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Seismic performances of dyke on liquefiable soils
Journal of Rock Mechanics and Geotechnical Engineering 5 (2013) 294–305
Journal of Rock Mechanics and GeotechnicalEngineering
Journal of Rock Mechanics and Geotechnical Engineering journal homepage: www.rockgeotech.org
Seismic performances of dyke on liquefiable soils Mingwu Wang a,∗ , Guangyi Chen a , Susumu Iai b a b
School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China Disaster Prevention Research Institute, Kyoto University, Kyoto 611-0011, Japan
a r t i c l e
i n f o
Article history: Received 15 July 2012 Received in revised form 26 March 2013 Accepted 23 April 2013 Keywords: Dyke Dynamic centrifuge test Effective stress analysis Liquefaction Seismic design Seismic responses
a b s t r a c t Various field investigations of earthquake disaster cases have confirmed that earthquake-induced liquefaction is a main factor causing significant damage to dyke, research on seismic performances of dyke is thus of great importance. In this paper, seismic responses of dyke on liquefiable soils were investigated by means of dynamic centrifuge model tests and three-dimensional (3D) effective stress analysis method which is based on a multiple shear mechanism model and a liquefaction front. For the prototype scale centrifuge tests, sine wave input motions with peak accelerations 0.806 m/s2 , 1.790 m/s2 and 3.133 m/s2 of varied amplitudes were adopted to study the seismic performances of dyke on the saturated soil layer foundation with relative density of approximately 30%. Then, corresponding numerical simulations were conducted to investigate the distribution and variations of deformation, acceleration, excess pore-water pressure (EPWP), and behaviors of shear dilatancy in the dyke and the liquefiable soil foundation. Moreover, detailed discussions and comparisons between numerical simulations and centrifuge tests were also presented. It is concluded that the computed results have a good agreement with the measured results by centrifuge tests. The physical and numerical models both indicate that the dyke hosted on liquefiable soils subjected to earthquake motions has exhibited larger settlement and lateral spread: the stronger the motion is, the larger the dyke deformation is. Compared to soils in the deep ground under the dyke and the free field, the EPWP ratio is much smaller in the shallow liquefiable soil beneath the dyke in spite of large deformation produced. For the same overburden depth soil from free site and the liquefiable foundation beneath dyke, the characteristics of effective stress path and stress–strain relations are different. All these results may be of theoretical and practical significance for seismic design of the dyke on liquefiable soils. © 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved.
1. Introduction According to results of field investigations of earthquake disasters in various countries, the earthquake-induced liquefaction is one of the most important factors that cause serious damage to dykes due to the sharp increase of excess pore-water pressure (EPWP) during strong earthquake (Wang and Luo, 2000; Wang et al., 2004), followed by effective stress reduction or even lost. Dyke safety is a major concern in human life and property, social economy, and cultural security. Consequently, research on
∗ Corresponding author. Tel.: +86 551 62901434. E-mail address: [email protected] (M. Wang). Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.
1674-7755 © 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jrmge.2013.06.001
seismic response and damage mechanism of dyke on the liquefiable soils is critically important in structure operation, dyke earthquake prevention, and disaster reduction. Evaluation of dyke seismic performances is basically carried out through laboratory tests and numerical simulations. Sharma and Bolton (1996), Wu et al. (2007) and Wang et al. (2008) discussed the seismic responses of the reinforced embankments, earth-rockfill dam and dyke on liquefiable soils by dynamic centrifuge tests, and some valuable results were obtained. Cai et al. (2001) studied the liquefaction characteristics of silty soil through the dynamic triaxial test and the resonant column test. Shao et al. (2001) and Wang et al. (2005) conducted a two-dimensional (2D) numerical analysis of seismic responses of the dyke on liquefiable soils. Ozutsumi et al. (2002) simulated the representative damaged river dykes during earthquakes in Japan. It is noted that the effective stress analysis method is widely used in analyses of numerous practical problems for evaluating seismic performances of dykes. However, most of the work was limited to the 2D boundary value problems. Up to now, there is no consensus on the damage mechanism of dyke hosted on the liquefiable soils subjected to strong motions yet. By means of three-dimensional (3D) effective stress numerical analysis method and centrifuge tests results, the paper attempts to
0 −4
get insights into the responses of dyke subjected to strong motions which include the deformation and acceleration of dyke, the variation of the EPWP and the evolution of effective stress path in liquefiable soils, for the purpose of providing a basis for seismic design.
