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Practices and Procedures for Site-Specific Evaluations of Earthquake Ground Motions (2012)

Chapter: CHAPTER FOUR Survey Responses and Relevant Literature

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Suggested Citation:"CHAPTER FOUR Survey Responses and Relevant Literature." National Academies of Sciences, Engineering, and Medicine. 2012. Practices and Procedures for Site-Specific Evaluations of Earthquake Ground Motions. Washington, DC: The National Academies Press. doi: 10.17226/14660.
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Suggested Citation:"CHAPTER FOUR Survey Responses and Relevant Literature." National Academies of Sciences, Engineering, and Medicine. 2012. Practices and Procedures for Site-Specific Evaluations of Earthquake Ground Motions. Washington, DC: The National Academies Press. doi: 10.17226/14660.
×
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Suggested Citation:"CHAPTER FOUR Survey Responses and Relevant Literature." National Academies of Sciences, Engineering, and Medicine. 2012. Practices and Procedures for Site-Specific Evaluations of Earthquake Ground Motions. Washington, DC: The National Academies Press. doi: 10.17226/14660.
×
Page 21
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Suggested Citation:"CHAPTER FOUR Survey Responses and Relevant Literature." National Academies of Sciences, Engineering, and Medicine. 2012. Practices and Procedures for Site-Specific Evaluations of Earthquake Ground Motions. Washington, DC: The National Academies Press. doi: 10.17226/14660.
×
Page 22
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Suggested Citation:"CHAPTER FOUR Survey Responses and Relevant Literature." National Academies of Sciences, Engineering, and Medicine. 2012. Practices and Procedures for Site-Specific Evaluations of Earthquake Ground Motions. Washington, DC: The National Academies Press. doi: 10.17226/14660.
×
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9 (a) density of soil , and strain-dependent normalized modulus reduction and damping curves. As indicated in the survey responses, the equivalent-lin- ear site response analysis method is, by far, the most widely used method for evaluation of site-specific ground motions. Advantages of the equivalent-linear method include its requirement for few, well-understood, input parameters, broad experience with its application, a large publicly avail- able database of input parameters, and minimal computa- tional effort. The most commonly used equivalent-linear computer code is SHAKE (Schnabel et al. 1972). Modified versions of this program include SHAKE91 (Idriss and Sun 1992) and SHAKE2000 (Ordonez 2000). DEEPSOIL (Hashash and Park, 2001, 2002; Hashash et al. 2011), ProShake (EduPro Civil Systems 1999), CyberQuake (Modaressi and Foer- (b) ster 2000). These programs use the same computational procedure as that applied in SHAKE, but they were devel- oped independently. The equivalent-linear model has also been incorporated in 2-D site response programs such as QUAD-4 (Idriss et al. 1973), derivatives of QUAD-4 (e.g., QUAD4M, Hudson et al. 1994), and in advanced 2-D and 3-D site response models such as FLAC (Itasca 2005; latest iteration is Version 6.0). Modified frequency-domain methods have also been developed (e.g., Assimaki and Kausel 2002; Kausel and Assimaki 2002) in which soil properties in individual layers FIGURE 3 Approximation of soil nonlinear behavior (a) are adjusted on a frequency-to-frequency basis to account Hysteresis loop of soil element loaded by a single cycle of shear for the strong variation of shear strain amplitude with fre- strain; (b) Variation of normalized modulus (G/Gmax ) and with quency. This approach is used as a proxy for representation shear strain () (modulus reduction and damping curves). of nonlinear site response analysis in time domain. Another, although rarely used, improvement includes the introduction solved in the frequency domain, and any given soil layer is of a vertical component of ground shaking into the analysis assumed to have a constant modulus and damping through- (Idriss et al. 1973). Vertical site response analysis remains a out shaking. Equivalent-linear site response analysis uses an research topic. iterative procedure in which initial estimates of G and are provided for each soil layer. Using those linear, time-inde- Another, less used method for equivalent-linear site pendent properties, linear-elastic analyses are performed response analysis is the random vibration theory (RVT, e.g., and the response of the soil deposit is evaluated. Shear Rathje and Ozbey 2006), based on the equivalent-linear strain histories are obtained from the results, and peak shear method. The advantage of this approach is that the user does strains are evaluated for each layer. Effective shear strains not need to develop input ground motion time histories, and are calculated as a fraction of the peak shear strains. The the analysis will directly provide a surface spectrum. Recent effective shear strain is then used to evaluate an appropriate work (E.M. Rathje, personal communication, 2011) shows G and using shear strain­dependent normalized modulus that the use of RVT with a single set of soil profile properties reduction and damping curves described earlier. The pro- results in amplifications of the peaks of the transfer function cess is repeated until the strain-compatible properties are that is not observed in conventional equivalent-linear analy- consistent with the properties used to perform the dynamic sis approaches. These peaks can be reduced if the soil profile response analyses and the analysis converges. properties are randomized (e.g., Monte Carlo simulation of material properties). Equivalent-linear modeling of site response is based on a total-stress representation of soil behavior. The soil proper- The equivalent-linear analysis approach has been in use ties needed for equivalent-linear site response analysis are since the advent of SHAKE in 1972. Hence, it is supported shear wave velocity Vs, used to compute Gmax = Vs2, mass by a number of verification studies, including back-analy-

