Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

ROCKING BEHAVIORS OF SDOF STRUCTURES ON SHALLOW

FOUNDATION VIA CENTRIFUGE TEST

J. G. Ha1, S. B. Jo1, M. T. Yoo2, J. S. Lee3, D. S. Kim4

ABSTRACT To assess the seismic load applied to the structure with a shallow foundation, it is required to consider the soil-foundation-structure interaction (SFSI). A series of dynamic centrifuge tests with Single-Degree-of-Freedom (SDOF) structures on the shallow foundation were performed to understand the effects of SFSI, particularly rocking effect, on seismic load. The test specimen was composed of a SDOF structure model, a shallow foundation and sub-soil deposits in an equivalent shear beam (ESB) container. The test parameters were the natural periods and heights of the SDOF structure models, the sizes of foundation and intensity of input earthquakes. To investigate the effect of SFSI, the structure responses measured from centrifuge test were compared with the fixed base structure responses subjected to the free field ground acceleration. When the periods of the structures were close to the site periods, the earthquake responses were significantly decreased by the rocking motion of the foundation. As the level of the ground acceleration increased, the seismic load and overturning moment of the fixed base models not considering SFSI were expected to increase proportionally. On the contrary, the seismic loads of the structures on the rocking foundation were limited by the ultimate moment capacity of the foundation. As the size of the footing increases, the seismic load of SDOF system increases due to higher ultimate moment capacity and the rocking stiffness of the foundation.

1Graduate Student Researcher, Dept. of Civil and Environmental Engineering, KAIST, Republic of Korea, Daejeon 2Post Doctor, Dept. of Civil and Environmental Engineering, Univ. of California, USA, California 3Assistant Professor, Dept. of CMI and Environmental Engineering, Wonkwang Univ., Republic of Korea, Iksan 4Professor, Dept. of Civil and Environmental Engineering, KAIST, Republic of Korea, Daejeon Ha J. G., Jo S. B., Yoo, M.T., Lee J. S. and Kim D. S. Rocking behaviors of SDOF structure on shallow foundation via centrifuge test. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

ROCKING BEHAVIORS OF SDOF STRUCTURES

ON SHALLOW FOUNDATION VIA CENTRIFUGE TEST

S. B. Jo1, J. G. Ha1, M. T. Yoo2, J. S. Lee3 and D. S. Kim3

ABSTRACT To assess the seismic load applied to the structure with a shallow foundation, it is required to

consider the soil-foundation-structure interaction (SFSI). A series of dynamic centrifuge tests with Single-Degree-of-Freedom (SDOF) structures on the shallow foundation were performed to understand the effects of SFSI, particularly rocking effect, on seismic load. The test specimen was composed of a SDOF structure model, a shallow foundation and sub-soil deposits in an equivalent shear beam (ESB) container. The test parameters were the natural periods and heights of the SDOF structure models, the sizes of foundation and intensity of input earthquakes. To investigate the effect of SFSI, the structure responses measured from centrifuge test were compared with the fixed base structure responses subjected to the free field ground acceleration. When the periods of the structures were close to the site periods, the earthquake responses were significantly decreased by the rocking motion of the foundation. As the level of the ground acceleration increased, the seismic load and overturning moment of the fixed base models not considering SFSI were expected to increase proportionally. On the contrary, the seismic loads of the structures on the rocking foundation were limited by the ultimate moment capacity of the foundation. As the size of the footing increases, the seismic load of SDOF system increases because the energy dissipation is less due to higher ultimate moment capacity and the rocking stiffness of the foundation

Introduction

The seismic behaviors of structure with shallow foundation on soil were highly affected

by the soil-foundation-structure interaction (SFSI). FEMA 440[1] developed a design procedure which considers a period lengthening and damping increase with the flexible base model. Another concept is the rocking foundation which is related with the deformation of foundation and yielding of soil. The design concept of rocking foundation suggested that inelastic deformations would accumulate at the soil-foundation system rather than the superstructure elements and has a potential advantage in reducing seismic load on structure during strong earthquake.

