Site- and soil-specific PSHA for nonlinear soil sites P. Bazzurro/i) C.A. Cornell^) & F.

Transcription

1 Site- and soil-specific PSHA for nonlinear soil sites P. Bazzurro/i) C.A. Cornell^) & F. EM ail: W Department of Civil and Environmental Engineering, Abstract This paper presents two applications of a Probabilistic Seismic Hazard Analysis (PSHA) methodology which is both site- and soil-specific. The ground motion hazard is evaluated at the surface either by oscillator-frequencydependent hazard curves for spectral acceleration, S (/), or by acceleration uniform hazard spectra associated with a given mean return period. The soil response is represented statistically via multiple nonlinear dynamic analyses of the soil column with uncertain properties. The ground motion estimates presented here are more precise than those which could be found by means of conventional PSHA with standard attenuation laws for generic soil conditions. The use of generic predictive equations may in fact lead to inaccurate results especially for soft soil sites, where significant amplification is expected at long periods, and for saturated sandy sites, where liquefaction or cyclic mobility may be expected for severe levels of ground shaking. Both such cases are considered in this article. Introduction The probabilistic site amplification of ground motions has been extensively studied by others.^^ The procedure proposed here, however, is fully probabilistic since it includes the variability both in the ground motion and in the soil parameters at the site. Moreover, the soil nonlinear response is evaluated by driving real rock ground motions through afiniteelement model of the column using a program

2 33 Earthquake Resistant Engineering Structures capable of predicting the pore water pressure build-up and dissipation. In practical applications this method can use a small number of records/runs, as few as ten or less, which is a big advantage if resources and/or "appropriate" records for a site are a major constraint. Results suggest, in fact, that sufficient accuracy is achieved without running many records at many magnitude and distance pairs. This implies that real accelerograms rather than simulated ones can often be used. Two case studies involving both a sandy and a clayey soil deposit are discussed here. Methodology For brevity, this section describes only the main features of the methodology. More details can be found in Bazzurro and Cornell.^ The effect of the soil on the intensity of the ground motion at the surface is studied in terms of a site-specific, frequency-dependent amplification function, AF(f), where / is a generic oscillator frequency: Qs( f\ - L ( ) where * (/) and (/) are the %-damped spectral acceleration values at the soil surface and at the bedrock, respectively. The behavior of AF(f) for multiple ground motion records has shown that S (/) is the most effective predictor variable for estimating AF(f) (at the same frequency /) among different bedrock ground motion parameters, such as magnitude, M, source-to-site distance, /?, Peak Ground Acceleration, PGA^, and spectral acceleration values, Sa(fsc), at the initial resonant frequency, f^, of the soil column. Furthermore, results showed that once the S (/) value of a record at the bedrock is known, the additional knowledge of M and /?, which implicitly define its average response spectrum shape, do not appreciably improve the estimation of AF(f) at the same frequency /. In other words, AF(f) conditioned on (/) is virtually independent on M and 7? (see Fig. 4 to come). The proposed method for computing surface hazard curves for Z = Sa(f) convolves the site-specific rock hazard curves for X %(/), which may be exogenously provided, with the Y AF(f) estimates obtained through nonlinear dynamic analyses of the soil. Bazzurro and Cornell^ describe also a different but equally effective approach which requires performing a PSHA for the site with a rock attenuation relationship appropriately modified to incorporate AF(f). The convolution in discretized form goes as follows:

3 Earthquake Resistant Engineering Structures 333 z,] () where GW(W) is the complementary cumulative distribution function (CCDF) of any random variable, W (e.g., GZ(Z) is the sought hazard curve for *(/), i.e., the annual probability of exceeding level z), and P[X = Xj] PX(ZJ) is the probability that the rock input level is Xj. The latter can be approximately derived by differentiating the rock hazard curve in "discrete" or numerical form. Gy\x is the CCDF of AF(f), conditional on a rock level amplitude Xj. Assuming lognormality of Y given X, the Gy\x is given by: in which $( ) is the widely tabulated complementary standard Gaussian CDF. Estimates of the distribution parameters of V, (i.e., the conditional median of F, rhy\x, and the conditional standard deviation of natural logarithm of F, 0\ny\x) can be found by driving a suite of n rock ground motion records through a sample of soil column representations (recall that the soil properties are uncertain) and then regressing, for each frequency /, the values of In Y on In A. For the two case studies presented later the values of <7^y j, were found to be between 0. and 0.3 for all oscillator frequencies, /, of interest, and to be virtually independent of the level Xj. When the dependence of AF(f) on (/) was not considered the a\^y values increased from 0. to 0.3 (at / around Hz to Hz) to 0.6 to 0.7 (at / around lohz) and then decreased to approximately at infinite / (i.e., PGA). This reduction in dispersion translates into requiring a smaller number of runs to attain the same accuracy,, in the estimate of the median AF(f). The number of records, n, needed to keep the standard error, &y\x-> of the regression line within a specified (" is given by n [&Y\x/Cf- To achieve ( = ±0% only ten analyses are sufficient. 3 Applications 3. Ground Motion Database For validating the procedure, we used a large database of 78 freefield surface rock strong ground motions from 8 different earth-