10 ses and comparison with other analysis models (e.g., Seed NONLINEAR TOTAL STRESS SITE RESPONSE et al. 1988; Idriss 1990; Dickenson et al. 1991; Idriss and ANALYSIS Hudson 1993; Kavazanjian and Matasovic 1995; Darragh and Idriss 1997; Rathje and Bray 2001; Baturay and Stewart In nonlinear site response analysis, the nonlinear behavior 2003). Based on the findings of these studies and authors' of the soil during cyclic loading can be represented, which experience, the following critique applies to the equivalent- makes it possible to move away from the inherent linear linear analysis: approximation of the equivalent-linear analysis approach. Cyclic hysteretic soil behavior during unloading and reload- · Equivalent-linear analysis is a total-stress analysis; ing is also represented in the nonlinear site response anal- hence, it does not account for pore pressure generation ysis. Furthermore, nonlinear analysis makes it possible to and its effect on material properties during shaking; explicitly include soil strength and the effects of seismic · This method is not recommended when the levels of pore water pressure generation on soil strength and stiff- shaking-induced shear strains are "high." There is no ness. These options have significant effects on site response consensus on the limiting ("high") shear strain level. in areas of very high seismicity (e.g., PGA 0.4 g) and/or Studies by the authors have shown that results of equiv- when soft and/or potentially liquefiable soils are present in alent-linear and nonlinear analyses start to diverge at local soil deposits. strains as a low as 0.1%­0.2%. At strains greater than 0.5%­1% at any depth (layer) within the soil profile, In total stress site response analysis, the explicit inter- the equivalent-linear analysis results are not neces- action of pore fluid with the soil matrix is neglected. This sarily reliable. Recently, Assimaki et al. (2008) pro- is an acceptable simplification under many conditions and posed the use of a frequency index that measures the is numerically efficient. Kwok et al. (2007) conducted a frequency content of incident ground motion relative detailed study of the total stress nonlinear site response anal- to the resonant frequencies of the soil profile. This ysis software. The study provides an excellent review of the index is then used in conjunction with the rock-outcrop various issues associated with this type of analysis. Kwok et peak ground acceleration (PGA) to identify conditions al. (2007) noted the following nonlinear software that were where incremental nonlinear analyses, including the evaluated as a part of the PEER 2G02 Project (2005­2007; equivalent-linear approach, should be used instead of J. Stewart Project Director): DEEPSOIL (Hashash and Park, approximate methodologies. 2001, 2002; Hashash et al. 2011); D-MOD_2 (Matasovic 2006; later upgraded to D-MOD2000); OpenSees (Ragheb Despite its apparent shortcomings, the total-stress equiv- 1994, Parra 1996, Yang 2000); SUMDES (Wang 1990, Li alent-linear analysis is likely to remain a tool of choice for et al. 1992); and TESS (Pyke 2000). The study was able many practicing engineers and may have a slightly differ- to identify key controlling parameters that are common to ent and expanded role. In particular, this approach is now all software. The study found that when input is properly used not only as the "first approximation" of site response, controlled, most of the software provided similar results. but also for calibration of more advanced models, including Hashash et al. (2010) provide a description of recent develop- nonlinear and effective-stress analyses. ments in nonlinear site response analysis and highlight key steps and issues required for conducting such analyses. Many of the modulus reduction and damping curves were based on small strain data (testing shear strain typically In nonlinear site response analysis the dynamic equation reaching 0.5% to 1.0%). These curves are then extrapolated of motion is solved in the time domain. The equation is com- at strain levels exceeding 0.5%­1%. However, the results monly written as: of site response analyses increasingly show calculated strains increasing to 1.0%, especially in soft soils. CalTrans [M ] {ü} + [C ] {} + [K ] {u} = - [M ] {üg}(1) (Jackura 1992) recognized that the implied strength associ- ated with the extended curves might either underestimate where [M ], [C ], and [K ] are the mass matrix, viscous or overestimate the actual strength of soils, so the agency damping matrix, and nonlinear stiffness matrix, respec- developed an-in house simplified procedure for "extension" tively; {u}, {}, and {ü} are, respectively, the displacements, of modulus reduction and damping curves. Recently, Chiu velocities, and accelerations of the mass [M ] relative to the et al. (2008) and Hashash et al. (2010) proposed advanced base, and {üg} is the acceleration of the base. procedures to remedy this arbitrary extrapolation of sub- ject curves in both equivalent-linear and nonlinear analysis. The stiffness matrix [K ] is derived from the nonlinear soil Most recently, Stokoe (K.H. Stokoe, personal communica- constitutive model selected to represent cyclic soil response. tion 2011) pointed out this problem and urged that a remedy In principle, all damping in the soil can be captured through approach be developed. the hysteretic loops in the soil constitutive model. However,

