ABSTRACT: Experimental studies on structure-foundation-soil interaction (SFSI) have been performed mainly on rigid or single-degree-of-freedom (SDOF) structures. Because of the simplification of structures, these studies may not be able to reveal the actual bending moment distribution in a building. In this study, the bending moment development at beam-column joints over the height of a building with SFSI was considered. Shake table tests were conducted on a single bay model which was constructed to represent a multi- storey prototype building. Buckingham’s π theorem was applied to obtain the properties of the model structure. A box with sand fill was used to simulate the behaviour of supporting soil. To achieve a more realistic confinement on the soil due to the weight of the structure, an approach was developed using artificial mass so that the actual weight of the structure is more accurately simulated. Shake table tests on the same structure with an assumed fixed base were also conducted as a reference case. The results show that when SFSI was considered, the lateral displacement of the model relative to the ground increased. SFSI reduced the kinetic energy in the upper floor of the structure.

KEY WORDS: Soil-foundation-structure interaction; Shake table test; Multi-storey structure, Structural uplift.

1 INTRODUCTION

SFSI has been recognized as one of the factors that can control the seismic performance of structures significantly. It has been observed that structures experiencing foundation soil plasticity have incurred less damage [1-6]. For a structure with a shallow foundation, seismic forces induced by ground excitation may cause structural uplift i.e. temporary and partial separation between footing and foundation soil, whenever the overturning moment exceeds the moment provided by the self-weight. The soil deforms and imposes its movements to the structural foundation. The activated inertia forces resulting from structural vibrations create additional response at the soil-foundation interface. Both phenomena occur simultaneously and affect the subsequent soil deformation.

Observations of buildings in past major earthquakes e.g. Housner [2], Anastasopoulus et al. [5] and Gazetas et al [6], showed that structures experiencing minor nonlinear SFSI with limited plastic soil deformation performed better than expected. Housner [2] was probably the first describing observations of the beneficial effect of nonlinear SFSI. During the Chilean Valdivia earthquakes of May 1960, a number of tall and slender structures survived strong ground shaking; whereas apparently more stable structures were severely damaged. These results triggered a number of investigations.

To study the nonlinear SFSI due to soil plastic deformation, numerous field and laboratory studies have also been conducted [7-10]. Centrifuge tests were performed to study the nonlinear load-deformation behaviour of a shallow foundation with plastic soil deformation. In centrifuge tests using concentric vertical and slow cyclic lateral load Gajan el al. [7, 8] investigated the performance of shallow foundations on moderately dense sand and saturated clay. It was reported that the moment capacity of soil did not reduce with the

accumulation of soil plastic deformation. On the other hand, non-uniform deformation of soil under footing rotation can result in uplift of footings. Deng and Kutter [9] have extended the centrifuge study to consider the footing embedment and variation of safety factors for vertical load bearing capacity. Another series of centrifuge experiments were conducted by Algie et al. [10] to study nonlinear interaction between soil and structural plastic behaviour. The experiment involved pseudo-dynamic test on small scale bridge models with a rigid pier and various footing sizes. The results showed as anticipated that a small bridge footing size could result in large plastic soil deformations.

Early shake table tests on the effect of structural uplift on a multi-storey building were performed by Huckelbridge and Clough [11, 12]. They concluded that allowing structures to uplift could reduce the ductility requirement. Another series of shake table experiments were carried out by Paolucci et al. [13] to replicate highway bridges founded on shallow foundations on sand. Load cells were placed at the soil-foundation interface to measure contact force. Results show SFSI can reduce the contact area between foundation and soil. This results in degradation of the rotation stiffness of the footing and an associated lengthening of the system fundamental period. However, this study considered only footings, and ignored the dynamics of the superstructure with actual foundation-soil systems.

Experimental studies on SFSI have been performed on the interaction between subsoil and a rigid body or SDOF structure. Because of the simplification of structural model, these studies may not be able to reveal the actual bending moment distribution in a building. In this study, the bending moment development at the beam-column joints along the height of a building including SFSI effect was investigated. Shake table tests were conducted on a single bay model which

Experimental investigation of bending moment distribution in a multi- storey building with SFSI

Xiaoyang Qin and Nawawi Chouw

Department of Civil and Environmental Engineering, Faculty of Engineering, the University of Auckland, New Zealand Email: xqin009@aucklanduni.ac.nz, n.chouw@auckland.ac.nz

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was constructed to represent a multi-storey prototype building. Buckingham’s π theorem [14] was applied to obtain the properties of the model members. The measurements obtained from the experiment are considered to reflect the bending moment development in the prototype. The structure was assumed to have a surface footing. A box with sand fill was used to simulate the behaviour of supporting soil. Shake table tests on the same structure with a fixed base were also conducted. The effect of SFSI on the bending moment distribution in the structure reduces with the height of the structure. The kinetic energy contained in the structure with a fixed base and SFSI was also considered.

