POST-CYCLIC RECOMPRESSION CHARACTERISTICS OF A CLAY SUBJECTED TO UNDRAINED UNI-DIRECTIONAL AND MULTI-DIRECTIONAL CYCLIC SHEARS

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1 NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July -5, 4 Anchorage, Alaska POST-CYCLIC RECOMPRESSION CHARACTERISTICS OF A CLAY SUBJECTED TO UNDRAINED UNI-DIRECTIONAL AND MULTI-DIRECTIONAL CYCLIC SHEARS H. Matsuda, T. T. Nhan, K. Nakahara 3, Đ. Q. Thien 4 and T. H. Tuyen 5 ABSTRACT In this paper, the effect of cyclic shear direction on the recompression characteristics of saturated clay subjected to undrained -directional and multi-directional cyclic shears was investigated. Normally consolidated specimens of kaolin were tested by using the multi-directional cyclic simple shear test apparatus. It is indicated from the results that the dissipation of excess pore water pressures is not affected by the cyclic shear histories. The vertical settlement following undrained cyclic shearing increases with the shear strain amplitude and at the same shear strain amplitude, the settlement induced by multi-directional cyclic shear is larger than those generated by -directional one. Furthermore, the post-cyclic settlement and the excess pore water pressure induced by -directional cyclic shear equal to those induced by multi-directional ones if the ratio of shear strain amplitude is at :, respectively and this ratio is independent of the number of cycles. For saturated granular materials, this ratio is about.5:.:. Professor, Dept. of Civil and Environmental Engineering, Yamaguchi University, Ube, Japan Doctor, Dept. of Engineering Geology and Hydro-Geology, Hue University, Hue City, Vietnam 3 Graduate Student, Dept. Civil and Environmental Engineering, Yamaguchi University, Ube, Japan 4 Doctor, Dept. of Engineering Geology and Hydro-Geology, Hue University, Hue City, Vietnam 5 Doctor, Dept. of Engineering Geology and Hydro-Geology, Hue University, Hue City, Vietnam Matsuda H, Nhan TT, Nakahara K, Thien ĐQ, Tuyen TH. Post-cyclic recompression characteristics of a clay subjected to undrained -directional and multi-directional cyclic shears. Proceedings of the th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 4.

2 NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July -5, 4 Anchorage, Alaska Post-Cyclic Recompression Characteristics of a Clay Subjected to Undrained Uni-Directional and Multi-Directional Cyclic Shears H. Matsuda, T. T. Nhan, K. Nakahara 3, Đ. Q. Thien 4 and T. H. Tuyen 5 ABSTRACT In this paper, the effect of cyclic shear direction on the recompression characteristics of saturated clay subjected to undrained -directional and multi-directional cyclic shears was investigated. Normally consolidated specimens of were tested by using the multi-directional cyclic simple shear test apparatus. It is indicated from the results that the dissipation of excess pore water pressures is not affected by the cyclic shear histories. The vertical settlement following undrained cyclic shearing increases with the shear strain amplitude and at the same shear strain amplitude, the settlement induced by multi-directional cyclic shear is larger than those generated by directional one. Furthermore, the post-cyclic settlement and the excess pore water pressure induced by -directional cyclic shear equal to those induced by multi-directional ones if the ratio of shear strain amplitude is at :, respectively and this ratio is independent of the number of cycles. For saturated granular materials, this ratio is about.5:.:. Introduction When a saturated soil is subjected to cyclic shear, the pore water pressure is produced. In the case of short-term cyclic loading such as during an earthquake, the cyclic loading is considered to be under the undrained condition, and under such undrained condition, the cyclic induced-pore water pressure is accumulated. As the time proceeds after cyclic loading, the cyclic-induced pore water pressure dissipates and results in the recompression of the soils which is occurred at the ground surface as vertical settlement. The so-called post-earthquake settlements of the ground have been observed after major earthquakes such as Hyogo-ken Nanbu earthquake in 995 (Fig. ) or 964 Niigata earthquake. Recently, it is reported that, after the Tohoku Pacific earthquake, the excessive ground settlement up to 6 cm leading to settlement and tilting of structures supported by the spread foundation []. In addition, it is widely known that during earthquake, soil layers are subjected to multi-directional cyclic shear with different strain amplitudes and frequencies []. Fig. shows the orbits of shear strain calculated from the acceleration-time histories of Hyogo-ken Nanbu Earthquake 995 which was recorded at the Professor, Dept. of Civil and Environmental Engineering, Yamaguchi University, Ube, Japan Doctor, Dept. of Engineering Geology and Hydro-Geology, Hue University, Hue City, Vietnam 3 Graduate Student, Dept. Civil and Environmental Engineering, Yamaguchi University, Ube, Japan 4 Doctor, Dept. of Engineering Geology and Hydro-Geology, Hue University, Hue City, Vietnam 5 Doctor, Dept. of Engineering Geology and Hydro-Geology, Hue University, Hue City, Vietnam Matsuda H, Nhan TT, Nakahara K, Thien ĐQ, Tuyen TH. Post-cyclic recompression characteristics of a clay subjected to undrained -directional and multi-directional cyclic shears. Proceedings of the th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 4.

