INTERNATIONAL SOCIETY FOR SOIL MECHANICS AND GEOTECHNICAL ENGINEERING
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This is an open-access database that archives thousands of papers published under the Auspices of the ISSMGE and maintained by the Innovation and Development Committee of ISSMGE. Dynamic centrifuge model test for performance-based design of grid-form deep mixing walls supporting a tall building
Junji Hamada & Tsuyoshi Honda Takenaka Research & Development Institute, Takenaka Corporation, Inzai, Chiba, Japan
ABSTRACT Dynamic centrifuge model tests in the 50 g field were conducted to investigate a failure behavior of DMWs in liquefiable sand during large earthquakes. A miniature model of DMWs was made of soil-cement with an unconfined compressive strength of about 4,000 kPa in order to investigate the behavior/toughness of the DMWs after yield and failure on seismic performance. The DMWs model that support the superstructure’s weight of 206 kPa, the natural period of 0.6 second were set in a laminar shear box, and repeatedly tested by increasing the acceleration level of the input motion recorded at TAFT earthquakes. The relationship between shear stress and shear strain of the DMWs, namely the nonlinearity of the DMWs was investigated. No significant settlement of the structure was observed even if the normal and shear stresses in the DMWs were assumed to have locally reached the tensile or shear criteria of soil-cement.
1 INTRODUCTION potential for liquefaction mitigation. However, the local failures of the DMWs are not acceptable in the existing Grid-form DMWs (Deep cement Mixing Walls) which is method of allowable stress design. If a local failure can be one of the ground improvement technique are recently appropriately taken into account, the DMWs can be employed as a new method to increase bearing capacity designed more rationally, using a performance-based of foundations in soft grounds as well as a seismic design method. So far, a lot of shaking table tests countermeasure against seismic liquefaction. In the on cement mixing walls have been carried out by using method, the high-modulus soil-cement walls confine the centrifuges (e.g., Babasaki et al., 1992). Most of them loose sand enclosed by the DMWs so as not to cause have been used acrylic resin models, the shear modulus excessive shear deformation during an earthquake. The of which is equivalent to that of real soil-cement in order method was developed in the late 1980s, and has to investigate an effect of preventing liquefaction during demonstrated that the grid-form DMWs effectively earthquakes. Several researchers recently conducted prevented liquefaction and liquefaction-induced damage centrifuge model tests on grid-form DMWs using real soil- in the 1995 Hyogoken-Nambu earthquake. Namely, cement models (Tamura et al., 2015; Khosravi et al., during the earthquake, quay walls were heavily damaged 2016; Honda et al., 2015). Khosravi et al. (2016) used the due to liquefaction-induced lateral flow, however, a 14- soil-cement with an unconfined compressive strength of story building with a foundation of cast-in-place concrete 450 to 770 kPa and investigated the effect of the area piles and the DMWs that was surrounded by the quay replacement ratio and improved depth on the global walls survived and no damage was observed in the pile responses of the soft clay ground. Unfortunately, the foundation (Tokimatsu et al., 1996). In Japan, the grid- above tests were conducted without setting form DMWs have been widely used in a lot of buildings superstructure models on the DMWs. Accordingly, they since 1995. The DMWs have been also applied to support were not able to reach a conclusion about how the inertial buildings directly, and are capable of restricting the force from superstructure affected the performance of the settlement of buildings during or after earthquakes to an DMWs. acceptable level. Recently piled raft foundations This paper describes centrifuge model tests in 50 g combined with the grid-form DMWs have been applied to field in order to investigate