Effects of Ground Motion Intensity Parameters on Soil-Foundation- Structure-Interaction and Site Response

Transcription

1 Effects of Ground Motion Intensity Parameters on Soil-Foundation- Structure-Interaction and Site Response M. Ghayoomi Department of Civil Engineering, University of New Hampshire, Durham, NH, USA S. Dashti Department of Civil, Environmental, and Architectural Engineering, University of New Colorado, Boulder, CO, USA ABSTRACT: The seismic response of a structure is strongly influenced by the properties of the earthquake motion experienced at its foundation, which is in turn influenced by Soil-Foundation-Structure-Interaction (SFSI) effects. The characteristics of the suite of ground motions selected for design affect the site s nonlinear response as well as the interaction between soil, foundation, and structure in analyses. In this study, dynamic centrifuge experiments were conducted on a Single-Degree-of-Freedom (SDOF) model building founded on dry, medium-dense sand inside a Flexible-Shear-Beam (FSB) container. A series of six earthquake motions with different characteristics was applied to the base of the container as input to the soil-structure system and the effects of Peak Ground Acceleration (PGA), Arias Intensity (I a ), and Shaking Intensity Rate (SIR) on different aspects of SFSI and site response were evaluated. More holistic intensity parameters, i.e. Arias Intensity and Shaking Intensity Rate, showed more consistent effects especially on site response and structural inertial response. In addition, the importance of index parameters containing both effects of intensity and frequency content is emphasized. INTRODUCTION The seismic performance of a soil-structure system is affected by the properties of soil, structure, and the earthquake motion. The characteristics of a complex, transient earthquake motion are commonly quantified by simple index parameters, such as the Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), or specific duration (D 5-95 ), and others. These parameters are, in turn, used in the selection of a suite of design ground motions at a given site. Knowledge of the most efficient ground motion parameters for predicting a given response (or demand measure) in soil or structure is critical in a reliable, performance-based seismic hazard analysis. As a result, a comprehensive understanding of the relative influence of various ground motion indices on site performance (shaking and settlement) and seismic Soil-Foundation-Structure-Interaction (SFSI) is necessary. Although simplistic indices such as PGA or PGV have been used in many applications, recent studies have indicated that more holistic motion indices incorporating different characteristics of ground shaking (as opposed to a single-time peak value) may correlated better with building damage and performance, site response, and SFSI (Travasarou et al. 23, Dashti et al. 2b, Campbell & Bozorgnia 22). For example, Dashti et al. (2b) showed via centrifuge testing that Arias Intensity (I a ) and Shaking Intensity Rate (SIR), which is effectively the slope of the Arias Intensity time history, strongly influenced site response and importantly the rate and magnitude of soil and building settlement. Over the past decades, SFSI has been extensively studied and its effects on soil deformation and structural demand have been evaluated empirically, analytically, and experimentally (e.g., Stewart et al. 999 a,b; Pecker and Pender 2; Pitilakis et al. 28; Dashti et al. 2a,b; Kausel 2). Two mechanisms of interaction could be simultaneously active in a soil-structure system; kinematic and inertial interaction (Stewart et al. 999a,b). The kinematic interaction explains the difference between the free-field soil response (FF) and a hypothetical stiff foundation, referred to as the Foundation Input Motion (FIM) (Kim & Stewart 23). The inertial interaction is developed due to the inertial vibration of the structural mass (Kramer & Stewart 24). To fully understand the SFSI response, each of these mechanisms should be evaluated both independently and collectively. In this study, a simple mass-foundation structural model was placed on a layer of dry, cohesionless soil stratum resting on rigid plate representing bedrock. The free-field and soil-structure responses were recorded during the application of six consecutive -D earthquake motions with different charac-