0
10
0
10
0
10
Time (s) (a) Case 1.
20
30
20
30
20
30
4
0
−4
Input acceleration (m/s2)
Fig. 1. Dynamic centrifuge test model (unit: mm).
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Input acceleration (m/s2)
Input acceleration (m/s2)
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Time (s) (b) Case 2.
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0
−4
Time (s) (c) Case 3.
Fig. 2. Input motion of each centrifuge model.
2. Centrifuge tests 2.1. Centrifuge model Three centrifuge models of different sine input motions were carried out to investigate the seismic performances of dyke during earthquakes. Model configuration is depicted in Fig. 1. The peaks of prototype input motions in the centrifuge tests (Cases 1, 2 and 3) are 0.806 m/s2 , 1.790 m/s2 , and 3.133 m/s2 , respectively. The programmed motion was excited parallel to the base of the container. The sinusoidal prototype input motions applied on the base of each model were shown in Fig. 2.
of 1.8 and mean grain size of 0.15 mm. The specific gravity of the sand is Gs = 2.63. The maximum and minimum void ratios are 1.11 and 0.7, respectively. The viscosity of the saturated sand consists of silica sand and de-aired methyl cellulose solution is 50 times larger than that of water. The groundwater table, as shown in Fig. 1, is considered as the surface of the liquefiable soil. 2.4. Model preparation and test procedure
All centrifuge tests were conducted by the DPRI Centrifuge, and the rigid container box and silica sand were used. The DPRI Centrifuge has an effective radius of 2.5 m, and its maximum centrifugal acceleration for static test is 200 g, and 50 g for dynamic test. Three centrifuge tests (acceleration 50 g) were conducted. A rigid rectangular container with internal dimensions of 150 mm × 450 mm × 300 mm (W × L × H) was applied on the centrifuge tests. For each test, a series of complete time histories were recorded, during and after shaking, by 4 accelerometers, 1 pore pressure transducer, and 1 vertical displacement transducer at the top of dyke surface (see Fig. 1). A data acquisition system was installed on the centrifuge to minimize electric noise. Digitals signals were transferred to the computer in control room via wireless communications.
The preparation and test procedure of the saturated centrifuge models presented in the study are basically described as follows: At first, weigh the soil container, install the accelerometers and pore pressure transducers at the proper orientation and locations, and pour the degassed metolose to the designated height of the container. Then, flow the dry soil into soil bin by a hopper to ensure the designed relative density. After making the test model, a vacuum system is used to remove air from the model. The height of sand surface is measured at 12 points and the initial height responding to the location is taken as the average height. After that, the container is moved onto the centrifuge platform and soil model is normally consolidated for 5 min. Next, make the dyke model by dry sand and install laser displacement sensor at the dyke model top. Finally, check the whole measuring system and start the test to reach a centrifugal acceleration of 50 g. The horizontal accelerations in the liquefiable soil and the container base, dyke horizontal accelerations and its top settlement, and EPWP are measured.
2.3. Soils
3. Numerical modeling
In prototype scale, the soil foundation, about 5.0 m in thickness and relative density of roughly 30%, is mainly comprised of silica sand resting on stiff bedrock. The dyke is constructed by the dry sand. The sand has a good gradation with uniformity coefficient
3.1. Outline of the effective stress analysis method
2.2. Instrumentations
A program FLIP3D (Finite element analysis program for LIquefaction Program) based on the effective stress analysis method,
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developed by Iai and Ozutsumi (2005) and Ozutsumi et al. (2002), was used to conduct numerical analysis. The constitutive model used in the program is a multiple shear mechanism model, proposed by Towhata and Ishihara (Shao et al., 2001). This model can reproduce the effect of the periodic principal stress axes deflection (Iai et al., 1992; Ozutsumi et al., 2002; Iai and Ozutsumi, 2005; Wang et al., 2005, 2008; Wang, 2012). The incremental stress–strain relationship was incorporated in the program, and it can be written in the vector-matrix notation as T
(j)
KL/U {m(0j) }{m(0j) } ({dε} − {dεp }) +
j=1
j=1
1 V I
(j)
KL/U =
i=1
(ij)
GL/U =
1 V
J I
T
GL/U {m(i j) }{m(i j) } {dε} (ij)
(1)
i=1
Fig. 3. Half computed mesh and output nodes and output elements (unit: m).