failure behavior of DMWs the real buildings. The field measurements on long-term subjected to dynamic loading from superstructure of a tall and seismic behaviors of the buildings supported by piled building and ground oscillation during large earthquake. In rafts with the DMWs were also performed to confirm the this study, the miniature model of DMWs was made of validity of their foundation designs (Yamashita et al., soil-cement in order to investigate the behavior/ 2012). Furthermore, Tanikawa et al. (2015) proposed a toughness of the DMWs after yield and failure during mechanical joint adding dents and bumps at a top surface large earthquakes. The relationship between shear stress of the DMWs in order to ensure transmitting large lateral and shear strain of the DMWs, namely the nonlinearity of forces such as unsymmetrical earth pressure or seismic the DMWs by gradually increasing the input motion step inertia force of superstructure into the DMWs. by step, was also investigated. Before these tests, Some researchers conducted numerical analyses comparative tests between acryl grid-form DMWs model using elasto-plastic models to investigate seismic and soil cement model with low-rise building (rigid weight) behaviors of grid-form DMWs (Namikawa et al., 2007; were conducted and described in reference (Hamada and Shigeno et al., 2017), and concluded that the local failures Honda, 2017). of the DMWs were not the causes of the reduction in the
Laminar shear box 1000
AH62~65 AH8 50 170 150 DH1 DH2 300 260 AV4 AV3 AV1 AH64 AV2 AH4 AH1 AH2 AH3 AH65 AH7 370 20mm 260mm AH52~55 AH0 260mm (a) Top View AH45 Accelerometer（V, H） AH35 200mm Piezometer AH34 AH55 AH44 AH63 Displacement transducer（V, H） AH33 AH54 AH62 AH43 DV2 DV1 AH32 AH53 AH42 AV4 AH7,8 AV3 AH52 Laminar shear box
DH2 AH6 WL=GL-20mm DMWs (Soil cement) AH16 AH26 AH45 50 AH35 AH5 W5 AH15 AH25 AH44 W25 W15 AH24 50 AH34 AH4 W4 AH14 200 AH43 W14 W24 AH23 50 AH33 AH3 W3 AH13 Dr76% AH42 W13 W23 AH22 AH32 AH2 W2 AH12 50 W12 W22 80 Dr95% AV1 DH1 AV2 AH1 W1 W11 W21 AH0
－direction +direction (Unit:mm) Shaking direction (b) Side View (c) DMWs Model and attached gauges Figure 1. Schematic view of the DMWs and high-rise building model with ground.
2 CENTRIFUGE MODEL TESTS steel structure model to increase a friction between the structure model and the DMWs. Centrifuge model tests were performed at an acceleration Silica sand No.6 produced in Iide, Yamagata of 50 g using the 7 m radius centrifuge at Takenaka R. & Prefecture, Japan was used as the soil for all test cases. D. Institute. The scaling ratio is 1/50. The superstructure The physical properties of the Iide sand are following; 50 was modeled to be a tall building, the natural period of 0.6 percent diameter, D50 of 0.28 mm, uniformity coefficient, sec in prototype scale. The shaking table tests were Uc of 1.9, specific gravity of soil particles of 2.657, conducted with liquefiable sand deposit. minimum density of 1.452 g/cm3, maximum density of 1.744 g/cm3. Relative density of the saturated model 2.1 Setting up Model Ground, DMWs and Structures ground is 76 %. Model improved soil-cement walls were also made from Iide sand, kaolin clay and blast-furnace Figure 1 shows schematic view of the tests. The DMWs slag cement type B, W/C=60%. Unconfined compressive models made of soil-cement was set in a laminar shear strength of the soil cement is from 1500 to 2000 kPa in box, and a lot of accelerometers, piezometers and curing time of 7 days and about 4000 kPa in curing time displacement transducers were set on the DMWs models, of 28 days. grounds and structures. The inner dimensions of the The DMWs model was produced according to laminar shear box are 1000 mm long, 300 mm width, 350 following steps. Step1: the soil-cement that has not set mm height. A 2 mm-thick membrane was attached inside was poured in the mold made of panel boards. Step 2: the box to make it watertight. Size of the DMWs model is after a week, the boards were removed. Step3: the DMWs 20 mm thick of soil-cement wall (1.0 m thick in prototype model was cured a month under wet condition. scale) and spaced 240 mm center-to-center apart (12 m in prototype). Sand papers were attached beneath the