3 depth of GL-6m in the N-S and E-W directions [3]. It is seen in this figure that the ground shaking during the earthquake induces multi-directional shear strain. 5 Settlement at the ground surface.5 N Settlement (cm) 5 Curve II Curve I Strain (%) W E Hyogo-ken Nanbu Earthquake Elapsed time (days) Figure. Settlement of the ground surface at Port Island before and after Hyogo-ken Nanbu earthquake on 7 th January, 995 [4] Strain (%) Figure. The orbits of shear strain calculated from the acceleration recorded at Hyogo-ken Nanbu Earthquake 995 [3]. S Figure 3. Outline of the multi-directional cyclic simple shear test device. Settlement and consolidation of soil subjected to cyclic loading can be divided into two categories: The one leading to failure and the other not leading to failure [5]. In which, settlement induced by earthquake characterized cyclic loading which belong to the first category and can be modeled by using undrained cyclic shearing followed by drainage. Ohara and Matsuda [6] investigated the effect of cyclic shear strain amplitude, number of cycles and over consolidation ratio on the pore water pressure buildup and the post-cyclic settlement by the strain-controlled -directional cyclic simple shear tests. Yasuhara and Andersen [7] investigated the consolidation of normally consolidated clay under consecutive series of

4 undrained cyclic loading and drainage by using stress-controlled -directional cyclic simple shear tests. Then, they proposed estimation methods of pore water pressure buildup and the postcyclic settlement [6-8]. Many researches have shown the settlement characteristics of clays induced by cyclic loading in detail [,9,]. Meanwhile, the effect of cyclic shear direction in multi-directional cyclic shearing on the settlement characteristics of clayey soil was only investigated in our recent researches [-5]. In this research, normally consolidated ite clay was tested by the strain-controlled -directional and multi-directional cyclic shears under undrained condition followed by drainage. The settlement characteristics in the recompression stage were described and investigated in detail for different cyclic shear conditions including cyclic shear direction, shear strain amplitude and number of cycles. Test Apparatus Undrained Uni-directional and Multi-directional Cyclic Simple Shear Tests Figure 3 shows the outline of the multi-directional cyclic simple shear test apparatus. This apparatus can give any types of cyclic displacement at the bottom of specimen from two orthogonal directions by using the electro-hydraulic servo system. A predetermined vertical stress can be applied to the specimen by the aero-servo system. The shear box is the Kjellman type in which the specimens were enclosed in a rubber membrane. The membrane-enclosed specimen is surrounded by a stack of 5 acrylic rings. Each acrylic ring has 75.4 mm in inside diameter and mm in thickness. In this condition, the specimen is prevented from the deformation in radial direction but permitted simple shear deformation during cyclic shear. Test Material, Procedures and Conditions The soil used in this study is ite clay, index properties of which are specific gravity G s =.77, liquid limit w L =47.8%, plastic limit w p =.3%, plasticity index I p =5.5 and compression index C c =.35. In order to prepare the specimen, ite clay powder was mixed with the de-aired water to form slurry having a water content of about 8%. After keeping the water content constant for one day, the slurry was de-aired in the vacuum cell for about half an hour, and then poured into the shear box of the simple shear test apparatus. The slurry was pre-consolidated under the vertical stress σ v = 49 kpa with the consolidation duration decided based on the obtained results for this by using the 3t method which has been introduced for the closing of consolidation period in laboratory tests (Fig. 4). This consolidation period was also based on the record of the dissipation of excess pore water pressure with time during pre-consolidation as shown in Fig. 5. After preconsolidation, the specimen has the void ratio of about.