To verify the mechanism of the rocking foundation, Kutter and his colleagues have performed centrifuge tests on models of shear wall and bridge piers and found that the critical area ratio is sensitive factor to rocking behavior from load-deformation results [2, 3, 4, 5, 6]. In

1Graduate Student Researcher, Dept. of Civil and Environmental Engineering, KAIST, Republic of Korea, Daejeon 2Post Doctor, Dept. of Civil and Environmental Engineering, Univ. of California, USA, California 3Assistant Professor, Dept. of CMI and Environmental Engineering, Wonkwang Univ., Republic of Korea, Iksan 4Professor, Dept. of Civil and Environmental Engineering, KAIST, Republic of Korea, Daejeon Ha J. G., Jo S. B., Yoo, M.T., Lee J. S. and Kim D. S. Rocking behaviors of SDOF structure on shallow foundation via centrifuge test. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

the same context, Gazetas and his group agree the energy dissipation capacity of rocking foundation and study about nonlinear rocking stiffness of foundation from finite element analysis [7, 8, 9]. Kim et al. (2013) has studied the effects of SFSI on the dynamic response of structures using real earthquake motions in centrifuge but the numbers of cases are limited to clearly understand the mechanism of rocking foundation.

In this study, a series of dynamic centrifuge tests with Single-Degree-of-Freedom (SDOF) structures on the shallow foundation were performed to understand the effects of SFSI on seismic load. The test specimen was composed of a SDOF structure model, a shallow foundation and sub-soil deposits in an equivalent shear beam container. The test parameters were the dynamic natural periods and heights of the SDOF structure models, the sizes of foundation, and intensity level of the input earthquakes. To investigate the effect of SFSI, the structure responses measured from centrifuge test were compared with the fixed base structure responses subjected to the free field ground acceleration. The effects of various parameters such as natural period and height of structure, footing size, and earthquake intensity on seismic force of structure were discussed based on the concept of rocking foundation.

Ultimate Moment Capacity and Maximum acceleration

The rocking of the foundation on soil may be visualized as a contact problem, with a

contact area moving from one side of the footing to the other as the foundation rotating shown in Fig. 1. As the magnitude of rotation increases, the foundation contact area with soil becomes smaller and moves towards the edge of the foundation due to uplift at the other side and the bearing resistance along the whole contact area may become equal to the ultimate bearing resistance. At this stage, this minimum contact area is defined as the critical contact area. In the case of rectangular foundation, the ultimate moment capacity is defined as Eq.1, when the contact area reaches critical point [5,6].

Figure 1. Illustration of the geometry and contact of the rigid footing with deformed soil surface [2].

= · 1 − (1)

where V is the applied vertical load under the foundation, L is the foundation length, Lc is the critical contact length required to support the vertical load.

Depending on the ultimate moment capacity and dimension of super structure, the maximum spectral acceleration is limited by Eq.2 and Eq.3.

= · · ≤ · · 1 − = (2)

≤ , = · · (1 − ) (3)

where mt is total mass of the structure and the foundation, ms is effective mass of the structure, and Sa,max is maximum spectral acceleration of a structure on the shallow foundation.

It is shown that the earthquake load of structure with shallow foundation has upper bound by mass ratio (mt/ms), the aspect ratio (h/L) and critical contact length ratio (L/Lc). Foundation yielding will limit the transmitted acceleration to the superstructure which leads to the safer structure but the designer should accommodate the permanent settlement and rotation of foundation with proper design. In this study, the concept of rocking foundation was assessed by changing footing length (L), height of structure (h), natural period of structure, and earthquake intensity