4 334 Earthquake Resistant Engineering Structures 0 00 Figure : Response spectra for % of damping of the selected records. quakes that occurred worldwide between 966 and 99. It is emphasized again, however, that in real applications only about 0 records would be needed. The magnitude range is between M and M7.4, while the shortest distances to the rupture are between Okm and 4km. Approximately 40% of such accelerograms were recorded during three earthquakes: the Loma Prieta (989), Landers (99), and Northridge (994) events in California. This concentration, however, does not statistically affect the results of the amplification analyses. In the amplification study we chose at random one horizontal component of each recording (Fig. ). The PGA^ values range from O.Olg to.g. These seismograms, which contain "true" signal up to a period of at least seconds, were applied directly at the base of the soil column without any prior deconvolution. This assumption, which implies same rock outcrop and bedrock motions, is known to underestimate the motion at the column base above a site-dependent / value usually around Hz.^ Deconvolution was not performed because a possible underestimation of the amplification at high / is not crucial for the majority of longer-period structures (e.g, taller buildings, bridges, offshore platforms, etc.) which may warrant a detailed soil amplification study like the one proposed here. 3. Soil Amplification Software and Soil Modeling The computer program adopted for computing the soil site effects is a modified version of thefiniteelement program SUMDES,^ which is based on the effective stress principle, vectored motion, transient pore fluid movement, and generalized material stiffness formulation. Unlike SHAKE/ SUMDES is capable of predicting the pore pressure build-up and dissipation and can adequately describe liquefaction and

5 Earthquake Resistant Engineering Structures 33 cyclic mobility phenomena. We used a inelastic constitutive reducedorder bounding surface model which is a special version of the hypoplasticity model with fewer material parameters. The boundary conditions (i.e., elastic base) were chosen to accommodate the rockoutcrop nature of the input. Both soil deposits are located in the Mediterranean Sea. The sandy deposit consists of sands and gravels with occasional presence of cobbles. The relative density is between 60 and 80% and the total unit weight is 0kN/m^. The behavior of this sand under undrained shear is dilative and the effect of pore pressure build-up and cyclic mobility can be relevant. This effect tends to soften the soil by increasing the shear strain level at which dilation occurs. The clayey deposit is cohesive (silts and clays) and soft with both normally and overconsolidated layers. The shear modulus at small strain levels, Gmax, was established based on both shear wave velocity. %,, measurements and on correlations between the cone (CPT) tip resistance and Vs. The G/Gmax versus shear strain curves were obtained from LieW..G In both cases, a soil column of 00m was modeled using 00 elements of one meter of thickness each. The median %, increases from 80m/sec below the mudline to 400m/sec at 00m of depth. The variability in the soil properties was included through a Monte Carlo approach by randomly varying the coefficient of permeability (TTQ), the shear and the compression viscous damping ratios at IHz (^ and c), the coefficient of lateral earth pressure at rest (A~o), the coefficient, GO, which defines the elastic shear modulus Gmax &t very low strain levels, the friction angle, 3>o, and the shear strain value, 74%, at 64% of G/Gmax- The seven basic RVs above were considered lognormally distributed with <J\nRV equal to for <>, &,, KQ, and GO; to 0. for <J>o; to 0.3 for 764%, and to 0.7 for TTQ. A distribution truncation at i<jin#v was included to prevent unrealistic parameter values. The spatial correlation among layers was characterized by a firstorder auto-regressive model.^ with lag-one correlation coefficient equal to 8. The thickness of each layer is not considered random. Within each layer perfect positive correlation is assumed for <&o, Go and 74% and all three are considered to be perfectly negatively correlated with both <j and ^- KO &nd <&o are assumed to be independent of all other RVs. 3.3 Amplification Study Results For both soil deposits, each one of the 78 records was driven through a different realization of the soil column. The 78 amplification func-