11 as a practical matter, most available soil constitutive mod- gration to solve the same dynamic equation. Program PSNL, els cannot properly represent measured soil damping at low currently under development (S.L. Kramer personal com- strains and significantly underestimate damping at these low munication, 2011; see description in Anderson et al. 2011) strains. Therefore, it is necessary to add damping through models soil profile as a continuum and can simulate dilation. the use of velocity proportional viscous damping [C ]. Most nonlinear codes are formulated to calculate site The dynamic equation of motion can be solved by response in one horizontal direction of shaking, although numerical integration. The numerical integration calls for some such as SUMDES (Wang 1990) and OpenSees temporal discretization (i.e., system of coupled equations (Ragheb 1994; Parra 1996; Yang 2000) allow for multidi- is discretized temporally) and solution by one of the avail- rectional shaking. able time-stepping schemes. Examples of time-stepping schemes include Wilson's algorithm (Clough and Penzien A sample 2-D finite element model (OpenSees) is shown 1993) and numerous variations of Newmark's algorithms in Figure 5. Such a model allows for simultaneous applica- (Newmark 1959). tion of excitation in both horizontal and vertical directions. To solve the equation of motion, it is necessary to dis- cretize the domain of interest, which in this case is the soil column. Two different approaches for discretization of the soil domain are available: (1) lumped mass discretization and (2) finite element discretization. Figure 4 shows a lumped mass model that depicts a hori- FIGURE 5 Mesh representation of 2-D Nonlinear Site zontally layered soil deposit (i.e., a soil deposit that can be Response Analysis of Embankment (Nikolaou 2011). represented by a 1-D model). Soil mass is lumped at the layer interfaces, and soil stiffness is represented by (nonlinear) Regardless of the discretization method used in nonlinear springs. The figure shows the hysteretic damping inherent site response analysis, the thickness of sublayers in a model with nonlinear springs and viscous damping, which is also has important consequences. The layer thickness determines part of the model. This model is used in nonlinear analy- the maximum frequency that can be propagated through a sis software such as DESRA-2/DESRA-2C, DESRAMOD, soil column. If the layer is too thick, the discretized domain DESRAMUSC, SUMDES, TESS, D MOD_2/D-MOD2000, may filter important components of the ground motion and and DEEPSOIL, and in many Japanese programs that are not thus underestimate the ground response. If layer thickness is reviewed here. too small, the computational cost can be too high. Therefore, as a practical matter, 1-D nonlinear site response models will usually have greater (i.e., finer) discretization than their 2-D and 3-D model counterparts, and thus will propagate higher frequencies and filter less of the input ground motion. The survey results in this study indicate that users of 2-D and 3-D software are not always aware of this important limita- tion. The graphical user interfaces can help alert the user to the maximum frequency that can be propagated. Several 1-D software (e.g., DEEPSOIL and D MOD2000) have such alerts incorporated in graphical users interfaces. Nonlinear Constitutive Models with Hysteretic Damping FIGURE 4 Lumped mass discretization for 1-D Nonlinear Hysteretic Site Response Model (Matasovic 1993). Nonlinear total stress site response analysis is generally done with relatively simplified soil constitutive models. A number of other programs discretize the soil domain These models evolved from the early stress-strain rela- by means of finite elements; the details of this approach are tionships of Ramberg and Osgood (1943) and Kondner not discussed here. For dynamic problems, the equations of and Zelasko (1963). The hyperbolic model introduced by motions are solved using an explicit time marching integra- Duncan and Chang (1970) for axial soil behavior, which tion algorithm. For example, TESS (Pyke 2000) and FLAC was based on the above-cited shear stress and strain behav- (Itasca 2005) use an explicit finite difference to solve the ior models, was accompanied by sets of generic material wave propagation problem. Programs such as OpenSees properties and hence allowed for an elegant and simple (Ragheb 1994; Parra 1996; Yang 2000), ABAQUS, and way to capture soil nonlinearity at small axial strains. All PLAXIS use a finite element method with explicit time inte- three models provided the basis for constitutive models

