**Transactions of the 17****th **_{International Conference on }**Structural Mechanics in Reactor Technology (****SMiRT 17)**

**Prague, Czech Republic, August 17 –22, 2003**

** Paper # K04-1**

**Statistical Soil-Structure Interaction Response of a Containment Building**

**Considering Soil Property Variability**

**Peter J. Rieck1) _{, Thomas W. Houston}1)**

1) Structural Dynamics Engineering Corp., Augusta, Georgia, USA

**ABSTRACT**

This paper develops the in-structure soil-structure interaction (SSI) response of a containment building founded on a layered soil site that considers the statistical variability of the founding soil properties. The soil profiles and compatible acceleration time histories are calculated using statistical variations of in-situ soil properties determined from site boreholes and soil testing. Individual soil profiles developed from a randomized log-normal description of the layered soil site are input into an iterative soil column seismic analysis program to develop the seismic strain compatible soil profiles and surface acceleration time histories consistent with the site specific design basis earthquake hazard.

Development of soil design response spectra based on the mean seismic hazard established for the site is recommended by the US Department of Energy [1] and is under consideration by the US Nuclear Regulatory Commission for the subsequent analysis, design and evaluation of nuclear power plants (NPP) [2]. When used in a SSI analysis, statistically derived soil profiles and response spectra (or acceleration time histories) consider all available soils information while avoiding designing for extreme values of site subsoil conditions that have a low probability of occurrence and, thereby, providing a method to select an appropriate level of seismic risk. Additionally, the use of statistically derived soil profiles is appropriate to develop Uniform Hazard Spectra (UHS) at the surface when given a UHS defined at bedrock. Statistically developed in-structure spectra (IRS) and structural responses are computed for a reactor containment building and are compared with those developed using soil profiles based on ASCE 4-98 soil modulus uncertainty factors [3]. The USNRC NUREG-0800 [4] provides guidance similar to ASCE 4-98 regarding the variation in soil properties to be used in SSI analyses.

The median and median plus one standard deviation (1 sigma) of in-structure response spectra (IRS) and structural responses (e.g. containment base shear) are developed based upon the SSI analysis results of thirty randomized soil columns and associated acceleration time histories. The structural responses are compared with the structural responses obtained using the deterministic ASCE 4-98 approach with a single acceleration time history and Best Estimate, Upper Bound, and Lower Bound soil column profiles.

**KEY WORDS: soil-structure interaction, seismic analysis, soil variation, response spectra, statistical analysis, nuclear**
power plant, reactor containment building.

**INTRODUCTION**

ASCE 4-98, Section 3.3.1.7 [3] and NUREG-0800 [4], Section 3.7.2, provide guidance to account for soil property uncertainties in the seismic analyses. Three sets of low strain soil properties are developed including the “Best Estimate” (BE) properties. “Upper Bound” (UB) and “Lower bound” (LB) properties are developed by multiplying and dividing the BE properties by the uncertainty factor 1 + Cv. The uncertainty factor is dependent upon the amount of soils data available. Cv can also be directly calculated by statistically evaluating the soils test data. At a minimum, Cv should not be less than 0.5 [3]. If sufficient soil data is not available, Cv = 1.0 should be used [3], [4]. ASCE 4-98 recommends conducting analyses that account for a range in low strain properties between the UB and LB properties. In practice, three analyses are often conducted, corresponding to the UB, LB, and BE soil properties. These analyses result in three sets of high strain soil properties and surface response spectra (or comparable acceleration time histories) to be used in three subsequent SSI analyses that model both the soil and supported structure. The three SSI analyses are used to develop the structural demands and IRS corresponding to the three different soil conditions. Generally, maximum demands and enveloped IRS are used in the subsequent design of the structure, systems and components.

**SUBGRADE SOIL PROFILE AND SSI MODEL**

The site soil profile used consists of three soil layers underlain by basalt bedrock as shown in Figure 1. The soil layer materials are representative of sandy gravel, gravel, and clay. Figure 1 shows the soil model being analyzed and a simplified sketch of the Containment Building finite element model used for all the SSI analyses. The soil shear moduli shown represent the BE in-situ low strain soil condition.