6 336 Earthquake Resistant Engineering Structures AVG MEDIAN AVG+STD "' - AVG-STD " ' AVG MEDIAN AVG+STD AVG-STD : 4 < (a) Sandy site (b) Clayey site Figure : Amplification functions for both soil deposits. tions are displayed in Fig.. The two wide peaks (at /^c^o.shz and Hz) identify thefirsttwo soil resonant frequencies. At f^ the two soil columns amplify on average more than three and four times the spectral acceleration at the bedrock, S^fsc], while PGAr is amplified on average by 40% and 00%. AF(f) displays a large variability particularly in the high frequency range (see solid lines in Fig. 4 to come). Some of the records induce a highly nonlinear behavior in the soil deposit with associated large deformations and the corresponding AF(f) do not exhibit the peaks mentioned above. On the other hand, other records have AF(f) well above one for the entire frequency range. This discrepancy is due to the difference both in intensities of the input ground motions and in the "strengths" of different realizations of the soil column. When the intensity increases (i.e., increasing values of M, PGAr, and S (/), and decreasing values of R) the AF(f) tends to diminish in amplitude and to flatten out, and fsc systematically decreases towards lower / values. The dependence of AF(f) on Sa(f) (i.e., locally at the same frequency, /) can be appreciated from Fig. 3. The negative correlation is statistically significant at frequencies around /^ and above. It is emphasized that nonlinear soil responses at frequencies above Hz have been recently observed.^ Fig. 4 shows the predictive power of different combinations of four bedrock ground motion intensity measures (M, /?, (/), and

7 Earthquake Resistant Engineering Structures n 0 o ^0 o 0 o 0 AF(f)=exp[0.07-*ln(Sj(f))-0.03*(ln(Sj(i))f 0. a'(f) (9) -^j^,,,...! 0. n.. ^ ', '?.', ' * '', Sa'(f) (9) (a) Sand: /=0.33Hz (b) Clay: /=0.33Hz.... _. _ o^8*fcp 0. AF(f) expf *ln(S ^(f)) 0 *(ln(s '(f))l^ 0. O.C Sa'(f) (g) (c) Sand: /=.0Hz» O.C ; -- *N*^ ; o». : AF(f) exp[ ln(sa (f)) 0.0 {ln(sa (f))] Sa'(0 (g) (d) Clay: /=.0Hz ; AF(f)=exp[ *ln(Sj(f))-0.3'{ln(Sj(f))f : 0. : ^%\: 0. O.C Sa'(f) (g) (e) Sand: /=.0Hz AF(f)=exp[ 'ln(Sj(f))-0.0*(ln(S/{f))f : : ^\: Sa'(f) (g) (f) Clay: /=.0Hz 0. 0 : AF(f)=exp( *ln(S/(f))-0.09*(ln(Sa'(f))f ' ; - "w-g^j^go - : "^ o*<*^ :. x. \ Sa'(f) (g) (g) Sand: PGAr (loohz) % ' 0. O : AF(f)=exp[ 'ln(Sj(f))-0.*(ln(Sj(f))f : ' (h) Clay: PGAr (loohz) \ '. Figure 3: Regression of AF(f) on S^(f) at different / values for both soil deposits.

8 338 Earthquake Resistant Engineering Structures 0.8 unconditional In AF(f)IM,ln(R) --- In AF(f)IM,ln(R),ln(PGAJ * lnaf(f)lln(s/(f)),[ln(s;(q)f lnaf(f)lln(s;(f)),[ln(s;(f))f,m, A[TWII«/O r/m n~/o r/*\\i^ K/I (a) Sandy deposit (b) Clayey deposit 00 Figure 4: Regression of AF(/) on M, E, %(/), and r] in terms of the standard error of estimation, &\naf(f}- comparison, we included the unconditional v\naf(f) curve, which describes the total variation in AF(f) from Fig. when no regression is done. The similarities between the two sites is remarkable. M and jr, even when coupled with PGAr, yield a higher error than %(/) alone. Hence to predict AF(/) it is more informative to know S^(f) than M, R and PGA^. When S^(f) is already included in the regression function the extra explanatory power provided by M (which carries information about the spectral shape) is negligible (compare 3^ and 4^ model). In different words, AF(f] conditional on S^(f} is virtually independent of M. The most important consequence, however, is that, given the low values of 0"in.4F(/) in (/)> the median AF(f) can be estimated within ±0% for all frequencies with the knowledge of S^(f) from only ten response analyses. Although record selection with no attention to M and R is always to be discouraged, these results show that there is no apparent predictive benefit in keeping the explicit dependence of M and R. During the selection more care should be devoted to ensure a wide range of %(/) for / values of interest rather than in selecting records with the most appropriate M and R values for the region around the site. Finally results not shown here for brevity,^ indicate that the portion of 0"in,4F(/) due to the uncertainty in the soil properties is of secondary importance with respect to that due to record-to-record variability.