12 that are presently in use. These models (Pyke 1979: Mata- sovic 1993; Matasovic and Vucetic 1993; Darendeli 2001) provide for better simulation of nonlinear stress-strain behavior and also allow for simulation of cyclic loading and reloading in accordance with certain rules. The stress- strain relationship in these models is generally established by: an initial loading curve; a series of rules that describe the backbone curve (see Figure 6 for definition of backbone curve); and unloading-reloading behavior rules required to establish cyclic loops. The most widely used rules are the Masing rules (Masing 1926) and extended Masing rules (Pyke 1979; Wang et al. 1980; Vucetic 1990). The extended Masing rules, including unloading-reloading rules, are used in several 1-D site response analysis soft- ware (DESRA 2C, TESS, D-MOD_2, DESRAMOD, D MOD2000, and DEEPSOIL). FIGURE 7 Evaluation of proposed damping reduction factor (a) modulus reduction and (b) damping curve using Darendeli's curves for cohesionless soils as target. FIGURE 6 Backbone curve as stress-shear strain relationship Note :MR = modulus re-matching only with extended Masing for monotonic loading. rules, MRD = approximate match of both modulus and damping with extended Masing rules, MRDF = modulus reduction and damping matching with non-Masing rules (after It has been long noted that the use of Masing rules, and Hashash et al. 2010). to some extent extended Masing rules, leads to an overes- timation of soil damping at large strains. This, in turn, may result in an underestimation of calculated ground motion Assimaki and co-workers (e.g., Assimaki et al. 2009) have intensity. To compensate for this phenomenon, Darendeli also made important contributions to a number of the above- (2001) proposed the introduction of reduction factors in cited issues related to site response. Their work includes the the development of his family of standard curves. Phillips incorporation of uncertainty in site response analysis and and Hashash (2009) used a similar approach to introduce addresses the issues related to unloading-reloading rules and a modification to the Masing rules (MRDF) and employed damping at larger strains. that in the MRDF model used in DEEPSOIL. Figure 7 from Hashash et al. (2010) illustrates the limitations of the Mas- Borja et al. (1999, 2002) developed a software called ing rules (MR) and extended Masing rules (MRD) in terms SPECTRA, a 1-D nonlinear total stress site response analy- of overestimation of damping at large strain levels (MR at sis program that uses a bounding surface plasticity model strains > 0.1%; MRD at strains > 1%) and improve- to simulate stress-strain behavior. SIREN (Oasys 2006) and ment in matching of both damping and modulus reduction LS Dyna (LSTC 1988) can be used to perform total stress curves with MRD and MRDF. Matasovic (1993) showed site response analysis. that using MR rather than MRD may result in a higher computed surface acceleration response and/or a shift in Viscous Damping Models the response spectrum when relatively high shear strains are induced in the profile. Philips and Hashash (2009) Most available constitutive models show very small hysteretic further showed that MRD, as compared with MRDF, may damping at small strains, which is inconsistent with measured result in a higher computed surface acceleration response soil behavior. Viscous damping is introduced to compensate and/or a shift in the response spectrum at strain levels for this deficiency. The amount of viscous damping is typi- exceeding approximately 1%. cally selected such that the sum of hysteretic and viscous