2 teristics. Then, the effects of PGA, Arias Intensity, and Shaking Intensity Rate on different aspects of SFSI and site performance (in terms of shaking and settlement) were examined. Specifically, comparisons of Free-Field (FF) surface motion with Base Motion (BM) at the base of the container, Foundation Motion (FM) with FF surface motion, and Structural Horizontal Motion (SHM) on the mass with FM are demonstrated and discussed. 2 CENTRIFUGE TESTS One dynamic centrifuge experiment was performed on a model soil-structure with shallow foundation. The test was executed in the 4 g-ton geotechnical centrifuge at the University of Colorado, Boulder (Ko 988). An in-flight hydraulic servo-controlled shake table was employed to apply the earthquake motions (Ketchum 989). The models were prepared inside a transparent, Flexible Shear Beam (FSB) container (Ghayoomi et al. 22, 23). The six earthquake ground motions were applied consecutively on a soil-structure model at 77g centrifuge spin acceleration. The results in this paper are presented in the prototype scale, unless stated otherwise. 2. Model layout A 26-m prototype, dry sand layer was dry pluviated to a relative density of approximately 6%. Nevada sand #2 with G s =2.65, e min =.59, and e max =.85 was used in the presented experiment. Then, the model structure was placed on the soil layer with - m embedment. Arrays of horizontal accelerometers were buried at different depths during pluviation. A combination of horizontal and vertical accelerometers was mounted on the model structure. A horizontal LVDT and several vertical LVDTs were employed to measure the horizontal displacements at the base of the container and settlements in the freefield and on the structure. The instrumentation layout is shown in Figure. 2.2 Structural model properties A 4-story, 2-m high and 6-m wide, building was chosen as the target structure. This structure was modeled using a simplified Single-Degree-Of- Freedom (SDOF) oscillator-foundation system with flexible walls. The.3 kg model with about 73% of the mass in the oscillator led to a base contact pressure of about 62 kpa. The first mode fixed-base natural period of the structure was estimated to be.25 second (i.e. 4 Hz natural frequency). The prototype SDOF system was then converted to model scale units for construction using the proper centrifuge scaling laws. 2.3 Ground motions Six earthquake motions were selected for this study. These motions, with the order of their application, are presented in Tables and 2. Arias Intensity (I a ) and Shaking Intensity Rate (SIR) of the motions were calculated using the following equations, respectively, and are listed in Table 2 (Arias 97 and Dashti et al. 2). I a t a 2 ( t) dt 2g () SIR I D (2) a where g is the gravitational acceleration, t is time, a is acceleration, I a5-75 is the change in Arias Intensity (I a ) from 5 to 75% of its total value, and D 5-75 is its corresponding time duration. The Peak Ground Velocity (PGV) and predominant period (T p ) of the motions are also presented in Table 2. The ground motions were selected so that they cover a wide range of intensities and frequency contents. The target motions were modified to address the shake table frequency limitations. The measured acceleration time histories of the motions at the base of the soil (Acc2) for the six motions are shown in Figure 2. The corresponding 5%-damped acceleration response spectra and Arias Intensity time histories of the measured base motions are shown in Figures 3 and 4, respectively. Table. Selected Suite of ground motions to apply at the base of the model container during centrifuge testing. Figure. Instrumentation layout of the centrifuge model (dimensions presented are in the prototype scale at 77g). No. Earthquake Station Year Motion ID Landers Joshua Tree 992 JOS 2 Loma Prieta Santa Cruz 989 SCZ 3 Northridge Newhall 994 WPI 4 Chi-Chi TCU 999 TCU 5 Landers Lucerne 992 LCN 6 Kobe Takatori 995 TAK