9 Earthquake Resistant Engineering Structures 'N 0 30'W 0 00'W 9 30'W 9 00'W 8 30'W 8 00'W 30'N 3 OO'N 3 OO'N 34 30'N 34 30'N 34 OO'N 34 OO'N 0 30'W 0 00'W 9 30'W 9 00'W 8 30'W 8 00'W Figure : Location of the site in the Santa Barbara Channel. 3.4 PSHA Results The two soil deposits were assumed to be located in the Santa Barbara Channel (SBC) (Fig. ), Southern California, for which a seism o- tectonic model was readily available. The site hazard was computed both by a conventional PSHA approach with the Abrahamson and Silva* attenuation law for generic soil conditions, and by the proposed convolution method applied to both soil deposits. The latter method makes use of the rock hazard curves found using the same attenuation relation*. The median AF(f) in Fig 3 and the v\naf(f) values in Fig 4 where used to estimate *(/) The UHS displayed in Fig. 6 show that using a generic soil attenuation law may lead to severe underestimation of the hazard for S*(/) below approximately /=Hz at low MRP values. The hazard at high frequencies (here above Hz) is overestimated by the predictive equation for generic soil conditions especially at high MRP values. The gap at high frequencies between the UHS found by convolution and by conventional PSHA, however, may be partly due to the application of rock outcrop motions directly to the column base. These differences in hazard prediction are due to the significant nonlinear response (Fig. 3) of the two soil columns considered in this studv.

10 340 Earthquake Resistant Engineering Structures CO* ss CO CO Transactions on the Built Environment vol WIT Press, ISSN n rock generic soil - sandy deposit (Eq. ) clayey deposit (Eq. ) 0 X a --# -----A ^r.^pzrrr.f.y (a) PE=0%/0yrs (MRP=7yrs) o. X-.,_. n CO CO.. n ^!%_ (b) PE=0%/0yrs (MRP=47yrs) o. n/'' X V^. CO CO ^[^^" -- " --.^/--A... ^ n (c) PE=%/0yrs (MRP=97yrs) (d) PE=%/0yrs (MRP=47yrs) Figure 6: Uniform Hazard Spectra (UHS) for the SBC site. (PE=Probability of Exceedance; MRP=mean return period.) 4 Summary and Conclusions Two applications of a practical soil- and site-specific PSHA method have been presented in this paper. Soil surface hazard estimates more precise than those provided by attenuation equations for generic soil conditions can be found by explicitly considering the nonlinear behavior of the deposit via an amplification function. The dynamic behavior of the soil at all oscillator frequencies can be accurately predicted with as few as ten ground motions which may be selected without particular attention to specific scenario events (i.e., M and R pairs) representing the hazard at the site. Each record is run through a different characterization of the soil column to account for uncertainty in the soil parameters. This effect is minor. Acknowledgments The authors gratefully acknowledge the financial support of U.S. Nuclear Regulatory Commission. This work has benefited greatly from the help of Dr. Norman Abrahamson and Dr. Walter Silva, who provided us with the PSHA software, the seismotectonic data, and

11 Earthquake Resistant Engineering Structures 34 the ground motion database. We also very thankful to Dr. William Joyner and Dr. Dave Boore for their insightful comments. References [] Abrahamson, N.A. & Silva, W.J, Empirical Response Spectra Attenuation Relations for Shallow Crustal Earthquakes, Seism. Res.., 68(), pp 94-7, 997. [] Bazzurro, P. & Cornell, C.A., Efficient PSHA for Nonlinear Soil Sites with Uncertain Properties, submitted to J. of Geotech. and Geoenvironmental Engrg., ASCE, 999. [3] Beresnev, LA., Atkinson, G.M., Johnson, P.A. & Field, E.H., Stochastic Finite-Fault Modeling of Ground Motions from the 994 Northridge, California, Earthquake. II. Widespread Nonlinear Response at Soil Sites, B.^.^.A., 88(6), pp 40-40, 998. [4] Electric Power Research Institute (EPRI), Guidelines for Site Spec%/zc Gmt/ncf Moh'ong, Rept. TR-093, Vol. -, Palo Alto, CA, November, 993. [] Faccioli, E., A Stochastic Approach to Soil Amplification, B.%%,4., 66(4), pp. 77-9, 976. [6] Li, X.S., Wang, Z.L. & Shen, C.K., SUMDES - A Nonlinear Procedure for Response Analysis of Horizontally-layered Sites Subjected to Multi-directional Earthquake Loading, Dept. of Civil Engrg., Univ. of California, Davis, March, 99. [7] Schnabel, P., Seed, H.B. & Lysmer, J., Modification of Seismograph Records for Effect of Local Soil Conditions, B.S.S.A., 6, pp , 97. [8] Steidl, J.H., Tumarkin, A.G. & Archuleta, R.J., What Is a Reference Site?, B.^.S'.A., 86(6), pp , 996. [9] Toro, G., Probabilistic model of soil-profile variability - Guidelines for Determining Design Basis Ground Motions, ed. J.F. Schneider, Electric Power Research Institute, EPRI TR-093, Vol., App. 6A, 993. [0] Whitman, R.V. & Protonotarios, J.N., Inelastic Response to Site-modified Ground Motions, J. of the Geotech. Engrg. Div., ASCE, 03(0), pp , 977.