-.9 with the dimensions of 75 mm in diameter and about mm in height. Since the B-value of the specimen before undrained cyclic shear B >.95 was confirmed by applying the load increment, the required saturation degree can be satisfied. After pre-consolidation is completed, the specimen was subjected to undrained cyclic shear for predetermined number of cycles (n), shear strain amplitude (γ) and phase difference (θ). In this study, the shear strain amplitude was in the range from γ =.5% to 3.% and the number of cycles was fixed as,, 5 and. The wave

5 form of the cyclic shear strain was sinusoidal (two way cyclic strain) with the period s (frequency f =.5 Hz). Figure 6 shows typical deformations of specimen, conceptually. Settlement (mm).. t t Time (min.) r 3t r ε 3 Pressure (kpa) Vertical stress Pore water pressure σ' v = 49kPa 4 5 σ' v = 49 kpa Figure 4. Settlement versus the logarithm of elapsed time in pre-consolidation test and the application of the 3t method for closing of consolidation period Elapsed time (min.) Figure 5. Dissipation of pore water pressure during pre-consolidation in shear box. Figure 6. Typical deformations of specimen under (a) -directional cyclic shear and (b) multi-directional cyclic shear at θ = 9. Typical records of cyclic shear strain and the respective orbits of shear strain amplitude under -directional and multi-directional cyclic shears with the shear strain amplitude γ =.% are shown in Figs. 7 and 8, respectively. In -directional cyclic shear test, the shear strain was applied to the specimen only in X direction (γ =.%) (Fig. 7a). So the orbit of cyclic shear strain forms linear lines (Fig. 8). In multi-directional cyclic shear tests, the shear strain was simultaneously applied to X direction (γ x ) and Y direction (γ y ) which are perpendicular to each other under the same shear strain amplitude (γ =.%) but at different phase differences (Figs. 7b-e). Then the orbits show from the elliptical lines for θ =, 45, 7 and the circle lines for θ = 9 which is commonly known as gyratory cyclic shear condition (Fig. 8). The effects of cyclic shear direction on the formation of the orbit are evidently shown in Fig. 8, and thus the cyclic shear direction is believed to be an important factor governing the dynamic properties of soil.

6 Shear strain (%) Shear strain (%) Figure 7. ; γ =.%; Uni-direction X direction Time (s) (a) Uni-direction ; γ =.%; θ = 45 Shear strain (%) Shear strain (%) - - ; γ =.%; θ = X direction Y direction Time (s) (b) Multi-direction (θ = ) - X direction Y direction X direction Y direction - Time (s) Time (s) (c) Multi-direction (θ = 45 ) (d) Multi-direction (θ = 7 ) ; γ =.%; θ = 9 Shear strain (%) ; γ =.%; θ = X direction Y direction Time (s) (e) Multi-direction (θ = 9 ) Typical records of cyclic shear waves in strain-controlled -directional and multidirectional cyclic simple shear tests conducted for shear strain amplitude of.%. Y shear strain γ Y (%) γ =.% θ= θ= 45 θ= 7 θ= 9 Figure X shear strain γ X (%) Patterns for shear strain in -directional and multi-directional cyclic simple shear tests conducted for shear strain amplitude of.%.