Centrifuge Test Procedure

The beam-type centrifuge facility in KAIST was used to perform all the tests reported here in 20 g and 40g centrifugal acceleration fields. Test results at 20g were only discussed in this paper. This facility has a platform radius of 5 m and a maximum capacity of 240 g-tons [10]. The model earthquake was generated by a self-balanced electro-hydraulic earthquake simulator mounted on the centrifuge. The base shaking acceleration could be exerted to a maximum value of 0.5 g in the prototype scale at 40 g of centrifugal acceleration. The allowable frequency range of the earthquake loading was from 30 Hz to 300 Hz on the model scale, and the utilization of the self-balanced shaking table for the sinusoidal and real earthquake motion was verified [11]. The soil container used in this study is the equivalent shear beam (ESB) type, which is composed of shear beam boxes so that the horizontal movement of the soil is allowed to reduce the reflection of the waves at the boundary of the container [12].

SDOF structures and foundation

The SDOF structure was composed of two thin steel plates and a lumped mass on the top as shown in Table 1. Changing the plate length and the lumped mass, six structure models were made to represent prototype structures with various natural periods and effective heights. Table 1 shows the effective mass and stiffness of the SDOF structure models at 1g. Four natural periods of structure is evenly selected from T=0.09s to 1.00 as prototype scale at 20gc (centrifugal acceleration). Among them, the height of two structures, SDOF2 and SDOF3, which periods are similar to site period, was reduced by half. These short-SDOF structures will induce smaller moment from the roof mass to foundation during earthquake and the maximum allowable spectral acceleration for a given foundation size will be higher even if the period of structure is similar.

Three sizes of square foundation were used in the experiments. Sides (length and width) of square were varied as 7cm (FND7), 10cm (FND10) and 14cm (FND14), and the depth of foundation was fixed as 3cm. Kim et al.(2013) were used 7cm sized-foundation which was difficult to observe the variation of rocking behavior with earthquake intensity increase, because it was too small to resist the rocking effects. In this study, the size of foundation and its ultimate moment capacity were varied. The interiors of the foundations were hollow, so the weight of the foundation was similar to that of the soil with the same external volume.

Table 1. Properties of SDOF structures.

Structures SDOF1 SDOF2 SDOF2H SDOF3 SDOF3H SDOF5

dimension (mm)

effective mass (kg) 0.229 0.270 0.270 0.800 0.800 1.131

stiffness (kN/m) 461.6 60.45 62.5 60.45 62.5 22.86

natural frequency (Hz)

226 76 76 44 44 20

natural period (sec) 0.0045 0.0132 0.0132 0.0227 0.0227 0.0500

Tn @20gc1) (sec) 0.09 0.26 0.26 0.45 0.45 1.00

damping ratio (ξ) 0.009 0.022 0.022 0.014 0.014 0.021

1)gc = centrifugal acceleration (g) Model Preparation and Earthquake motions

The sand used in this experiment was dry silica sand with minimum and maximum dry densities of 12.44 and 16.35 kN/m3. Dry silica sand was poured into the model container from a sand raining system at a constant falling height to provide a uniform specimen with the relative density about 80%. Accelerometers were embedded into the soil at pre-determined locations during the model preparation stage. Under 20gc centrifugal acceleration, the depths of the prototype soil layer were 12m. Based on the shear-wave velocity profile of the soil layer measured by a bender element array [13], the site period of the prototype soil layer was estimated as 0.25s in 20gc.

A typical test layout is presented in Fig. 2. Test specimens were composed of a Single-Degree-of-Freedom (SDOF) structure model, a shallow mat foundation and sub-soil deposit in a soil container. After pluviation of sand to 57cm, the shallow foundation was placed and re-pluviation for embedment was performed. Accelerometers for measuring seismic behaviors of the soil and the structure were installed like blue circles shown in Fig. 2.

Structural motions at the roof with SFSI effects were measured directly in the centrifuge test, but it includes the effects of the foundation as well as the structure. The net motion of structure for the flexible-base was estimated by removing the horizontal foundation motion and rocking motion, which was calculated from difference between two vertical motion and foundation length, from measured roof motion. A fixed base structural responses without SFSI effects can be calculated from the measured free-field ground motion in the experiments [14].