A uniform distribution is used to sample the soil layer depth variation. The total depth variations of the soil layer depths are constrained to fit within the bedrock depth variation.

Table 1 lists the soil profile low strain material properties. For each soil layer, the best estimate soil shear modulus is the median shear modulus as obtained from the available soils data sample. The upper and lower bound soil moduli represent the median value plus and minus one standard deviation as determined from the log-normal distribution of the test sample. Cv, in the last column of Table 1, described in ASCE 4-98 as the coefficient of variation, correlates with the coefficient of variation in the log-normal distribution and is used to develop the UB and LB shear moduli.

GUB = GBE x (1 + Cv) (1)

GLB = GBE / (1 + Cv) (2)

The corresponding upper and lower bound shear wave velocities are determined from the shear moduli and density. Table 1 also lists the soil layer densities, Poisson’s ratios and shear wave velocities for the site profile.

For the sandy gravel layer, the ASCE 4-98 coefficient of variation is determined to be 1.81 based on the statistical sampling of the available data. The gravel layer test data showed very little variation and resulted in a Cv that was less than 0.5. Accordingly, a Cv of 0.5 is assigned to meet the minimum ASCE 4-98 recommendation. The clay layer test data sample size is not sufficient to develop a reliable Cv. Therefore, a Cv of 2.0 was assigned, again following the ASCE 4-98 recommendation.

Sandy Gravel G = 4,398 ksf

Gravel G = 9,771 ksf

Clay G = 5,009 ksf

Bedrock Half-Space G = 70,419 ksf Basemat

12.5 ft ( + / - 2.50 ft )

47.25 ft ( + / - 3.75 ft )

51.25 ft ( + / - 4.60 ft )

**Figure 1 SSI Model of best Estimate Soil and Containment Building **

Containment Structure

**Table 1 Summary of Soil Profile Low Strain Material Properties**

**Layer** _{Variation}Property**Density _{(kcf)} (1)**

**Poisson’s**

_{Ratio (v)}

_{(ft/sec)}Vs

_{(ksf)}G(1)**Cv**

Lower Bound (L.B.) 785 2,431 1.81

Best Estimate (B.E.) 0.127 0.25 1,056 4,398 1.00

**Sandy**
**Gravel**

Upper Bound (U.B.) 1,420 7,957 1.81

L.B. 1,285 6,514 1.50

B.E. 0.127 0.3 1,574 9,771 1.00

**Gravel**

U.B. 1,928 14,657 1.50

L.B. 898 2,505 2.00

B.E. 0.100 0.25 1,270 5,009 1.00

**Clay**

U.B. 1,796 10,018 2.00

L.B. 3,020 42,495 1.66

B.E. 0.150 0.34 3,888 70,419 1.00

**Basalt**

U.B. 5,005 116,691 1.66

(1) k = 1000 lbf = 454 kgf)

**SEISMIC INPUT**

The seismic input for the site is defined as an outcrop motion at the bedrock level. For purposes of this study, the spectrum represents the mean seismic hazard for the site when considering the performance requirements of the structure [1]. The site seismic hazard dynamic characteristics are expressed as the design acceleration response spectrum shown in Figure 2. The spectrum of the acceleration time history used in the soil column analyses to develop strain compatible soil properties is also shown in Figure 2. The seismic hazard spectrum is based on 5% of critical damping and has a zero period acceleration (zpa) of 0.125 g and amplified plateau of 0.293 g. The acceleration time history of the spectrum shown in Figure 2 is used as input into all the soil column analyses to develop strain compatible soil properties and the surface response spectra.

**Figure 2 Site Seismic Hazard Spectrum **

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0.10 1.00 10.00 100.00

**Frequency (Hz)**

**Acceleration (g)**

Seismic Hazard Time History Spectrum Hazard Spectrum:

**DETERMINISTIC ANALYSES**

Following the ASCE 4-98 and NUREG-0800 recommendations, three SSI analyses were conducted using the BE, LB and UB soil properties with the SASSI [6] computer program. Resultant peak structural demands, accelerations, base shears and overturning moments are presented in Table 2.