3 Acceleration Table 2. The characteristics of the measured motions at the base of the model container during the centrifuge tests. No. PGA PGV I a SIR T p T m (cm/s) (s) (s) JOS - SCZ - WPI - TCU - LCN - TAK Time (s) Figure 2. Acceleration time histories of the measured base motions. Figure 4. Comparison of Arias Intensity time histories of the achieved motions at the base of the container. The base motions present a range of intensities, durations and frequencies. Importantly, the predominant period of the motions (shown in Table 2) inversely represent the dominant frequency content of the motions and vary around the fixed-base natural period of the structure (.25 s). This can help in further evaluating the effects of motion frequency content on SFSI. 3 FREE-FIELD RESULTS The data recorded from acceleration #5 and LVDT #7 in the far-field, were considered as the free-field soil surface acceleration and settlement measurements, respectively. The application of each motion caused certain soil settlement, which, in turn, changed the relative density of sand prior to the next experiment, as shown in Figure 5. The overall change was about 3% in free-field at the end of all six motions, which is not significant considering the uncertainty involved in capturing the target soil relative density during specimen preparation. However, this change should be considered in evaluating SFSI effects and site response analyses. Figure 5. The change in the initial relative density (Dr) of Nevada sand in the free-field due to application of consecutive earthquake motions. Figure 3. Comparison of 5%-damped spectral acceleration of the achieved motions at the base of the container. To evaluate site response without the effect of the structure, the three ground motion indices (PGA, I a, and SIR) in the free-field (FF) soil surface are compared with those at the base of the container (base motion, BM) in Figure 6. The PGA amplification

4 SIR FM SIR FF PGA FM I afm PGA FF I aff FM/FF Transmissibility Function trend in this figure didn t follow the expected trend, i.e. lower amplification for stronger motions due to higher induced shear strains, lower shear modulus, and higher damping. This might be attributed to the slight increase in sand relative density, particularly after the first motion, or to the different intensity build-up patterns or different frequency contents of the motions, which affected PGA amplification. A more consistent nonlinear trend in I a and SIR amplification was observed in Fig. 6. As a result, Arias Intensity may be a more efficient parameter in evaluating site response and ground motion amplification from BM to FF..5.5 PGA BM 2 2 I abm JOS motion is shown in this figure. Typically higher settlement was observed comparing with the freefield surface settlements. The main portion of settlements occurred when the absolute acceleration is higher than a threshold acceleration (e.g..g)..5.5 Figure 7. Acceleration transmissibility function during for the TCU motion Frequency (Hz) SIR BM Figure 6. Comparisons of intensity parameters of BM and FF motions..5.5 PGA FF.5 2 I aff 4 FOUNDATION RESPONSE The acceleration time history measured at the foundation level is referred to Foundation Motion (FM), which is different from FIM, in this paper. Kim and Stewart (23) showed that the amplitude of horizontal motion decreases from FF to FM due to base slab averaging. To observe this behavior, an example of FM/FF transmissibility function for the TCU motion is shown in Figure 7. To evaluate SFSI, transmissibility functions were obtained as smoothed frequency response transfer functions of the FM/FF motion ratio, calculated using the following equation. ( f ) xy S ( f ) xy Sxx ( f ) T (3) where S xx and S xy are the power and cross spectral density functions of acceleration time histories of input and output motion, i.e., x and y. As expected, the amplitude of the motion reduced from FF to FM for frequencies greater about 2 Hz. The change in the motion indices from FF to FM is shown in Figure 8, showing a general reduction trend in all three indices. The structural settlement during the JOS motion is shown in Figure 9. In addition, the absolute acceleration time history of the.5 SIR FF Figure 8. Comparison of motion indices from FF to FM. Figure 9. Free-field surface and structural settlement due to JOS motion. 5 OSCILLATOR REPONSE The inertial interaction is commonly ~ evaluated with the period lengthening ratio (i.e., T / T ), the ratio of flexible- to fixed-base natural period of the structure. Higher intensity motions lead to soil softening, which influencing the flexible-base period of the structure (T ~ ). Since T is a constant, it is expected