7 Test Results and Discussions Excess Pore Water Pressure of a Clay Subjected to Undrained Uni-Directional and Multi- Directional Cyclic Simple Shear As a result of undrained cyclic shear, excess pore water pressure (U dyn ) increases with the number of cycles. Figure 9 shows the typical changes of the excess pore water pressure ratio which is defined by U dyn /σ v, where σ v is the initial effective stress, during undrained directional and multi-directional cyclic simple shear tests conducted for shear strain amplitude γ =.%,.4% and.%. It is seen in this figure that the excess pore water pressure ratio increases with the number of cycles and at the same number of cycles, the larger the shear strain amplitude, the higher the excess pore water pressure ratio increases. In addition, at the same shear strain amplitude, the excess pore water pressures ratio induced by multi-directional cyclic shear (θ =, 45, 7 and 9 ) are significantly larger than those generated by directional one. For the multi-directional shear tests, the excess pore water pressure ratio increases with the phase difference. The similar behavior is also seen in Fig., in which the excess pore water pressure ratio is plotted against shear strain amplitude for different number of cycles. Therefore, the cyclic shear direction, shear strain amplitude and number of cycles are the important parameters affecting the pore water pressure buildup in cohesive soils subjected to undrained -directional and multi-directional loading. Figure 9. Excess pore water pressure ratio U dyn /σ' v σ' v =49kPa θ= 7 θ= 45 θ= θ= 9 θ= 9 γ=.% θ= θ= 7 γ=.4% θ= 45 θ= 7 θ= 45 θ= θ= 9 γ=.%. Number of cycles n Relations of excess pore water pressure ratio induced by -directional and multidirectional cyclic shears versus number of cycles for γ =.%,.4% and.%. Excess Pore Water Pressure Dissipation of a Clay Subjected to Undrained Uni-Directional and Multi-Directional Cyclic Shears The dissipation of excess pore water pressure after undrained cyclic shear is plotted against elapsed time in Fig. for several typical tests. It is seen in Fig., the excess pore water pressure induced by undrained cyclic shear are totally dissipated after about minutes, irrespective of shear strain amplitude and cyclic shear direction. This duration almost agrees with the result obtained by using the 3t method and the dissipation duration of excess pore water pressure during the pre-consolidation test, which were plotted in Figs. 4 and 5, respectively. Therefore, this observation suggests that the dissipation of pore water pressure in cohesive soils seems to be not affected by cyclic shearing histories.

8 Excess pore water pressure ratio U dyn /σ' vo Excess pore water pressure ratio U dyn /σ' vo,8,6,4,,,,8 σ' v = 49kPa n = 5,6,4 θ = 9 θ = 7 θ = 45 θ = σ' v = 49kPa n = Excess pore water pressure ratio U dyn /σ' vo Excess pore water pressure ratio U dyn /σ' vo,8,6,4, θ = 9 θ = 7 θ = 45 θ = σ' v = 49kPa n =, θ =, σ' v = 49kPa θ = n =,, Experiments showing the same U dyn /σ v if the ratio of shear strain amplitude is at :, θ = 9 θ = 7 θ = 45,8,6,4 θ = 9 θ = 7 θ = 45 Figure. Relations of excess pore water pressure ratio induced by -directional and multidirectional cyclic shears versus shear strain amplitude for different number of cycles. Figure. Excess pore pressure, U dyn (kpa) ; σ' v = 49kPa; n = Experiments showing the same U dyn -t relations if the ratio of shear strain amplitude is at :. γ (%) θ = Elapsed time, t (min) Excess pore water pressure dissipation versus elapsed time relations of subjected to undrained -directional and multi-directional cyclic shears