2 SHAKE TABLE EXPERIMENT

Prototype structure 2.1

In this work, the prototype structure comprises a four-storey building with 3 m floor height and 36 m2 floor area. The seismic mass is 30 tonnes for each floor and 25 tonnes for the roof. The structural frame consists of 310UC158 steel columns and 360UB44.7 steel beams (Es=200 GPa). The beam-to-column stiffness ratio is 0.121 with a 170 mm thick concrete slab on each floor. A shallow foundation with a size of 6 m x 6 m and a total weight of 55 tonnes is considered. The fundamental period of the structure with an assumed fixed base is Tn = 0.74 sec (fn = 1.35 Hz).

Figure 1. Prototype structure.

Model scaling 2.2

Because of laboratory restriction a MDOF model was used to represent the prototype structure. By applying Buckingham π theorem [14], the relationships between physical parameters, that define the model behaviour, were found. Qin et al. [15] has proposed a dimensionless variable to obtain the relationship between the dynamic properties of a prototype and its corresponding scaled-down model. Five physical parameters were considered, i.e. collective lateral stiffness, mass, time, length and acceleration. Based on Buckingham π

theorem [14] and Hooke’s law, Qin et al. [15] has demonstrated that the dynamic response of a structure during an earthquake can be represented by a reformulated Cauchy number. The scaled factors for the considered parameters can then be obtained.

Because the uplift behaviour of a structure is affected by the weight of the structure, the gravity effect on structural uplifts cannot be neglected, when a scale model is used [16]. The physical property of the scale model should be selected so that its dynamic behaviour is the same as that of the full-scaled structure. Table 1 summarizes the scale factor for each physical parameter.

Table 1. Scale factors.

Parameter Scale factor Lateral stiffness 1200

Mass 1200 Time 1

Length 10 Acceleration 10

The selected scale factors lead to the scaled MDOF

aluminium model in Figure 2 with a height of 820 mm. The frequency of the model was 1.35 Hz which is identical to the one of the prototype. Since the model response was considered only in the excitation direction, the desirable lateral stiffness of column and beams were only achieved in the in-plane direction and a surface footing with a thickness of 15 mm, and dimensions of 750 mm and 450 mm for the in the in-plane and out-of-plane directions was utilized, respectively.

The plastic deformation in the beams was simulated by the rotation at the beam-to-column connection. A component made of mild-steel with 1.6 mm thickness and 28.5 mm width was used. The size was selected so that the fundamental frequency of the model and the beam-to-column stiffness ratio are identical to that of the prototype structure.

Figure 2. Experimental setup of structure on sand.

To conduct the shake table test on the scaled MDOF model,

Northridge near-source earthquake was applied (Figure 3). The ground motion was scaled according to New Zealand Design Spectrum [17]. To apply the excitation in the experiment, the excitation was also scaled by the scale factor.

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Figure 3. Ground excitation.

Artificial mass simulation 2.3

Because the gravitational acceleration cannot be scaled in the shake table experiments, the scale factor of acceleration cannot be applied to scale the gravity effect. The model used in the experiment would be heavier that the model obtained from similitude, resulting in an inaccurate vertical confinement on the supporting soil. The moment capacity of the soil is a function of the applied vertical confinement. An overweighed model will increase moment capacity.

To achieve a more realistic simulation of SFSI effect, part of the masses of the model was supported externally by a rigid frame. The left side of Figure 2 shows the corresponding artificial masses (mh1). Each of these masses were allowed to slide on the frame in the horizontal direction and connected to the floor mass by a rigid rod. This configuration can provide the necessary inertia of model in the horizontal direction. At the same time the soil experiences the correct weight resulting from mv1.

Setup and instrumentation 2.4

The aim of this experiment was to investigate the benefit of the nonlinear soil-foundation-structure interaction on the structural behaviour in earthquakes. Two sets of experiments were performed. The first experiment was to investigate the seismic performance of the structure with an assumed fixed base. In this test the supporting ground was assumed to be rigid. The plastic deformation of the supporting soil and the footing is ignored. The second experiment incorporated the deformation of the supporting soil. This experiment was conducted by placing the structure in a sand box of 1 m x 0.8 m. It was filled with 0.4 m depth of river sand. In order to obtain a proper distribution of soil particle, prior to each test, the river sand was rained from height between 0.5 m to 0.6 m into the sand box [18].

The physical parameters of the model to be quantified were the drift developed at each storey, horizontal displacement at each floor with respect to the shake table and bending moment (BM) at each column base. Four draw-wire sensors were attached to the centre of each floor for measuring the horizontal displacement. Diagonal portal gauge was used to obtain the relative inter-storey drift of each floor. Bending moments at the base of each column were obtained from strain gauges measurements.