5 SIR SHM PGA SHM I ashm SIR SHM PGA SHM I ashm that by increasing the intensity of the motion T ~ increases. However, the frequency content of the input motion, in relation to the natural period of the structure and the site, is also expected to influencet ~. The fixed- and flexible-base natural period are inverse of fundamental frequency of the fixed- and flexiblebase structure ( f and ~ f ), respectively. The transmissibility function, as in Equation 3, was used to estimate frequency response transfer function of the structure while x and y represent acceleration time history measurements on the foundation and structural mass, respectively. The first peak in transfer functions were selected as fundamental natural frequency of the system. ~ T / Variations in the measured T due to change in motion index parameters are shown in Figure. I a and SIR demonstrated a more consistent correlation with the period lengthening ratio in comparison with PGA. Specially, the period lengthening ratio can be linearly approximated by I a, because I a is a ground motion parameter that is affected by intensity, duration, and importantly the frequency content of the motion. FF to FM and then and increase from FM to SHM. The changes of intensity parameters from FF to SHM are shown in Figure 2. In general, it is difficult to evaluate the oscillator s response only by considering the free-field motion. As expected, the trends were not as consistent as those of Figures 8 and. However, the I a and SIR demonstrated a fairly consistent amplification pattern. The only outlier in these plots occurred during the WPI motion, which experienced a de-amplification from FF to SHM. The motion s characteristics in Table 2 suggest that the WPI motion had a higher mean period (T m ) compared to other motions. This observation emphasizes the importance of frequency content characteristics of the earthquake motion in SFSI..5.5 PGA FM I afm SIR FM Figure. Comparison of motion indices from FM to SHM Figure. Effect of motion indices on the period lengthening ratio..5 PGA FF 2 4 I aff In order to better evaluate the oscillator response, the Structure Horizontal Motion (SHM) recorded on the structure mass to FM comparisons of index parameters are shown in Figure. All three indices increased from foundation to the oscillator indicating a general amplification. However, I a and SIR followed a more consistent nonlinear amplification trend. This is in accordance with the trends in Figure, which indicates the suitability of Arias Intensity (I a ) and Shaking Intensity Rate (SIR) in SFSI analyses of oscillator-to-foundation response. 6 STRUCTURAL SYSTEM RESPONSE Considering Figures 8 and simultaneously, the intensity of the motion experienced a decrease from SIR FF Figure 2. Comparison of motion indices from FF to SHM. Figure 3 helps evaluate the overall amplification of the motion indices from BM to SHM. The PGA followed an inconsistent trend from the base to the oscillator. Both I a and SIR were amplified consistently, which signifies the importance of considering more holistic intensity measures as opposed to a one time value.

6 SIR SHM PGA SHM I ashm 7 CONCLUSIONS Soil-Foundation-Structure-Interaction (SFSI) effects may play an important role in the performance of the structure and its damage potential. The characteristics of the ground motion are known to significantly influence kinematic and inertial interactions. In a performance-based design framework, it is important to identify efficient ground motion index parameters that correlate well with the key aspects of site response and SFSI. In this study, the effect of two intensity parameters, Arias Intensity (I a ) and Shaking Intensity Rate (SIR), where were more holistic compared to one-time intensity parameters like PGA, were evaluated experimentally on several aspects of SFSI..5.5 PGA BM SIR BM I abm Figure 3. Comparison of motion indices from BM to SHM. Overall, I a and SIR showed more consistent trends compared to the PGA when comparing the motions recorded in the free-field (FF), base of the container (BM), foundation of the structure (FM), and the mass of the oscillator (SHM), as well as soil and structural settlements. These two index parameters which bring in the influence of intensity, frequency content, and duration as opposed to just the intensity also showed better correlations with structural period lengthening due to inertial interaction. The settlement rate of the soil in the free-field and the structure also appeared to follow the rate of Arias Intensity time history of the input motion. Employing more holistic ground motion index parameters (e.g., I a, SIR, etc.) are recommend for the selection of ground motions in SFSI analyses or design. More than one index parameter is recommended, as one parameter alone may not reveal important aspects of site and structural performance. 8 REFRENCES Arias, A., 97. 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