Table 1. Peak accelerations and residual settlements Residual Peak Acceleration (cm/s2) settlement (mm) Step Ground DMWs Structure number Base Structure inner DMWs Free field Transverse Longitudinal Substructure Superstructure AH1 AH5 AH25 AH35, AH45 AH55, AH65 AH6 ave.(AH7,AH8) DV1 DV2 1 51 67 73 70, 67 63, 61 68 160 1.9 1.9 2 163 162 185 168, 162 137, 131 153 313 16.7 (18.6) 18.1 (20.0) 3 197 210 386 215, 212 165, 156 186 391 10.1 (28.7) 10.2 (30.3) 4 347 334 418 317, 322 195, 213 215 501 35.5 (64.2) 34.1 (64.4) 5 477 511 759 412, 448 239, 235 238 519 37.5 (101.7) 36.2 (100.6)
) 1 2 AH1(Base) AH5(inner DMWs) AH25(Free field) 0.5 0 -0.5 -1
Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s)
) 1 2 AH5(inner DMWs) AH6(Substructure) AH55(Long.) AH45(Trans.) 0.5 0 -0.5 -1
Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s) )
2 2 1.5 AH6(Substructure) AH7(Superstructure) 1 0.5 0 -0.5 -1 -1.5 -2 Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s)
Figure 2 Time histories of accelerations (Step 1, input acc. of 51 cm/s2)
80 σ ' W4(inner DMWs) W24(Free field) W14(Near field) 60 v 40 20 pressure (kPa)pressure
Excess PorewaterExcess 0 0 20 40 60 80 100 120 Time (s) Figure 3 Time histories of measured excess pore water pressures (Step 1, input acc. of 51 cm/s2)
Water table appears 1.0 m below the ground surface 2.2 Test Results in prototype. The structure consisted of two steel plates whose weights were 11.54kg and 16.89 kg, that Table 1 also shows residual settlements of the models. correspond to a building average contact pressure of 206 The values in parentheses are integrated values from kPa. The value was obtained based on the total area of beginning of step 1 (input acceleration of 51 cm/s2). The basement. Ground enclosed by DMWs was made by settlements reached over 100 mm after the step 5 (input digging the ground about 5 mm so as not to contact the acceleration of 51 cm/s2). raft. So, whole inertial force of the structure can act Figures 2 and 3 show time histories of measured directly to the DMWs. accelerations and excess pore water pressures, Table 1 shows the test step numbers and the respectively at step 1 when liquefaction was not observed corresponding peak accelerations at the base (input), inside and outside the DMWs, W4, W14 and W24. It was ground and structures at each step. Hereafter, test results observed phase difference between vibrations of the are converted into the prototype scale. The TAFT wave superstructure and the ground because natural period of was used as an input shaking motion throughout the the superstructure model, about 0.6 sec is larger than tests. The wave’s peak acceleration level was tuned from predominant period of the ground, about 0.45 sec. a small level to a large level, gradually increased step by step.
) 2 2 AH1(Base) AH5(inner DMWs) AH25(Free field) 1 0 -1 -2
Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s)
) 2
2 AH5(inner DMWs) AH6(Substructure) AH55(Long.) AH45(Trans.) 1 0 -1 -2
Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s) )
2 4 3 AH6(Substructure) AH7(Superstructure) 2 1 0 -1 -2 -3 -4 Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s) Figure 4 Time histories of accelerations (Step 2, input acc. of 163 cm/s2)
80 σ ' W4(inner DMWs) W24(Free field) W14(Near field) 60 v 40 20 pressure (kPa)pressure
Excess PorewaterExcess 0 0 20 40 60 80 100 120 Time (s) Figure 5 Time histories of measured excess pore water pressures (Step 2, input acc. of 163 cm/s2)
) 6 2 AH1(Base) AH5(inner DMWs) AH25(Free field) 4 2 0 -2 -4 -6
Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s)
) 6
2 AH5(inner DMWs) AH6(Substructure) AH55(Long.) AH45(Trans.) 4 2 0 -2 -4 -6
Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s) )
2 6 4 AH6(Substructure) AH7(Superstructure) 2 0 -2 -4 -6 Acceleration (m/s Acceleration 2 4 6 8 10 12 14 16 18 20 Time (s) Figure 6 Time histories of accelerations (Step 5, input acc. of 477 cm/s2)
80 σ ' W4(inner DMWs) W24(Free field) W14(Near field) 60 v 40 20 pressure (kPa)pressure
