Rate of earthquake-induced settlement of level ground H. Matsuda Department of Civil Engineering, Yamaguchi University,

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1 Rate of earthquake-induced settlement of level ground H. Matsuda Department of Civil Engineering, Yamaguchi University, Abstract When a clay layer is subjected to cyclic shear, the excess pore water pressure is accumulated and after the earthquake, it dissipates with time and then the ground subsidence occurs. In this paper, to predict the rate of post-earthquake ground settlement, cyclic simple shear tests under the constant volume conditions are performed for a saturated kaoline and after the cyclic shear tests, the excess pore water pressures are dissipated and the coefficients of consolidation C^ are obtained for different test conditions. In tests, number of strain cycles was changed as 10, 30, 50, 100 and 200, and the shear strain amplitude was also changed in the range from 0.05% to 2.0%. Based on the test results, the rates of earthquakeinduced settlement of the level ground are calculated for different accelerograms. 1 Introduction When clay layers are subjected to the earthquake motion, the excess pore water pressures are generated and accumulated in the clay. Since the coefficient of consolidation of a clay is much smaller than that of sand, during the earthquake, the rate of the dissipation of excess pore water pressure is negligibly small and after the earthquake, the excess pore pressures are gradually dissipated and simultaneously the ground subsidence occurs. By the cyclic simple shear tests, it has been confirmed that when a saturated kaoline is subjected to the cyclic shear, the settlement of about 5% in strain occurs. As for the rate of the settlement, from a few reports about in situ measurements, there can be seen a tendency that the settlement occurs very rapidly. The reason is that the clay subjected to cyclic shear might be under the pseudo overconsolidated conditions. However, the dissipation characteristics of the accumulated excess pore pressure have not been clarified

2 322 Soil Dynamics and Earthquake Engineering Further, since the distribution of the excess pore pressures at the end of the earthquake motion is not uniform, which depends on the response of the shear strain during the earthquake, it is not so easy to estimate the rate of the postearthquake settlement of clay layers. So, in this paper, cyclic simple shear tests under the constant volume conditions were performed for the saturated kaoline and after the cyclic shear tests, the excess pore water pressures were dissipated. Then the effects of the cyclic shear strain on the rate of the dissipation were observed and test results were applied to the prediction of the rate of postearthquake settlement of a model clay layer. 2 Reconsolidation tests on a clay subjected to cyclic shear The apparatus used in this study is the dynamic simple shear test device as shown in Fig. 1. The dimension of the specimen is 75mm in diameter and 20mm in height. The sample used in this study is kaoline powder; the specific gravity G^ of the sample is 2.718, the liquid limit M^ is 47.4% and the plastic limit ^ is 31.0%. The clay powder was mixed with the water to make a slurry. After the slurry was deaired in the vacuum cell, the slurry was poured into the shear box and preconsolidated for 22 hours under the consolidation pressure of o^=49kpa. Subsequently, the specimens were subjected to the uniform cyclic shear strain; the amplitude was varied in the range from 0.05% to 3.00%. During cyclic shear tests, the drainage from the upper surface of the specimen was permitted and the specimen height was kept constant. Then the horizontal displacement, shear resistance, vertical stress and the pore water pressure at the base of the specimen were measured. The wave form of the cyclic shear strain was sinusoidal (two way cyclic strain) and the period was 2.0s. After the cyclic shear test, the reconsolidation pressure of 49 kpa was applied to the upper loading plate. Then the settlement of the specimen and the pore water pressure at the base of the specimen were measured with time. Consolidation Pressure Linear Motion Bearing Upper Loading Plate Figure 1: The strain-controlled cyclic simple shear test apparatus.

3 -l.or Soil Dynamics and Earthquake Engineering Number of Cycles n Figure 2: The reduction in vertical effective stress during cyclic shear. The decrease in the vertical effective stress ratio A o^/o^ with the number of strain cycles n are shown in Fig.2. It has been shown that when a normally consolidated kaoline was subjected to cyclic shear strain under the undrained condition, excess pore water pressure increased with the number of strain cycles n and the following equation was derived, e.g. O-hara & Matsuda/ ; (i) *v. a+p*» ^ In this study, during the cyclic shear tests the specimen height was kept constant and so, the change in vertical stress A o\ agrees with the excess pore water pressure u^ in eqn( 1) By using the A o^ in place of u^, eqn( 1) is rewritten as follows. Ao V,, '* -7-=^^ (2) In Fig.2 symbols show the observed results and the solid curves show the results obtained by eqn(2). Agreements between them are reasonable. After the cyclic shear test, the vertical stress on the upper surface of the specimen was increased up to the preconsolidation pressure o^. Then the excess pore water pressure generated in the specimen was dissipated from the upper surface. In Fig 3, relationships between the degree of consolidation 1+Ug/A o\ and the elapsed time are shown; where Ug is the excess pore water pressure measured at the base of the specimen. It is seen that the larger the strain amplitude increases, the faster the excess pore water pressure dissipates. To show how fast the excess pore water pressures dissipate, it is possible to obtain the dynamic coefficient of consolidation C^ by using t^, corresponding to 50% primary consolidation in Fig.3. In this study, many reconsolidation tests were carried out, in which the