Comparing two motions, flexible and fixed, is the one of the main purposes for this study.

Figure 2. Schematic of centrifuge test and definition of fixed and flexible motion

To observe the effects of the input motion, various earthquake motions were utilized for the centrifuge tests; Ofunato, Hachinohe, Northridge, and Kobe records together with sweeping sine wave. By maintaining the waveform of the earthquake but changing the peak acceleration, staged earthquake loadings from low to high amplitudes were applied. The effects of soil nonlinearity on SFSI were observed by changing earthquake intensities in stage tests. The input motion was applied at the bottom of the model container and amplified through the soft soil layer.

Test Results and Discussions

Even though there are a lot of test data sets for the seismic behaviors for SDOF structures

on shallow foundation from the centrifuge tests, test results of SDOF3 with Northridge earthquake motion are only reported as representative data due to the page limits. Measured Displacement

Typical horizontal displacements at roof and foundation together with the foundation rotation were directly compared for 3 foundation sizes in Fig. 3. Displacements of each locations were obtained by converting from acceleration to displacements by using a double integration method. In a case of FND7 shown in Fig. 3-(a), the displacement by the rocking motion was greater than the net displacement of the structure, meaning that structural motion is significantly affected by the foundation rocking.

It is interesting to note that there are differences in the absolute peak values of rocking motion even if the input base motion is similar for three cases. In Fig. 3-(a), the peak value of rocking motion is about 0.02m, but for the case of FND14 in Fig. 3-(c) it is less than 0.01m. On the contrary, those of structural roof motion were appeared as the opposite trend to the rocking motion. As the foundation size is getting larger, the structural roof motions were increased relative to the rocking motion, indicating that large foundation has ability to resist the rotation behavior and make the structural response larger.

(a) Foundation L: 7cm (b) Foundation L: 10cm

(c) Foundation L: 14cm

Figure 3. Displacement time history responses of SDOF 3 measured from the centrifuge tests

(Northridge earthquake, Input PGA about 0.2g) Comparison between Fixed and Flexible motions

The net lateral displacement of roof which subtracted the effects of horizontal and rotational foundation motions was compared with the fixed based motion calculated from the free-field ground accelerations. Fig. 4 shows the comparisons for the SDOF 3 model on the three foundation size cases with Northridge earthquake input. Generally, the flexible based motion was smaller than the fixed based motion, but there is a difference between two motions in proportion to the foundation size. The flexible motion in the case of FND7 is significantly smaller than the fixed motion. These results could be related to the substantial amplitude of rocking motion depicted in Fig.3. It can be mentioned that rocking foundation and its corresponding energy dissipation can significantly decrease the inertia force of the structure models.

On the other hands, the flexible base motion in case of FND14, in which the effect of rocking motion was relatively small, the peak amplitude of the flexible base motion was similar to the peak value of the fixed base motion. The oscillation pattern for FND14 was also similar to that in the fixed base motion contrary to the case of FND7.

In Fig. 5, the pseudo-accelerations estimated from the net displacements (i.e. soil-foundation-structure interaction model, SFSI model) are compared with the pseudo-accelerations predicted from the fixed base model. The results were arranged in the figures by the natural periods of SDOF structures, and the effects of foundation size on seismic behavior were compared at each figure by changing earthquake intensity. Differences between the two pseudo-accelerations eloquently show effects of SFSI.

(a) Foundation L: 7cm (b) Foundation L: 14cm

(c) Foundation L: 14cm

Figure 4. Comparison of displacement time history responses of SDOF 3 between fixed and

flexible motion (Northridge earthquake, Input PGA about 0.2g)

In most cases, the flexible base motion was similar or slightly less than the fixed base motion which is close to the one-to-one line in the small earthquake intensity. It can be explained that structural response is a little reduced due to SFSI such as period lengthening and damping increase.