3 EXPERIMENTAL RESULTS

Effect of nonlinear SFSI on the lateral displacement 3.1

If SFSI was considered, footing rotation can take place. This will result in an additional horizontal displacement. The horizontal displacement of the model on sand will be increased. The demand of separation distance between adjacent structures should be increased if SFSI is considered. Figure 4 shows the comparison of the maximum horizontal relative displacement (u) at each floor. The maximum displacement of the model on sand is higher than that of the model with an assumed fixed base. In the case considered the maximum horizontal displacement at the top floor including SFSI effect is 79.32 mm, while that of the model with an assumed fixed base is only 52.64 mm.

Figure 4. Effect of SFSI on the maximum lateral displacement.

Effect of SFSI on the bending moment 3.2

It is anticipated that the bending moments BM in each floor (the sum of the bending moment in all columns of a storey) will be decreased due to nonlinear SFSI. Figure 5(a) shows the bending moments in the ground floor. SFSI reduces the bending moment development in the columns. With an assumed fixed base the maximum bending moment in the ground floor was 15.72 Nm (solid line). With SFSI, the maximum bending moment in the same floor was reduced to 4.84 Nm (dashed line), i.e. a reduction of 69.21%.

For the bending moment in the first floor (Figure 5(b)), SFSI also reduces the maximum bending moment. The maximum bending moment in this floor was respectively 4.05 Nm and 8.65 Nm for the model with and without SFSI effect, i.e. a reduction of 53.18%. As anticipated the effect of activated rigid body rotation resulting from the soil deformation has the largest influence on the development of bending moments at the base.

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Figure 5. Reduction of bending moment at the (a) ground and (b) first floor due to SFSI.

Figure 6 shows the bending moment development in the second and third floor. As expected the bending moment in these floors with and without SFSI effect was not much different. The maximum bending moment in the second floor with and without SFSI was respectively 2.20 Nm and 2.65 Nm, i.e. a reduction of 17%. The corresponding maximum bending moment in the top floor was respectively 1.16 Nm and 1.24 Nm, i.e. a reduction of 6%.

It is also found that the frequency of the column response in the higher floors was higher than those in the lower floors of the structure. As shown in Figure 6(b), the frequency of bending moment development in the third floor was higher than that in bending moment development in the ground floor. This might be caused by the impact of footing on the soil during uplift. If SFSI is considered, footing can temporary separates from the supporting soil and then step back on the foundation soil. This can cause an impact force on the footing and column, resulting in a high frequency vibration in the upper floors. This can result in possible damage of non-structural component attached at the columns located at the upper floors of a structure.

Figure 6. Effect of SFSI on the bending moment at the (a) second and (b) third floor.

Effect of SFSI on the inter-storey drift 3.3

Figure 8 shows the comparison of lateral drift developed at each storey of the model with and without SFSI effect. SFSI reduces the storey drift. With a fixed base assumption the lateral drifts at each storey were very similar. When SFSI effect was considered, the top floor experiences the largest decrease of the storey drift.

Figure 9 shows the maximum lateral drift at each storey. For the model with an assumed fixed base, the maximum drift at each storey was around 5%. With the effect of SFSI, the storey drift reduces to approximately 2% for the first and second floors, 3% at the third floor and 1% at the top floor. The decrease of storey drift is beneficial to the seismic resistance of structures, since the smaller the relative displacement between the floors is, the more unlikely that the structure will experience damage.

However, the reduction of drift due to SFSI varies with the height. It appears that the contribution of the higher modes to the response of the model increased due to SFSI. In the case considered the largest maximum lateral drift occurred at the third floor, and it was significantly larger than those of other floors.

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Figure 8. Drift development at the (a) ground floor, (b) first, (c) second and (d) third floor.

Figure 9. Influence of SFSI on the maximum drift.

Effect of SFSI on the kinetic energy 3.4

The kinetic energy (Ek) was obtained by integrating Equation 1.

)(mvdvEk (1)

where v and m are the velocity and mass at each floor of the model, respectively. Figure 10(a) shows the kinetic energy at the first floor. The dashed and solid lines represent the model with SFSI and an assumed fixed base, respectively. The energy at this with SFSI effect was similar to that of the model with an assumed fixed base.

Figure 10(b) shows the kinetic energy at the top floor. The kinetic energy reduced when SFSI effect was considered. After about the 13th second, the energy developed at this floor with SFSI effect was significantly smaller than that in the fixed base structure. At the 20th second of the excitation, the kinetic energy in the model with SFSI is 56% of that in a fixed base structure.

Figure 10. Kinetic energy at the (a) first and (b) top floors.