13 damping is equal to the total damping measured for the given leigh damping frequencies, so this frequency-independent soil type. Historically, the important role of viscous damp- approach eliminates a potentially confusing step in input ing in site response analysis was not well understood; it was development. thought that this was mostly needed for numerical stability. This assumption led to significant confusion in the way it was employed and, in some cases, led to unrealistic results in nonlinear site response analysis resulting from either over or under damping. Viscous damping represents soil damping at a very small strain, so its value is generally small, typically in the range of 0.5% to 5%. It can be directly obtained from the intercept of the damping curve with the vertical axis in the damping versus shear strain curve. The most commonly used formulation for evaluation of viscous damping is Rayleigh damping. The Rayleigh damp- ing is frequency dependent and can be evaluated as: c = R m + R k(2) FIGURE 8 Schematic illustration of viscous damping change with frequency (after Park and Hashash 2004). where R and R are the Rayleigh damping coefficients (Rayleigh and Lindsay 1945) and m and k are elements of the mass and stiffness matrices, respectively. NONLINEAR SITE RESPONSE ANALYSIS WITH PORE WATER PRESSURE CHANGE Figure 8 illustrates how Rayleigh damping, expressed through c, changes with frequency. The viscous damp- The cyclic loading of saturated soils is accompanied by pore ing ratio can be brought closer to a constant value of the water pressure (pwp) generation and dissipation. If the gen- target damping ratio (tar) by specifying c at only one erated pore water pressures are sufficiently large, the soil frequency (e.g., at f 2 in Figure 8), which is termed the stiffness and strength are significantly reduced and ulti- simplified Rayleigh damping formulation; at two frequen- mately, in some soils, liquefaction can occur. In nonlinear cies (at f 1 and f 2), which is termed the full Rayleigh damp- site response analysis with pwp generation, the response ing formulation (Hudson 1994); and at four frequencies of the soil to cyclic loading accounts for the generation of (at f 1 through f4), which is termed the extended Rayleigh excess pwp during cyclic shearing of the soil as well as dis- damping formulation (Clough and Penzein 1993; Park and sipation of these excess pore water pressures during and Hashash 2004). Park and Hashash (2004) have shown that after the cyclic loading. The representation of dissipation/ the use of simplified Rayleigh damping results in signifi- redistribution of pwp influences soil stiffness (modulus) cant errors and the extended Rayleigh is computationally and strength (shear stress) during shaking, which results in expensive; hence, they suggest the use of full Rayleigh a more realistic simulation of site response. The pwp dis- damping formulation. Kwok et al. (2007) recommended sipation/redistribution is discussed in a later section. This use of the full Rayleigh damping formulation in nonlinear section discusses pwp generation. (total stress) site response analysis whereby the first fre- quency is equal to the fundamental frequency of the soil The influence of pwp changes during cyclic loading is column, and the second frequency is equal to 5 times the incorporated in soil constitutive modeling in two ways: (1) fundamental frequency. Full Rayleigh damping is avail- semi-empirical pwp generation models used in combination able in a number of software, including ABAQUS, Cyber- with total stress soil models; and (2) effective-stress models Quake (Modaressi and Foerster 2000), D-MOD2000, whereby the pwp change is computed as the change between DEEPSOIL, FLAC, OpenSees, SIREN (Oasys 2006), LS- total stresses (or loads) and effective stresses, computed DYNA (LSTC 1988). through the soil constitutive model. Philips and Hashash (2009) introduced a new viscous Semi-Empirical Pore Water Pressure Generation Models damping formulation that is independent for frequencies, which is more consistent with the current understanding of In this class of models, pwp generation is calculated using soil response within the seismic frequency range of inter- semi-empirical models. At the beginning of shaking (i.e., at est (Park and Hashash 2008). This formulation, used in time t = 0), stress-strain relationships of the soil are identi- DEEPSOIL, does not require the user to select frequencies. cal to that of the total stress models because pwp is zero. As Many users of site response analysis are not fully aware shaking progresses, pwp is generated and cyclic degradation of the implications associated with the selection of Ray- (of clay microstructure) starts. Subsequently, the effects of

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TRB’s National Cooperative Highway Research Program (NCHRP) Synthesis 428: Practices and Procedures for Site-Specific Evaluations of Earthquake Ground Motions identifies and describes current practice and available methods for evaluating the influence of local ground conditions on earthquake design ground motions on a site-specific basis.

The report focuses on evaluating the response of soil deposits to strong ground shaking.

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