9 In order to show new effect of cyclic shear on the pore water pressure, further comparisons are given for the excess pore water pressure ratio induced by -directional and multi-directional cyclic shears which are denoted by red arrows in Figs. and. It is seen that the ratio of excess pore water pressure induced by undrained cyclic shears equals to each other with the results that the shear strain amplitude of the -directional tests are two times higher than those of the multi-directional ones and this relation is independent of shear strain amplitude, number of cycles and the elapsed time. Post-Cyclic Settlement versus Elapsed Time Relations of a Clay Subjected to Undrained Uni-Directional and Multi-Directional Cyclic Shears Vertical settlement in strain ε v (%) Vertical settlement in strain ε v (%) θ= 9 θ= 7 θ= 45 θ= σ' v = 49kPa n =,, Vertical settlement in strain ε v (%) Vertical settlement in strain ε v (%) θ= 9 θ= 7 θ= 45 θ= σ' v = 49kPa n =,, 8 θ= 9 θ= 7 σ' v = 49kPa 6 n = θ= 45,,,, Experiments showing the same ε V if the ratio of shear strain amplitude is at :. Figure. θ= 9 θ= 7 θ= 45 θ= σ' v = 49kPa n = 5 4 θ= Relations of post-cyclic settlement induced by undrained -directional and multidirectional cyclic shears versus shear strain amplitude for various number of cycles. The relations between the post-cyclic vertical settlement in strain (ε V ) and shear strain amplitude under -directional and multi-directional cyclic shears are shown in Fig. for various number of cycles. It is observed that the larger the shear strain amplitude (γ) and number of cycles (n) result in the higher post-cyclic settlement. At the same γ and n, the settlements induced by undrained multi-directional shears are larger than those induced by the undrained -directional ones, and for multi-directional shears, the settlement increases with the phase difference (θ).

10 Therefore, the vertical settlement of cohesive soil subjected to undrained cyclic shear is significantly affected by the cyclic shear direction, shear strain amplitude and number of cycles. The data showing the relations of post-cyclic settlement induced by undrained directional and multi-directional cyclic shear (at θ = 9 ) versus elapsed time are plotted in Fig. 3 for various shear strain amplitudes and number of cycles. It is seen in Fig. 3 that the settlements of soil specimen almost finish after about minutes, irrespective of shear strain amplitude and cyclic shear direction. This duration agrees with the dissipation duration of cyclic induced-excess pore water pressure which was shown in Fig.. After this time, the gradients of the settlement-time curves become constant. In addition, further comparisons in Figs. and 3 given by red arrows indicating that the post-cyclic settlements induced by undrained cyclic shearing become equal to each other with the condition of that the shear strain amplitudes of the -directional tests are two times higher than those of the multi-directional ones and this relation remains unchanged with the elapsed time. Matsuda et al.[3] investigated the effect of cyclic shear direction on the properties of saturated granular materials, including Toyoura sand, Genkai sand and granulated blast furnace slag (GBFS) by using the same multi-directional cyclic simple shear test apparatus and concluded that the amplitude of -directional cyclic shear strain, for effective vertical stress reduction and post-cyclic settlement, can be evaluated to be equal to.5 -. times of the amplitude of multi-directional cyclic shear strain. Settlement in strain, (%) ε V (%) Settlement in in strain, (%) ε V (%),, 4, 6, 8,,,,, Elapsed time (min), 4, 6, 8,,,, Elapsed time (min) Figure 3. γ (%) θ = 9 σ' v = 49kPa n = γ (%) Settlement in strain (%) θ = 9 Settlement in strain (%) σ' v = 49kPa n = 5,, 4, 6, 8,,,,, Elapsed time (min), 4, 6, 8,,,, Elapsed time (min) γ (%)..4.. θ = 9 σ' v = 49kPa n = γ (%) θ = 9 σ' v = 49kPa n = Elapsed time, t (min.) Elapsed time, t (min.) Experiments showing the same ε V -t relations if the ratio of shear strain amplitude is at :. Relations of post-cyclic settlement induced by undrained -directional and multidirectional cyclic shear (θ = 9 ) versus elapsed time for different shear strain amplitudes and number of cycles.