Excess PorewaterExcess 0 0 20 40 60 80 100 120 Time (s) Figure 7 Time histories of measured excess pore water pressures (Step 5, input acc. of 477 cm/s2)
Figures 4 and 5 show time histories of the results at inner DMWs, AH5 has several sharp peaks caused by 2 step 2 (input acceleration of 163 cm/s ) when liquefaction soil’s cyclic mobility behavior. was observed outside the DMWs, W14 and W24. Acceleration response spectra (linear elastic, 5 % And Figures 6 and 7 show time histories of the results damping) for measured motions in step 1, 2 and 5 are at step 5 (input acceleration of 477 cm/s2) when shown in Figures 8 and 9. liquefaction was observed even in the area enclosed by At step 1, the responses of DMWs, AH45, AH55 and DMWs, W4. It is shown that the measured acceleration ground enclosed by it, AH5 were almost the same, and
450 1200 3000 Base AH1 Base AH1 Base AH1 400 inner DMWs AH5 inner DMWs AH5 inner DMWs AH5
) 1000 Free field AH25 2500 Free field AH25
Free field AH25 2 ) ) 2 350 2 DMWs Trans. AH45 DMWs Trans. AH45 DMWs Trans. AH45 DMWs Long. AH55 DMWs Long. AH55 300 DMWs Long. AH55 800 2000
250 600 1500 200
150 400 1000
100 200 500 Pseudo spectral acceleration (cm/s accelerationspectral Pseudo Pseudo spectral acceleration (cm/s acceleration spectral Pseudo 50 (cm/s acceleration spectral Pseudo
0 0 0 0.1 1 0.1 1 0.1 1 Period (s) Period (s) Period (s) (a) Step1 (51cm/s2) (b) Step 2 (163cm/s2) (c) Step 5 (477cm/s2) Figure 8 Acceleration response spectra (Ground and DMWs)
DMWs Long. AH55 0.6 s 0.68 s DMWs Long. AH55 DMWs Long. AH55 800Substructure AH6 1600 2500 Superstructure (ave.AH7,AH8) Substructure AH6 0.62 s Substructure AH6 700 1400Superstructure (ave.AH7,AH8) Superstructure (ave.AH7,AH8) ) ) 2 ) 2
2 2000 600 1200
500 1000 1500
400 800
1000 300 600
200 400 500
100 (cm/s acceleration spectral Pseudo 200 Pseudo spectral acceleration (cm/s acceleration spectral Pseudo Pseudo spectral acceleration (cm/s acceleration spectral Pseudo
0 0 0 0.1 1 0.1 1 0.1 1 Period (s) Period (s) Period (s) (a) Step1 (51cm/s2) (b) Step 2 (163cm/s2) (c) Step 5 (477cm/s2) Figure 9 Acceleration response spectra (Structure and DMWs) the response at free field, AH25 was slightly larger than where AHi is a displacement at the point of AHi that at ground enclosed by DMWs. The response of the calculated by double integrations from the measured superstructure (average of AH7 and AH8) was amplified acceleration of aAHi using the frequency components from at natural period of around 0.6 sec. and the response of 20 Hz to 0.05 Hz; aAHi is an acceleration at the point of substructure, AH6 was almost same as DMWs, AH55, AHi shown in Figure 1; h is a distance between namely the substructure did not slip at the top of DMWs. accelerometers; ms1 is a mass of superstructure; ms2 is a In step 2, liquefaction occurred at free field, thereby the mass of substructure and mg5-2 is a mass of ground response at free field increased at long-period region. The separated to each layer of 5, 4, 3 and 2. responses of ground enclosed by DMWs, AH5 and transvers wall of DMWs, AH45 were similar, however the h= 7.5 m one of longitudinal wall, AH55 was slightly smaller than ms1= 1442 ton those. In step 5, liquefaction occurred even in the area ms2= 2111 ton enclosed by DMWs, the response of longitudinal wall, mg5= 4.25m× AWhole ×s = 1458 ton AH55 became smaller than that of the base, AH1 in the mg4=mg3= 2.5m× AWhole ×s = 857 ton range under 0.9 sec. And the response at inner DMWs, mg2= 1.75m× AWhole ×s = 600 ton 2 AH5 was considerably smaller than that of transvers wall AWhole=13m×13m=169 m of DMWs, AH45. The response of the superstructure was 3 s=2.03 t/m amplified at period of around 0.68 sec., so it is considered the natural period was slightly increased because of Figures 11 (a) and (b) show the relationship between rocking motion. the shear strain of the longitudinal DMWs, DMW and the Figure 10 shows the relationship between the shear assumed shear stress of the longitudinal DMWs, DMW. It strain of the inner ground, eg and the shear stress of the is assumed that lateral load was supported only by two whole improved ground, eg. The inertial forces of sheets of longitudinal DMWs. These values are defined structure and soil enclosed by the DMWs were assumed as follows: to be the lateral load acting on the DMWs. These values are defined as follows: DCM =(AH55-AH52)/h (3) eg =(AH5-AH2)/h (1) DCM=((aAH7+aAH8)/2×ms1+aAH6×ms2+aAH5×mg5 +a ×m +a ×m +a ×m )/A (4) eg =((aAH7+aAH8)/2×ms1+aAH6×ms2+aAH5×mg5 AH4 g4 AH3 g3 AH2 g2 DMW_L