4 324 Soil Dynamics and Earthquake Engineering Or 1 10 Elapsed Time (min) Figure 3: Relationships between the degree of consolidation 1+Ug/Ao^ and the elapsed time. 100 SRR (Stress Reduction Ratio) Figure 4: Relationships between C^/Q, and the Stress Reduction Ratio (SRR). number of strain cycles % was changed as 10, 30, 50, 100 and 200, and the shear strain amplitude was also changed as mentioned before. In Fig.4, the relationships between C^/C^ and the Stress Reduction Ratio (SRR) are shown. Where Q is the coefficient of consolidation for OCR=1 and SRR is defined by the following equation

5 Soil Dynamics and Earthquake Engineering 325 SRR Ao /o (3) Although a scattering is seen, there is a tendency that C^/Q, decreases with the increase in SRR. The broken lines in Fig. 4 were obtained by the method of least square applied to the respective results for nf=\q, 30, 100 and 200, and the solid line was obtained from all plots. Therefore, the following equation is derived. Where a and b are the experimental constants. For the solid line in Fig. 4, 67=24.35, Z>= were obtained. 3 Rate of earthquake-induced settlement of level ground In this paper, the rate of earthquake-induced settlement was calculated for a level ground as shown in Fig. 5. The ground, which is underlain by a base rock, consists of a horizontally sedimented clay layer of H=5m. In the calculations, clay layers were divided into 10 layers (N=10) and from the shear strain-time histories obtained by the earthquake response analysis, e.g. Schnabel, Lysmer & Seed^, Seed & Idriss^, the post-earthquake settlements were predicted according to the prediction process, e.g. Matsuda*. As shown in Fig. 6, accelerograms used in this study are for the El Centro earthquake of 1940, Hachinohe earthquake of 1968, Kaihoku earthquake of 1978, Niigata earthquake of 1964, Taft earthquake of 1952, and a simulated earthquake that was generated by random numbers. The distributions of the vertical volumetric strain e^ and the total postearthquake settlements for all accelerograms are shown in Fig. 7. In the process of (4} G.L. Layer 1 H, Layer 2 H, H Layer N H, Base Rnrlc,, " Earthquake Motion Figure 5: Model ground used in the calculation of earthquake-induced settlement.

6 326 Soil Dynamics and Earthquake Engineering Hachinohe Earthquake _ li _ L J _ 1 _ L _ L _ I I _ Figure 6: Accelerograms used in the calculations = g y^tx ^ ElCentro (53.69mm) Hachinohe (45.45mm) -A Niigata (33.85mm) Kaihoku (27.02mm) -e- Taft (45.65mm) Simulated (30.80mm) Volumetric Strain e^ (%) 3.0 Figure 7: The earthquake-induced settlement of a model clay layer.

7 Soil Dynamics and Earthquake Engineering 327 the settlement calculation, since the distribution of SRR in the clay layer is obtained, it is possible to calculate C^ for each sublayer by using eqn(4). During the earthquake motion, the excess pore water pressure is accumulated in the clay layer and after the earthquake it decreases gradually and simultaneously the ground surface settles up to the values as shown in Fig.7. Immediately after the end of earthquake, the distribution of the excess pore water pressure is shown in Fig. 8 for the case of the El Centre earthquake. When we could know the coefficient of consolidation and the initial distribution of the excess pore water pressure, it is possible to calculate the decrease in the excess pore water pressure with time. By using the dynamic coefficient of consolidation C^ given by eqn(4), the changes in the distribution of the excess pore water pressure were calculated and were also shown in Fig. 8. After one day from the earthquake, the distribution of the excess pore water pressure describes a parabola, which has a meaning that the excess pore water pressure close to the ground surface once increases and then gradually decreases. It is seen that after ten days, more than 95% of the excess pore water pressure is dissipated. To compare rates of the post-earthquake settlement with those of the consolidation settlement induced by the static surcharge load, the average degrees of consolidation were calculated and shown in Fig 9. The effects of the differences in the accelerograms are not significant. However, the rate of post-earthquake settlement is notably faster than that of the static consolidation. Practically, it has been reported, e.g. Jaime, Romo & Jassor, that the post-earthquake settlement occured immediately after the earthquake, and so, the results obtained in this study are reasonable Pore Water Pressure Ratio Figure 8: Isochrones after the earthquake 0.8

8 328 Soil Dynamics and Earthquake Engineering ElCentro Earth. Hachinohe Earth. 4 Conclusions Elapsed Time (days) Figure 9: Rates of the post-earthquake settlement. In this paper, the rates of earthquake-induced settlement of a model clayey layer were calculated based on the cyclic simple shear test results. In conclusion, the larger the SRR (^stress reduction ratio) increases, the smaller the dynamic coefficient of consolidation becomes and therefore, the rate of settlement induced by the earthquake is faster than that of consolidation settlement induced by the static surcharge load. References l.o-hara, S. & Matsuda, H. Study on the settlement of saturated clay layer induced by cyclic shear, Soils and Foundations, 1988, 28, 3, Schnabel, P. B, Lysmer J. & Seed, H.B. Shake a computer program for earthquake response analysis of horizontally layered sites. EERC Reports, (EETfO 72-72), 1972, Seed, H. B. & Idriss, I M Soil moduli and damping factors for dynamic response analyses. EE7?O7&%xvYj, feetzc 70-70), 1970, Matsuda, H. Prediction of post-earthquake subsidence in laminated clay-sand layers, Proc. of 5th U.S. National Conference on Earthquake Engineering, 1994,2, Jamie, A.P., Romo, M.P. & Jasso, MR Seismic induced settlement in a building, 8th Pan-American Congress on Soil Mechanics and Foundation 1987,