**Table 2 ASCE 4-98 SSI SSI Analyses – Peak Structural Demand Summary**

**Acceleration (g)** **Shear (k) (1)** _{Moment (ft-k)} (1)

**Soil**

**Case** **Top of**

**Basemat** **ContainmentTop of** **Top of InteriorStructure** **ContainmentBase of** **Base of InteriorStructure** **ContainmentBase of**

**Base of**
**Interior**
**Structure**

**L.B.** 0.214 0.989 0.537 20,200 5,189 2,388,000 173,700

**B.E.** 0.238 0.996 0.527 15,960 6,536 2,302,000 255,800

**U.B.** 0.301 0.948 0.897 16,720 10,160 2,191,000 371,300

(1) k = 1000 lbf = 454 kgf)

The seismic demands are the result of interacting structural resonances developed when soil and structure natural frequencies are excited by the frequencies inherent in the design basis ground motion. It is seen in Table 1, that the UB soil case governs most of the responses and subsequently most of the design. However, it is noted that the Containment Structure base shear and moment are governed by the LB soil case. The BE case is governing only for the acceleration at the top of the Containment Structure.

Containment Building IRS for the three structural locations corresponding to the Basemat, top of the Containment Structure and the top of the Interior Structure are presented in Figures 3a, 3b, and 3c. The spectra are developed for 5% damping. When using the ASCE/NRC approach, the same time history developed for the BE soil conditions is used for all three soil cases. In general, it can be expected that the frequency content for a surface response spectrum (or time history) would be lower when generated consistently for the LB soil case and higher for the UB soil case.

The use of soil case consistent time histories would increase the IRS low frequency region response for the LB soil case and the high frequency region response for the UB soil case.

The broad response shown at the basemat level in Figure 3a reflects the broad frequency content of the bedrock design basis earthquake [Figure 1] transmitted through the soil.

The magnitude of the response at the top of the containment shown in Figure 3b indicates a strong resonance of low frequencies associated with the overall building mass and soil and the lower frequency component specific to the containment structure. This same low frequency response carries over into the interior structure response shown in Figure 3c. The higher frequency response of the interior structure is seen directly related to the soil case under consideration.

**Figure 3a ASCE 4-98 5% Damping IRS - At Basemat**

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.1 1.0 **Frequency (hz)** 10.0 100.0

**Acceleration (g)**

**STATISTICAL ANALYSES**

In using the statistical approach, thirty SSI analyses are conducted. The thirty soil columns and time histories used represent the variability of the soil stiffness and layer thickness. In each soil column, the shear modulus for each layer and the bedrock was picked using a Monte Carlo simulation of the log-normal distribution of the soil layer test data within three standard deviations of the median (BE) shear modulus. In addition to developing random soil properties, random soil layer depths are also generated. The random selection of soil layer depth (or layer thickness) is based on a uniform distribution of the measured depths variation shown on Figure 1.

**Table 3 30 Statistically Varied SSI Analyses – Peak Structural Demand Summary**

**Acceleration (g)** **Shear (k) (1)** _{Moment (ft-k)} (1)

**Statistical**

**Attribute** **Top of**
**Basemat**

**Top of**
**Containment**

**Top of Interior**
**Structure**

**Base of**
**Containment**

**Base of Interior**
**Structure**

**Base of**
**Containment**

**Base of**
**Interior**
**Structure**
**Minimum** 0.109 0.375 0.323 7,544 3,149 898,200 129,400

**Mean** 0.222 0.855 0.568 17,316 6,615 2,167,440 248,977

**Maximum** 0.339 1.172 0.745 26,900 9,932 3,216,000 373,700

**Median** 0.232 0.920 0.586 18,765 7,096 2,239,978 247,385

**Median+1 SD** 0.312 1.203 0.729 25,428 9,526 3,027,578 328,646

**Figure 3c ASCE 4-98 5% Damping IRS - Top of Interior Structure**

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.1 1.0 **Frequency (hz)** 10.0 100.0

**Acceleration (g)**

Lower Bound Best Estimate Upper Bound

**Figure 3b ASCE 4-98 5% Damping IRS - Top of Containment Structure**

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

0.1 1.0 **Frequency (hz)** 10.0 100.0

**Acceleration (g)**

By considering variations in both the material and geometric attributes, a more thorough representation of the available soils data that directly affect the seismic response of supported structures is utilized.