2 (j) (j)
(r (j) ) kF cF
2 (−/2)(j) (−/2)(j) cF
{[r (−/2)(j) ] kF
2 (j) (j)
+ (r (j) ) kS cS } (3)
R(ij)
(j)
(ij)
where KL/U and GL/U are the tangential bulk moduli for the virtual plane strain mechanism and the shear mechanism, respectively; the subscripts ‘L’ and ‘U’ denote loading and unloading in the jth plane, respectively; {m(0j) } and {m(i j) } are the stress direction vectors for the 2D volumetric mechanism and the ith virtual simple shear mechanism in the jth plane; r (j) is the radius of a sphere that has a contact normal along the direction with the jth plane; V is (j) (j) the volume of the representative volume element; kF and kS are the normal and tangential contact stiffness with contact normal in (j) (j) the direction within the jth plane; cF and cS are the correction (i j) factors; R is a class of contacts of which contact force and contact normal are parallel to the jth plane, having the direction between ( i − /2)/2 and ( i + /2)/2, relative to the {x(j)} axis within the jth plane and the relevant quantities specifying the direction are given by i = (i − 1)
I
(i = 1, 2, . . . , I, sets of zones)
(4)
The EPWP generation due to dilatancy is modeled by the concept of liquefaction front. In the normalized stress space defined with the isotropic stress ratio S = p/p0 and the deviatoric stress ratio r = /(−p0 ), where = ( 1 − 3 )/2, the liquefaction front is specified by
S=
⎧ S0 (for r ≤ 0.67 sin ϕp ) ⎪ ⎪ ⎪
⎪ ⎨ 2 S0 + ⎪ ⎪ ⎪ ⎪ ⎩
0
(2)
R(ij)
0.33 sin ϕp sin ϕf
+
(r − 0.67 sin ϕp ) sin ϕf
Residual settlement (mm)
J
Measured Computed −500
−1000
−1500 0
1 2 3 Acceleration (m/s2)
4
(a) Residual settlement. Maximum lateral displacement (mm)
{d } =
500 Computed
400 300 200 100 0 0
1 2 3 Acceleration (m/s2)
4
(b) Maximum lateral displacement.
2 (5)
Fig. 4. Deformations at dyke top.
(for r > 0.67 sin ϕp )
w p1 ⎧ ⎪ ⎨ 1 − 0.6 w 1 S0 = ⎪ w p2 ⎩ +S (0.4 − S ) 1
w1
1
(for w ≤ w1 )
3.2. Simulation model (6)
(for w > w1 )
where the normal shear work w is defined as a ratio of cumulative plastic shear work to equivalent elastic energy. The parameters S1 , w1 , p1 and p2 characterize the cyclic accumulation of the excess water pressure ratio obtained by laboratory tests. ϕf , ϕp and r are the internal friction angle, phase transformation angle and deviatoric stress ratio, respectively. More details on this numerical analysis method can be found in Iai et al. (1992) and Wang (2012).
Based on the 50 g centrifuge tests, corresponding numerical models of different earthquake intensities were carried out to investigate seismic performances of the dyke on liquefiable soils. The numerical models were constructed according to the dimensions of the centrifuge tests. The half model mesh behind the middle section of the X–Y plane crossing the coordinate point (0, 0, 3.75 m) used in the analysis was shown in Fig. 3. The finite element model consists of 2761 nodes and 3480 elements. The locations of the output elements A, B and C, the output nodes D, E, F, G and H were illustrated in Fig. 3. Pore-water element and multi-spring
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Table 1 Soil parameters for numerical analysis. Soil
(g/cm3 )
Gma (MPa)
Kma (MPa)
ϕf (◦ )
ϕp (◦ )
Liquefiable foundation Dry sand in the dyke
2.00 1.67
53.02 212.7
138.3 554.7
38.37 44.02
28 –
S1
w1
p1
p2
c1
0.005 –
1.413 –
0.6 –
1.112 –
1.566 –
Notes: Kma , rebound modulus; Gma , shear modulus; ϕf , angle of internal friction; ϕp , phase transformation angle; S1 , w1 , p1 , p2 , c1 , dilatancy parameters.