11 Conclusions The main conclusions of this research are as follows: () The number of cycles, shear strain amplitude and cyclic shear direction significantly affect the excess pore water pressure buildup and vertical settlement of saturated clay subjected to undrained -directional and multi-directional cyclic shears. However, the duration for finishing the dissipation of cyclic shear induced-pore water pressure and the post-cyclic settlement is similar to the one obtained from consolidation tests performed on soil specimen which has not been subjected to cyclic shearing and therefore this property is not affected by the cyclic shearing histories. () The excess pore water pressure ratio and the vertical settlement of a clay subjected to undrained -directional and multi-directional cyclic shears become equal to each other when the shear strain amplitude of the -directional tests are two times higher than those of the multi-directional ones. For saturated granular materials, this proportion is about References. Tokimatsu K, Katsumata K. Liquefaction-induced damage to buildings in Urayasu city during the Tohoku Pacific earthquake, Proc. Int. Symp. on Engineering Lessons Learned from the Great East Japan Earthquake ; Ansal A, Iyisan R, Yildirim H. The cyclic behavior of soils and effects of geotechnical factors in microzonation, Soil Dynamics and Earthquake Engineering ; (5): Matsuda H, Shinozaki H, Okada N, Takamiya K, Shinyama K. Effects of multi-directional cyclic shear on the post-earthquake settlement of ground, Proc. of 3 th World Conf. on Earthquake Engineering 4; No Matsuda H. Estimation of post-earthquake settlement-time relations of clay layers, Journal of JSCE Division C, JSCE 997; 568(III-39): 4-48 (in Japanese). 5. Yasuhara K. Consolidation and settlement under cyclic loading, Proc. Int. Symp. on Compression and Consolidation of Clayey Soils 995; Ohara S, Matsuda H. Study on the settlement of saturated clay layer induced by cyclic shear, Soils and Foundations 988; 8(3): Yasuhara K, Andersen KH. Recompression of normally consolidated clay after cyclic loading, Soils and Foundations 99; 3(): Matsuda H, Nagira H. Decrease in effective stress and reconsolidation of saturated clay induced by cyclic shear, Journal of JSCE Division C, JSCE ; 659(III-5): (in Japanese). 9. Yasuhara K, Hirao K, Hyde AFL. Effects of cyclic loading on undrained strength and compressibility of clay, Soils and Foundations 99; 3(): -6.. Fujiwara H, Yamanouchi T, Yasuhara K, Ue S. Consolidation of alluvial clay under repeated loading, Soils and Foundations 985; 5(3): Matsuda H, Nhan TT, Ishikura R, Andre PH. Excess pore water pressure accumulation and recompression of sarturated clay subjected to multi-directional cyclic simple shear, Proc. of the Geotec Hanoi ; Matsuda H, Nhan TT, Ishikura R, Hendrawan AP. Accumulation of excess pore water pressure and post-cyclic settlement of saturated soft clay subjected to multi-directional cyclic simple shear, Proc. of the nd International Conference on Transportation Geotechnics ; Nhan TT, Matsuda H, Thien ĐQ, Tuyen TH, An TTP. New criteria for cyclic failure of normally consolidated clays and sands subjected to form and irregular cyclic shear, Proc. of the International workshop Hue Geo- Engineering ; Matsuda H, Nhan TT, Ishikura R. Excess pore water pressure accumulation and recompression of saturated soft clay subjected to -directional and multi-directional cyclic simple shears, Earthquake and Tsunami Journal 3; 7(4): Matsuda H, Nhan TT, Ishikura R. Prediction of excess pore water pressure and post-cyclic settlement on soft clay induced by -directional and multi-directional cyclic shears as a function of strain path parameters, Soil Dynamics and Earthquake Engineering 3; 49:

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