Numerical analysis of the effect of preloading on the seismic risk of buildings on liquefaction-susceptible sites F. Lopez-Caballero, A. Modaressi and Silvana Montoya-Noguera Ecole Centrale Paris

The aim of this work is to assess numerically the efficiency of the soil densification using preloading techniques on the improvement of liquefiable sandy profiles and of the response of the overlying structure to shaking

Numerical model studied A structure founded on a layered soil/rock model was considered. The soil profile is composed of 20m of loose sand. The shear modulus of the soil increases with depth with average value 213m/s. An elastoplastic multi-mechanism model is used to represent the soil behaviour on the top 20m. The deformable bedrock is placed at 20m depth. An isotropic linear elastic behaviour with a Vs equal to 550m/s is assumed. The ground water table level is placed at 1m below the surface.

The structure was a two-story concrete building with height 4 The structure was a two-story concrete building with height 4.2m and width 4.0m. The mass of the building is assumed to be uniformly distributed along beam elements and the columns are supposed massless. The fundamental period of the structure is equal to 0.24s. In order to simulate the structure plastic hinge beam-column elements are used.

178 records were chosen from the Pacific Earthquake Engineering Research Center database. The events range between 5.2 and 7.6 in magnitude Recordings have: site- to-source distances from 15 to 50km dense-to-firm soil conditions (i.e. 360m/s < Vs 30m < 800m/s).

The figure shows the mean and the response spectra curves of the input motions. It can be noted that the mean response spectra is consistent with the response spectra of Type A soil of Eurocode8

In order to simulate the construction and demolition of the preload embankment, the calculations are performed in two steps. Since soil behaviour is a function of the effective stress state for nonlinear elastoplastic models, initial in-situ stress state due to gravity loads are computed. A sequential construction and demolition of the embankment is performed.

In order to assess the effect of preloading, two embankment heights were studied, 5 and 9m. The fill length is 18m and 36m and the length at the crest is 2m and 4m for the two cases respectively. The embankment is constructed and demolished at a rate of 0.22 m/day and it stays in place during 11 days before the application of the seismic event. After this period according to the computations all over pore pressures are dissipated.

Model used and its validation The elastoplastic multi-mechanism model developed at Ecole Centrale Paris, known as ECP model is used to represent the soil behaviour.

Fig. shows the responses of the drained cyclic shear tests obtained by the model of the sand at consalidation stress 30, 50, 100 and 150kPa. The tests results are compared with the reference curves given by Seed et al. the obtained G/Gmax and damping curves match satisfactorily

Under undrained conditions the predicted test results are compared with the typical curves given by Seed and Idriss for sands at different densities. We can notice that the obtained curves match relatively good with the one corresponding to SPT − N60 = 5

To study the model predictions of the effect of prestressing on the cyclic strength some isotropic consolidation tests were simulated Three levels of prestress ratio (PR =σv−max/ σv−c) were studied. Figure displays the liquefaction curves obtained for the two initial stresses and three PR values. It is noted that the cyclic liquefaction strength increases as the prestress ration increases, similarly to the measured

Results The responses obtained by the model without preloading. As shown in the figure, considering excess pore pressures, for all simulations, in the mean response obtained, the liquefaction phenomenon does not occur. Yet, in some cases the liquefaction is found principally between 2 and 10m depth. Assuming that the liquefaction appears when the pore pressure ratio greater than 0.8, a liquefaction probability profile could be estimated. Figure 6: a) Obtained pore pressure excess in the soil profile and b) Evolution of liquefaction probability with depth. Case before preloading.

The settlement of the structure is computed as the difference between the settlement of the structure foundation and the free field settlement Figure 7(a) shows as expected, the co-seismic settlement value increases with an increase in the Arias intensity (IArias) value, that is, an increase into the input seismic energy. Figure 7(b) shows that the obtained settlements (S) as a function of the foundation width (Bf ) normalized by the thickness of the liquefiable layer (DL) compared with the boundaries proposed by Liu and Dobry of available case histories and centrifuge tests. Thus, the obtained settlements are consistent with the previously proposed relationships. Figure 7: a) Scatter plot of obtained co-seismic settlement values as a function of IArias and b) Scatter of obtained normalized settlement against normalized foundation width. Case before preloading.

Finally, with regard to seismic response of the structure, the computed maximum top displacement (utop) and its corresponding base shear force (V ) are presented. The corresponding capacity curve obtained by modeling the static pushover test is also plotted. According to this figure, it is noted that the structural response is completely linear. Figure 8: Structural dynamic response obtained for the building at SSI condition. Case before preloading. This is due principally to the liquefaction phenomenon below the foundation which decreases the motion applied at the structure

Preloading simulation Now, the change in soil state due to the construction and demolition of the embankment is analyzed. As expected, the application of preloading produces an overconsolidation on the soil (PR). Figure 9a show s that the 5m embankment influences the soil behaviour down to 5m deep. Comparing the induced horizontal effective stress under the foundation, it is interesting to note that near the surface level, a residual horizontal stress appears at the end of the demolition of the embankment (Fig.9b). Figure 9: Effect of preload on a) the induced pre-stress ratio (PR) and b) the induced Δσyy in the soil foundation.

Results after preloading Concerning the seismic response of the profile, Figure 11 provides a: comparison of the evolution of pore pressure ratio (ru) as a function of time and depth for the same earthquake for one case before and after preloading (Hembk=5m). This comparison indicates that preloading decreases strongly the pore pressure build up below the foundation. Consequently, it is expected that in general the liquefaction probability must decrease. Figure 11: Comparison of liquefaction ratio evolution under the foundation centreline in time and depth for a case a) without and b) with preloading SSI condition.

Indeed, the maximum liquefaction probability decreases from 21% in the reference case to 14%, when the 9m high embankment is considered. Figure 12: Effect of embankment height on the evolution of liquefaction probability with depth.

As illustrated in this figure, the seismic structural settlement obtained after soil improvement is greatly reduced as a consequence of soil stiffening. It can be also seen, for example, that for a 5m preload embankment, the reduction is most important for the settlements lower than 5cm.

However, as illustrated in the figure, due to the soil stiffening effect, the structural deformation levels are increased. The higher the embankment height, the higher the structural deformation. Yet, it can be observed that non-linear behavior is not reached for a preload embankment 9m high. Figure 14: Structural dynamic response obtained for the building at SSI condition. Case after preloading (Hembk=9m).

Figure 16 evaluates the effect of the introduction of the improvement methods of liquefaction on the behavior of the superstructure. The settlement of the structure is reduced by the use of embankment. However, regarding the variation of Interstory Drift of the structure, it appears that in all cases, it increases because of the soil stiffening effect Figure 16: Scatter plot of variation of interstory drift ΔΙSD with respect to variation of induced settlement Δsettl, a) Hembk=5m and b) Hembk=9m.

Conclusions A series of finite element parametric analyses were performed to investigate the effects of preloading on the liquefaction behavior of both a soil profile and a structure. A typical soil-structure model has been used

The analyses showed that: The use of the preloading reduces the excess pore pressure generation into the soil profile. As a consequence, for a given seismic hazard the liquefaction probability decreases • the seismic settlement of the building decreases The two-story building on the mitigated site showed higher building deformation, but it remained to tolerable values from the structural point of view.

As liquefaction seismic risk of buildings usually corresponds to excessive settlements, the analysis illustrated that preloading is an effective tool to mitigate liquefaction seismic risk of buildings.

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