300 Dyke bottom Liquefiable soil
0
−100
0
1
2 3 Acceleration (m/s2) (a) Residual lateral displacement.
4
Liquefiable soil 150
0
- 150 0
1
2
3
4
Acceleration (m/s2) (a) Lateral displacement.
Dyke bottom
0
Liquefiable soil −200
Maximum settlement (mm)
Residual settlement (mm)
0
Dyke bottom
Maximum lateral displacement (mm)
Residual lateral displacement (mm)
100
−400
−600
−800
0
1
2 3 Acceleration (m/s2)
- 200
- 400
Dyke bottom Liquefiable soil
- 600
4
- 800
(b) Residual settlement.
0
1
Fig. 5. Residual deformations at dyke bottom and in liquefiable soil.
2 3 Acceleration (m/s2)
4
(b) Settlement. Fig. 6. Maximum deformations at dyke bottom and in liquefiable soil.
element were used to simulate the excess pore-water and soils, respectively. Input waves shown in Fig. 2 at prototype scale were adopted to measure the motions on the base of container box in the centrifuge tests. The seismic response analysis was performed for the duration of 30 s. To simulate the actual conditions of centrifuge test, the bottom boundary of the analytical domain was set at the base of liquefiable soil layer. The ground motions were applied on the fixed bottom boundary. A vertical roller condition was assigned for both sides, behind and front boundaries. Before the dynamic response analysis under undrained condition, a static analysis was performed considering gravity to simulate the initial stress in site. The numerical integral is done by Wilson- method ( = 1.4) at time step of 0.01 s. Also, Rayleigh damping (˛ = 0.000, ˇ = 0.004) was used to ensure the stability of the numerical solution process.
3.3. Model parameters The parameters of soil layer used for the numerical analysis were listed in Table 1. The parameters were determined from the soil layer used for centrifuge tests and from laboratory test results. The shear modulus was specified from the relative density. Table 2 The residual settlements at the dyke top (at prototype scale). Case
Measured values (mm)
Computed values from 3D numerical modeling (mm)
Case 1 Case 2 Case 3
11 1001 1402
18 1112 1324
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Fig. 7. Comparisons of settlement time histories between centrifuge tests and simulations.
Fig. 8. Computed and measured settlements in the dyke and the liquefiable soil.
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Fig. 9. Comparison of time histories of lateral deformation.
The angles of internal friction were estimated by referring to the drained shear strength obtained from the results of triaxial consolidated-undrained (CU) shear test. The shear dilatancy parameters were specified by a simple method (Iai et al., 1992). 4. Results and discussions The results from prototype scale tests and numerical predications are presented and comparative analyses are elucidated in the below. 4.1. Deformations The residual deformations for the dyke top after 30 s shaking were depicted in Fig. 4 and the corresponding results were listed in Table 2. The deformation at dyke top represented by the crest settlement was compared with that measured after shaking (Fig. 4). The computed residual and the maximum deformations in dyke bottom soil and liquefiable soil during earthquake are depicted in Figs. 5 and 6, respectively. It can be observed that the motion intensity has a minor effect on the residual lateral displacement of soil at dyke bottom and in liquefiable soil. But the residual settlement increased with the increase of motion intensity. It is also found that the maximum deformation increased with the increase of motion intensity, and the value at dyke bottom was much larger than that in liquefiable soil. The comparison of settlement responses between the centrifuge tests and numerical simulations was illustrated in Fig. 7. In Cases 2 and 3, where the soils were liquefied, the deformations were
1.001 m and 1.402 m, respectively, significantly larger than that in the Case 1 (0.011 m), where the soil is not liquefied during shaking. It is clear that, the stronger the motion was, the larger the deformation of dyke was. There was a good agreement in computed and measured settlements (see Fig. 7). And the lateral displacement was less than that at the dyke top. The results also matched with the observed phenomena of larger deformation and serious damage for the dyke on the liquefiable soils after earthquake. Fig. 8 illustrates settlement time histories at the dyke bottom and the liquefiable foundation under dyke (at depth of 2.5 m). It is shown that the settlement at the dyke axis increased with the shaking intensity. The residual settlement at the dyke bottom for Cases 1, 2, and 3 were 3.9 mm, 679.6 mm, and 819.1 mm, respectively (see Fig. 8a, c, and e), and for the liquefiable soil under dyke, the corresponding settlements were 0.8 mm, 251.5 mm, and 299.3 mm, respectively (node G) (see Fig. 8b, d, and f). The predicted lateral displacement time histories at the dyke top, the dyke bottom and the middle of the liquefiable foundation for three numerical models were depicted in Fig. 9. It can be found that the maximum lateral displacements at the dyke top, the dyke bottom, and the middle of foundation in Case 1 were 7.1 mm, 5.1 mm, and 2.1 mm, respectively. And the residual lateral displacements were all less than 0.5 mm (see Fig. 9a, d, and g). However, in Case 3, the maximum lateral displacements were 291.3 mm, 280.0 mm, and 151.3 mm, respectively. The corresponding residual lateral displacements were 101.0 mm, 6.5 mm, and 1.0 mm, respectively (see Fig. 9c, f, and i). It is concluded that the lateral displacement increased significantly, and the residual deformation at the upper dyke was also increased
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Fig. 10. Comparison of horizontal acceleration responses between centrifuge tests and simulations for Case 1.
