinear 1D site response analyses

Comparison of 1D linear, equivalent-linear, and nonlinear site response models at six KiK-net validation sites

Studies of earthquakes over the last 50 years and the examination of dynamic soil behavior reveal that soil behavior is highly nonlinear and hysteretic even at small strains. Non-linear behavior of soils during a seismic event has a predominant role in current site response analysis. The pioneering work of H. B. Seed and I. M. Idriss during the late 1960’s introduced modern site response analysis techniques. Since then significant efforts have been made to more accurately represent the non-linear behavior of soils during earthquake loading. This paper reviews recent advances in the field of non-linear site response analysis with a focus on 1-D site response analysis commonly used in engineering practice. The paper describes developments of material models for both total and effective stress considerations as well as the challenges of capturing the measured small and large strain damping within these models. Finally, inverse analysis approaches are reviewed in which measurements from vertical arrays are employed to improve material models. This includes parametric and non-parametric system identification approaches as well as the use of Self Learning Simulations to extract the underlying dynamic soil behavior unconstrained by prior assumptions of soil behavior.

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Recent Advances in Non-Linear Site Response Analysis

Strong ground motions from the Mw=6.6 2007 Niigata-ken Chuetsu-oki earthquake were recorded by a free-field downhole array at a nuclear power plant. Site conditions consist of about 70 m of medium-dense sands overlying clayey bedrock, with groundwater located at 45 m. Ground shaking at the bedrock level had a geometric mean peak acceleration of 0.55g, which reduced to 0.4g at the ground surface, indicating nonlinear site response. One-dimensional ground response analysis of relatively weak motion aftershock data provides good matches of the observed resonant site frequencies and amplification levels, provided small-strain damping levels somewhat larger than those from laboratory tests are applied. Nonlinear ground response analyses of strong-motion data using laboratory-based modulus reduction and damping relations valid up to moderate strain levels (<∼0.5%) produce unrealistic strain localization at a velocity contrast. A procedure is presented to more realistically represent the large-strain por...

Elastic and Large-Strain Nonlinear Seismic Site Response from Analysis of Vertical Array Recordings

Blind predictions of ground response at the Turkey Flat vertical array site during the 2004 Parkfield earthquake were performed using a series of nonlinear and equivalent-linear ground-response analysis codes. In this article, we report the out- come of the blind predictions, compare the predictions to measurements (released after the predictions were made), and provide discussion on residuals between the data and model predictions. The prediction exercise considered various sources of material variability and model variability. Specifically, these analyses utilized five dif- ferent nonlinear analysis codes, each exercised with a suite of small-strain shear-wave velocity profiles and modulus reduction/damping curves that encompass the range of reported material properties. Below the site frequency of about 5 Hz, velocity profile variability dominates the computed response variability. Upon full release of strong- motion data from the site, the predictions were generally found to be biased towards underprediction at high frequencies. Sensitivity analyses and results of recent geophy- sical testing at the site suggest this underprediction bias is most likely a result of in- accuracies in prior estimates of near-surface shear-wave velocities. Analyses performed with the recent profile show no significant bias except at the site frequency, where the response is overpredicted.

Nonlinear Ground-Response Analysis of Turkey Flat Shallow Stiff-Soil Site to Strong Ground Motion

One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.

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Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

One-dimensional seismic ground response analyses are often performed using equivalent-linear procedures, which require few, generally well-known parameters (shear wave velocity, modulus reduction and damping versus shear strain, and soil density). Nonlinear analyses provide a more robust characterization of the true nonlinear soil behavior, but their implementation in practice has been limited, which is principally a result of poorly documented and unclear parameter selection and code usage protocols. Moreover, the benefits and potentials of nonlinear analysis relative to equivalent linear are not well defined. In this paper, we present preliminary results of a “benchmarking study” of nonlinear ground response analysis procedures. Key issues that are discussed include: (1) use of reference strain, which can be readily estimated as a function of plasticity index and effective stress, in lieu of dynamic shear strength as a parameter defining the nonlinear backbone curve; (2) strategies for managing excessive large-strain material damping that occurs when Masing’s rule is applied to the backbone curve to evaluate hysteretic damping; (3) specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motion recorded at depth in a vertical array); and (4) specification of viscous damping, specifically the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target.

Practical implementation of analysis routines for nonlinear seismic ground response analysis

One-dimensional seismic ground response analyses are often performed using equivalent-linear procedures, which require few, generally well-known parameters (shear wave velocity, modulus reduction and damping versus shear strain, and soil density). Nonlinear analyses provide a more robust characterization of the true nonlinear soil behavior, but their implementation in practice has been limited, which is principally a result of poorly documented and unclear parameter selection and code usage protocols. Moreover, the benefits and potentials of nonlinear analysis relative to equivalent linear are not well defined. In this paper, we present preliminary results of a “benchmarking study” of nonlinear ground response analysis procedures. Key issues that are discussed include: (1) the use of a simple curve-fitting parameter to describe the shape of the backbone curve, avoiding the need to determine dynamic shear strength (which is often unavailable); (2) strategies for managing excessive large-strain material damping that occurs when Masing’s rule is applied to the backbone curve to evaluate hysteretic damping; (3) specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motion recorded at depth in a vertical array); and (4) specification of viscous damping, specifically the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target.

Overcoming Hurdles that Limit the Application of Nonlinear Seismic Ground Response Analysis in Engineering Practice

Blind predictions of Turkey Flat ground motions are carried out using a series of nonlinear ground response analysis codes. The prediction exercise is structured in two phases so as to formally consider several sources of uncertainty. The first phase involves analysis of the site response considering various sources of material variability and model variability. Specifically, these analyses utilized five different nonlinear analysis codes, each exercised with a suite of small strain shear wave velocity profiles and modulus reduction/damping curves that encompass the range of reported material properties. The second phase of this prediction exercise involves comparisons of results obtained by independent analysis teams for a "baseline" set of material properties. This second phase of work is of interest to see how much variability in estimated ground motions arises from user-to-user differences in code usage and parameter selection when all users have the same basic information on site condition and the same code. We compare the contributions of all these sources of variability (shear wave velocity, nonlinear curves, code-to-code for the same user, and user-to-user for the same code) and identify the most critical sources for the Turkey Flat site.

Zhaohui Yang

Papers

Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

Practical implementation of analysis routines for nonlinear seismic ground response analysis

Overcoming Hurdles that Limit the Application of Nonlinear Seismic Ground Response Analysis in Engineering Practice

Utilizing nonlinear seismic ground response analysis procedures for turkey flat blind predictions