+aAH4×mg4+aAH3×mg3+aAH2×mg2)/AWhole (2)
where 200 2 STEP5 ADMW_L=13m×1m×2sheets=26 m 150 STEP4 STEP3 Hyperbolic curves (Hardin-Drnevich (HD) model) 100 estimated by the initial shear stiffness of 800 MPa, and STEP2 the ultimate shear stress of 1200 kPa (0.3Fc, where STEP1 50 Fc=4000kPa) were also described in Figures 11 (a) and (b). The estimated curves agreed well with test results. 0 Figures 12 and 13 show time histories of shear stress -50 of the longitudinal DMWs, DMW generated by inertial force
Shear (kPa) Shear stress of structure, DCM_structure, (Equation (4’)) and inertial force -100 of enclosed soil, DCM_ground, (Equation (4’’)) at step 2 and step 5, respectively. The each components of the shear -150 stress oscillate with phase difference at both steps likewise. -200 -6000 -4000 -2000 0 2000 4000 6000 DCM_structure=( ( aAH7 +aAH8)/2×ms1+aAH6×ms2) Shear strain (μ) /ADMW_L (4’) Figure 10 Relationship between shear strain and shear stress of whole improved ground DCM_ground=(aAH5×mg5+aAH4×mg4+aAH3×mg3+aAH2×mg2) 200 /ADMW_L (4’’)
HD model Total by inertial force of enclosed soil by inertial force of structure 300 100 STEP1 200 100 0 -100
Shear stressShear (kPa) -200 0 -300 2 3 4 5 6 7 8 9 10 11 12 Time (sec)
Shear (kPa) Shear strain Figure 12 Time history of components of shear stress of -100 longitudinal DMWs (step 2, input acc. of 163 cm/s2)
Total by inertial force of enclosed soil by inertial force of structure 600 -200 400 -500 -400 -300 -200 -100 0 100 200 300 400 500 200 Shear strain (μ) 0 -200 -400 (a) Longitudinal DMWs (at small strain) stressShear (kPa) -600 2 3 4 5 6 7 8 9 10 11 12 Time (sec) 900 HD model Figure 13 Time history of components of shear stress of STEP5 longitudinal DMWs (step 5, input acc. of 477 cm/s2) 600 STEP4 STEP3 Unfortunately, there are no pictures of DMWs after STEP2 300 STEP1 shaking of step 5 because additional steps of large shaking tests had conducted after that. Photo 1 shows 0 DMWs after similar case studies of this case. The natural period of the superstructure is about 0.41 sec, namely the height of superstructure is lower than that of this case. -300 Shear (kPa) Shear stress Same five steps with almost same input accelerations, the peak input acceleration of 507 cm/s2 were conducted. The -600 photo (a) in Photo 1 shows the top view of the DMWs. The cracks on the longitudinal wall and transverse walls -900 can be seen. The photos (b) in Photo 1 show the outside -3000 -2000 -1000 0 1000 2000 3000 views of the transverse walls after removing model sand. Shear strain (μ) Obvious cracks were observed at center part of the both transvers walls. The photo (c) in Photo 1 shows the inside (b) Longitudinal DMWs (at large strain) views of the longitudinal wall after removing model sand Figure 11 Relationship between shear strain and shear and clear crack was observed. The crack width seems stress relatively large in photo (c), but the width was expanded when the model sand was removed after the tests. It is
considered that the cracks of the longitudinal walls were significant settlement was observed in the tested structure caused by the inertial force of structure and it is presumed though the stress would reach tensile or shear criteria at a that the cracks in transverse walls were caused by either part of the grid-form DMWs. or both of the deformations of the inner ground enclosed by DMWs and the outside ground.
ACKNOWLEGEMENTS
The authors are grateful to Dr. K. Yamashita of Takenaka R&D Institute for his constructive comments on the experimental results. Shaking direction REFERENCES
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