for Cases 2 and 3 when the foundation was liquefied. While for Case 1 of low earthquake intensity, the lateral displacement and residual deformation for the dyke and the liquefiable soil were much smaller. It is also seen that the subsidence value was much larger than lateral displacement value. The residual settlement at the dyke top was 14 times the residual lateral displacement in Case 3. 4.2. Accelerations The computed and measured horizontal acceleration responses of the dyke and the liquefiable soil were depicted in Figs. 10–12. The time histories of vertical acceleration were illustrated in Fig. 13. For Case 1, the computed peaks of horizontal acceleration were 0.8273 m/s2 , 0.8207 m/s2 , 0.8193 m/s2 , and 0.7956 m/s2 at the dyke top, the dyke bottom, in the liquefiable soil under dyke, and in the liquefiable soil of the free site, respectively. And the amplification
coefficients associated with input waves were 1.027, 1.019, 1.017 and 0.988, respectively (see Fig. 10a, c, e, and g). The measured values with respect to input motions were 1.039, 1.072, 1.037, and 1.124, respectively. However, the peak values of horizontal acceleration in Case 3 were 0.6409 m/s2 , 0.6112 m/s2 , 0.6997 m/s2 , and 1.2302 m/s2 , respectively. And the amplification coefficients in Case 3 were 0.2046, 0.1951, 0.2233 and 0.3927, respectively (see Fig. 12b, d, f, and h). It is indicated that for Case 1, the horizontal acceleration behaved similar waveform with minor change, because the maximum amplitude at the dyke top only increased by 3.9% with respect to the input motion, and decreased by 3.1%, compared with the measured value of the dyke bottom. For Cases 2 and 3, the peaks of horizontal acceleration at the dyke bottom and in the middle of dyke decreased significantly, while they only increased by 0.3% and 4.9% respectively with reference to that of dyke bottom. It can be concluded that the horizontal acceleration decreased sharply when the saturated foundation
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301
Fig. 11. Comparison of horizontal acceleration responses between centrifuge tests and simulations for Case 2.
was liquefied. Besides, the waveform of horizontal acceleration in the liquefiable soil was different from that in the dyke with a longer vibration period (see Fig. 12). The computed horizontal acceleration responses had a good agreement with the measured values. The predicted vertical accelerations in the dyke and the liquefiable soil were shown in Fig. 13. It is observed that the vertical accelerations of soil in the vicinity of the dyke central axis decreased with the increase of buried depth, but were smaller than the value of horizontal accelerations at the same location. The vertical accelerations at the dyke top were up to 0.0363 m/s2 , 0.7706 m/s2 , and 0.2967 m/s2 for Cases 1, 2, and 3, respectively.