The thirty sets of structural demands and IRS analyses correspond to the range of soil profile material and geometry variation that extends over three standard deviations from the best estimate values. Figure 4 shows the thirty acceleration response spectra for the Basemat.

At this time there is no formal regulatory requirement regarding the number of soil columns necessary to obtain the median spectrum. Using more or fewer columns may change the median response. The authors’ experience for several sites is that thirty columns are sufficient to achieve a reasonably stable median. However, this number should be confirmed on a site specific basis, especially when highly variable soil conditions exist. Regulatory guidance regarding this statistical approach and the appropriate number of soil column analyses is expected in the near future.

Figure 4 shows the Basemat response spectra resulting from the SSI analyses using the thirty statistically varied soil columns and consistent time histories. The two heavier lines are the enveloped maximum and minimum spectral responses. It is seen that depending upon the particular soil columns being analyzed there are significant response differences. The Basemat zero period accelerations (zpa) vary from a minimum of 0.109g to a maximum of 0.339g [Table 3], an increasing difference of over 200%. The zpa for the top of the Containment Structure exhibits an even greater variation, 0.375g to 1.172g. The soil conditions forming the basis of these maximums and minimums represent extreme conditions wherein the many interactive modes activated by the earthquake are either reinforced or attenuated. Over-consideration of extreme values in design is avoided by using median responses.

The median and median + 1 and 2 standard deviations (sigmas) IRS developed using the statistical approach are presented in Figures 5a, 5b, and 5c. The ASCE deterministic enveloped spectra are also included for comparison.

**COMPARISON OF ANALYSES RESULTS**

Figures 5a, 5b, and 5c show the median spectra are significantly less than the ASCE approach derived IRS for all locations. At the Basemat, Figure 5a, the enveloped spectrum somewhat matches the median + 1 sigma spectrum. However, it is seen that the envelope spectrum significantly exceed the mean + 1 sigma spectra for the top of the Containment Structure, Figure 5b, and the top of the Interior Structure, Figure 5c.

Structural demands are compared in Table 4.

**Figure 4 30 Statistically Varied SSI Analyses - Basemat 5% IRS**

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

0.1 1.0 **Frequency (hz)** 10.0 100.0

**Acceleration (g)**

**Figure 5a Basemat 5% IRS **

1.5 2.0 2.5 3.0

**Table 4 Comparison of Peak Structural Demand Summary**

**ZPA Acceleration (g)** **Shear (k) (1)** _{Moment (ft-k)} (1)

**Statistical**

**Attribute** **Top of**

**Basemat** **ContainmentTop of** **Top of InteriorStructure** **ContainmentBase of** **Base of InteriorStructure** **ContainmentBase of**

**Base of**
**Interior**
**Structure**
**ASCE Envelope** 0.301 (UB) 0.996 (BE) 0.897 (UB) 20,200 (LB) 10,160 (UB) 2,388,000 (LB) 371,300 (UB)

**Median** 0.232 0.920 0.586 18,765 7,096 2,239,978 247,385

**Median+1 SD** 0.312 1.203 0.729 25,428 9,526 3,027,578 328,646

**Median+2 SD** 0.418 1.575 0.907 34,457 12,786 4,092,106 436,600

(1) k = 1000 lbf = 454 kgf

**DISCUSSION OF RESULTS**

The seismic structural demands presented in Table 4 and IRS in Figures 5 can be used for the design of the Containment Building. The significance and importance of potential soil material and geometry variation for a typical Containment Building is demonstrated by the large difference in the deterministically demands presented in Table 3 and the fullness of the maximum and minimum bounded statistically derived spectra shown in Figure 4, when all thirty