The rocking motion induces the damping between the foundation and the sub-soil by increasing the inelastic strain of the soil, which decreases the lateral forces and net displacement of the structure. For the long-period structure (SDOF4), since the periods of the structures were significantly larger than the site period, the lateral forces were small and the rocking effect decreased. Thus, the flexible base accelerations were close to the accelerations of the fixed base structures.

Generally, as the level of the input accelerations increased, the flexible base accelerations converged to certain limits, and thus were significantly less than those of the fixed base structure responses. It is interesting to note that there are certain limits of spectral accelerations depending on the footing sizes even if the structure model is identical. Those limits were related to the moment capacity of the foundation. The estimated maximum accelerations by Eq. 3 are plotted for three foundation sizes in Fig. 5. Generally, the estimated maximum accelerations agree with the flexible base accelerations of the structures evaluated from the measured data, and were much smaller than the fixed base accelerations. This result indicates that the seismic load of the structures was limited by the ultimate moment capacity of the foundation, and Eq. (3) predicted the ultimate moment capacity of the mat foundation with reasonable precision.

(a) SDOF 1 (b) SDOF 2

(c) SDOF 3 (d) SDOF 5

Figure 5. Comparisons of fixed and flexible motions with foundation size and earthquake intensity

Moment-Rotation relationship

As mentioned above, SFSI effects including rocking effect can reduce the real earthquake motion compared to the fixed base motion which is adopted in conventional design. It means that the shallow foundation on the soft soil has the capacity of energy dissipation by rocking during the earthquake. To observe this energy dissipation, the normalized overturning moments at foundation bottom were expressed with the rotation angle of the foundation in Fig. 6.

Fig. 6-(a) shows the results for the weak intensity earthquake. The hysteresis loops have small inner area and show the linear behaviors of foundation. It means that the energy dissipation and nonlinear behavior of shallow foundation were not appeared because of the small rocking. On the other hands, in the results of Fig.6-(b), the plenty amount of energy dissipation and nonlinear behaviors were occurred due to substantial rocking motions during strong earthquake motion.

While overall phenomena are similar in three foundation cases, it is interesting to note that the initial rocking stiffness of FND14 is larger than that of FND7 and the loops of FND14 are still converged within the ultimate moment capacity under strong earthquake motion even though other cases are diverged.

(a-1) Foundation L: 7cm

(a-1) Foundation L: 7cm

(a-2) Foundation L: 10cm

(a-2) Foundation L: 10cm

(a-3) Foundation L: 14cm

(a-3) Foundation L: 14cm

(a) Week Earthquake Motion (input PGA : 0.08g)

(b) Strong Earthquake Motion (input PGA : 0.20g)

Figure 6. Comparisons of typical moment rotation behaviors with foundation size and earthquake intensity

Conclusions

A series of dynamic centrifuge model test was performed and test results were assessed to evaluate the effects of SFSI on seismic behaviors of SDOF structure with shallow foundation. When the natural period of the structure was close to the site period, rocking effect became important, which decreased the net displacement of the structure. Thus, the response of the structure was significantly less than the response predicted by using fixed base model. It

indicates that conventional design method may overestimate the response of the structures. In addition, these SFSI effects including rocking effects can be changed by the

foundation sizes. As the size of the footing increases, the seismic load of SDOF system increases because the energy dissipation is less due to higher ultimate moment capacity and the less rocking energy dissipation of the foundation. Through this study, the effects of SFSI on the seismic load applied to the structure were assessed based on the concepts of rocking foundation with various foundation sizes and earthquake intensities.

Acknowledgments

The experiments are carried out in KOCED Geo-Centrifuge Facility using KREONET. This research was supported by a grant (11 Technology Innovation D02) from Construction Technology Innovation Program funded by Ministry of Land, Infrastructure and Transport of Korean government.

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