4 CONCLUSIONS

In this work, shake table tests were conducted on a multi-storey model to investigate the response of structure with SFSI effect. In order to ensure that the shake table test result reflects the prototype response, Buckingham’s π theorem was applied to obtain the properties of the model members. To correctly simulate the weight of the structure and the activated inertia, external masses are considered. The structure was assumed to have a surface footing. A box filled with sand was used to simulate the behaviour of supporting soil.

The experimental result has revealed that: Rotation of footing will occur if SFSI is considered.

This will increase the horizontal displacement of structure relative to the ground.

SFSI reduces the bending moment in the structure. However, the amount of reduction decreases with the height of structure.

The inter-storey drift of the structure can be reduced by SFSI. In the considered case, the maximum inter-storey drift took place at the second floor.

SFSI was effective in reducing the kinetic energy at the higher floor. However, the kinetic energy in the lower floor of the model was not reduced.

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ACKNOWLEDGMENTS

The authors would like thank to the Ministry of Business, Innovation and Employment for the support through the Natural Hazards Research Platform under the Award 3703249.

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in the 22nd February Christchurch earthquake. Earthquake Reconnaissance Report 2011; Australian Earthquake Engineering Society, May 2011.

[2] GW. Housner, The behavior of inverted pendulum structures during earthquakes. Bulletin of the Seismological Society of America 1963; 53(2): 403-417.

[3] M J. Mendoza and G. Auvinet, The Mexico earthquake of September 19, 1985 Behaviour of building foundations in Mexico City. Earthquake Spectra 1988; 4(4): 835-852.

[4] R. Ulusay, O. Aydan and M. Hamasa, The behaviour of structures built on active fault zones: Example from the recent earthquakes of Turkey. Structural Engineering and Earthquake Engineering 2002; 19(2): 149-167.

[5] I. Anastasopoulus, G. Gazetas, M. F. Bransby, M. C. R Davies, A. El. and Nahas, Shallow foundations over rupturing normal faults: Analysis and experiments. 4th International Conference on Earthquake Geotechnical Engineering 2007; Thessaloniki, Greece, June 25-28. Paper 1581.

[6] G. Gazetas, M. Apostolou, and J. Anastasopoulos, Seismic uplifting of foundations on soft soil, with examples from Adapazari (Izmit 1999 earthquake), in Foundations: Innovations, observations, design and practice 2003. London: Thomas Telford.

[7] S. Gajan, B. L. Kutter, J. D. Phalen, T. C. Hutchinson and G. R. Martin, Centrifuge modelling of load deformation behaviour of rocking shallow foundations. Soil Dynamics and Earthquake Engineering 2005; 25: 773-783.

[8] S. Gajan, B. L. Kutter, and J. M. Thomas, Physical and numerical modeling of cyclic moment-rotation behaviour of shallow foundations. Proceedings of the 16th International Conference on Soil Mechanics and Geotechnical Engineering 2005; September, Osaka, Japan. 2: 795-798.

[9] L. Deng, and B. L. Kutter, Characterization of rocking shallow foundations using centrifuge model tests. Earthquake Engineering and Structural Dynamics 2012; 41(5): 1043-1060.

[10] T. Algie, Nonlinear rotational behaviour of shallow foundations on cohesive soil. PhD thesis, 2011, the University of Auckland

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[12] AA. Huckelbridge and RW. Clough, Earthquake simulation tests of a nine- storey steel frame with columns allowed to uplift. Report No UCB/EERC 77-23 1977; University of California, Berkeley, Earthquake Engineering Research Centre.

[13] R. Paolucci, M. Shirato, and M. T. Yilmaz, Seismic behavior of shallow foundations: shake table experiments vs. numerical modeling. Earthquake Engineering and Structural Dynamics 2008; 37, 577-597

[14] E. Buckingham Illustrations of the use of dimensional analysis. On physically similar systems. Physics Review 1914; 4(4): 354-377.

[15] X. Qin, Y. Chen, and N. Chouw. Effect of uplift and soil nonlinearity on plastic hinge development and induced vibrations in structures. Advances in Structural Engineering 16.1 (2013): 135-148.

[16] X. Qin and N. Chouw, Experimental investigation of uplift effect on structures in earthquakes. Proceedings, New Zealand Society for Earthquake Engineering Conference, 2010.

[17] Standards New Zealand. Structural Design Actions Part 5: Earthquake actions New Zealand - Commentary, NZS 1170.5 Supplement. 2004; Wellington, New Zealand: Standards, New Zealand.

[18] X. Qin, Y. Chen, and N. Chouw. Experimental investigation of nonlinear structure-foundation-soil interaction. Proceedings of the 9th Pacific Conference on Earthquake Engineering. 2011.

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