**Figure 5b Top of Containment 5% IRS **

0.0 2.0 4.0 6.0 8.0 10.0 12.0

0.1 1.0 **Frequency (hz)** 10.0 100.0

**Acceleration (g)**

Statistical Median Statistical Median + 1 SD Statistical Median + 2 SD ASCE Deterministic Envelope

**Figure 5c Top of Interior Structure 5% IRS **

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.1 1.0 **Frequency (hz)** 10.0 100.0

**Acceleration (g)**

The deterministic approach generally relies on the responses obtained by using extreme value soil properties, as determined by Equations 1 and 2. (Note: The statistical approach also uses the guidance provided for Cv. When the actual statistical variation of the measured soil layer data is less than 0.5, a variation of 0.5 is assigned.)

The governing deterministic structural demands presented in Table 3 result from either the UB and LB conditions. Only one demand, acceleration at the top of the Containment Structure, is governed by BE soil conditions. In Table 4 shows the deterministic structural demands generally correspond in magnitude to statistical demands having non-exceedance probabilities of 50% or 80%. Only the zpa acceleration at the top of the Interior Structure is close to a 90% non-exceedance probability.

The deterministically developed enveloped IRS, shown in Figure 5, are also inconclusive with respect to non-exceedance probability. In general they approximate the 80% non-non-exceedance associated with the median + 1 sigma statistically developed spectra.

**CONCLUSIONS**

The use of statistical SSI analyses to develop in-structure seismic demands and response spectra provides can quantify the effect that soil property variation and uncertainty has on the NPP structural response. The SSI analysis example presented in this paper demonstrates the significance that variation and uncertainty in soil properties has on the seismic response of the supported structure. Quantification of the seismic demands with respect to soil property variation and uncertainty is in the form of non-exceedance probabilities.

The use of enveloped seismic demands developed using a minimum of three deterministic SSI analyses, following recommendations by ASCE and NRC guidelines [3] [4] does not provide sufficient information to assure soil

uncertainty is adequately addressed. The example in this paper shows that enveloped deterministically derived SSI structural demands and spectra have a non-exceedance probability comparable to 80%, with some demands having significantly higher or lower non-exceedance probabilities.

Statistical SSI analyses require significant analytical and computer resources. In the example presented, thirty SSI analyses, modeling soil and structure, are conducted. This is an order of magnitude more then needed for the three deterministic analyses conducted. More than thirty analyses may actually be needed, depending on the actual quality of the soil site and available soil test data. The availability of faster processing computers having high data storage capabilities makes such multiple analyses more practical.

Statistical SSI analyses become more important with the increasing use of probabilistic risk assessments to evaluate the safety of critical structures and processes in high seismic environments [1].

The calculated non-exceedance probabilities are independent of the hazard input motion.

Statistical SSI analyses consider full variability of soil material properties and soil/bedrock layering variability inherent in the test data

Statistically developed responses when analyzed using seismic input motions having known hazard levels (e. g. a uniform mean hazard level, UHS, as prescribed for DOE sites) provide a means of providing seismic input to

subsequent system and component analyses that is consistent with the design basis hazard level.

**REFERENCES**

1.DOE-STD-1020-94, Change Notice #1, “Natural Phenomena Hazards Design and Evaluation Criteria for Department of Energy Facilities,” U. S. department of Energy, Washington, DC, January 1996.

2. NUREG/CR-6728,”Technical Basis for Revision of Regulatory Guidance on Design Ground Motions: Hazard and Risk-Consistent Ground Notion Spectra Guidelines,” U. S. Nuclear Regulatory Agency, Office of Nuclear Regulation, October, 2001.

3. ASCE 4-98, “Seismic Analysis of Safety-Related Nuclear Structures and Commentary,” American Society of Civil Engineers Standard, 2000.

4. NUREG-0800, “Standard Review Plan,” U. S. Nuclear Regulatory Agency, Office of Nuclear Regulation.