4.3. Excess pore-water pressure The measured and computed time histories of EPWPs in the ground at depth of 3.75 m were illustrated in Fig. 14. The computed EPWP ratio at different depths and different distances to
the dyke central axis were shown in Fig. 15, with locations shown in Fig. 3. It can be seen that, the soil at depth of 3.75 m for Case 1 did not liquefy, while Cases 2 and Case 3 did. The computed values were in agreement with the measured values. In Fig. 15a, for the soil at depth of 1.125 m (element A), the EPWP ratio first increased up to 0.883, then quickly decreased with shaking intensity, because the EPWP in the shallow soil was easy to dissipate. However, for Case 3 its EPWP in the soil at depth of 3.75 m (element C) increased sharply and reached a high and stable value with the shaking intensity (see Fig. 15c). Its EPWP ratio increased up to 0.964 after the seismic duration of 3.02 s, which indicates that the soil was liquefied in Case 3. Therefore, it may be concluded from the computed results that the overlying stress in the soil at depth of 3.75 m was bigger than that at depth of 1.125 m, and the deep soil was easier to liquefy than the shallow soil. The EPWP in the soil at depth of 1.125 m (element B) in free field with no constraints of overburden stress was bigger than that in the soils at same depth under the dyke (element A), and wide variation
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Fig. 12. Comparison of horizontal acceleration responses between centrifuge tests and simulations for Case 3.
range of EPWP is seen in Fig. 15a and b. These were in a good agreement with the observed phenomena in the centrifuge tests. However, in Case 1 the ratio of EPWP in soil was almost zero (see Fig. 15d), which suggests that the soils did not liquefy. These results agree with the previous discussions regarding deformation and acceleration. 4.4. Behaviors of shear dilatancy The behaviors of shear dilatancy of liquefiable soil during shaking were illustrated in Fig. 16. The locations of output elements were shown in Fig. 3. It is seen that the residual shear strains in Cases 2 and 3 were much larger than that in Case 1 at the same location. Soil residual shear strain in free field (element B) is larger than that under the dyke (element A). The soil residual shear strain (element B) at depth of 1.125 m in Case 3 increased up to 13.9%, but in Case 1 it was only 0.2% (see Fig. 16b and e). It is concluded that
the soils under the dyke behaved different characteristics of stress paths compared with soils in free field. In Case 3, the soil shear strain during each cycle showed plastic deformation due to the liquefaction lateral spread, while the residual shear strain in free field developed along increase direction, and the effective stress path under the dyke appeared symmetrically due to the overlying stress. For element C at depth of 3.75 m, residual shear strain was smaller than that in the element A. It can be seen that at the first segment of stress path, the shear stress increased with shaking for the first two cases, but in Case 3 its shear stress decreased sharply when soil was liquefied; while in Case 1 the peak value almost kept constant. This agreed with the previous discussions of EPWP. The shearing power under the dyke was bigger than that in free field at the same depth. Besides, the shearing capacity induced by the shear stress and the shear strain was a dominant factor of soil liquefaction under the dyke, but in free field the axial stress difference and the axial strain difference were the major factors. These
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Fig. 13. Computed vertical acceleration responses in the dyke and the liquefiable soil.
Fig. 14. Excess pore-water pressure curves in the liquefiable soil.
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Fig. 15. Ratio of excess pore-water pressure curves in the liquefiable soil.
Fig. 16. Shear dilatancy behaviors in liquefiable foundation.
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soils underwent shear failure rather than liquefaction because of the constantly applied deviator stresses due to gravity before and during the earthquake shaking. 5. Conclusions In this paper, the seismic performances of dyke on liquefiable soils subjected to different motion intensities were discussed by means of centrifuge tests and the 3D effective stress analysis incorporated with a multiple shear mechanism model, and some major conclusions can be drawn as follows: (1) The predicted results obtained from the numerical simulations are in good agreement with that from centrifuge tests, which suggests that the proposed numerical models used to analyze the seismic performances of dyke on the liquefiable soils are effective and reliable. (2) The vertical and the lateral displacements of soil at the top of dyke central axis are larger than those at the bottom, and the vertical displacement is higher than the lateral one. The vertical deformation increases with the increase of earthquake intensity, especially when the dyke foundation is liquefied. Much attention should be paid to the seismic design and rational countermeasures. (3) The deep liquefiable soil under the dyke is much easier to liquefy than the shallow soil, and the EPWP in free field is larger than that under the dyke at the same depth. The liquefiable soils in free field and under dyke bottom present different behaviors of shear dilatancy during shaking. (4) The problem of seismic performances of dyke on the liquefiable soils is a complex problem. The dyke deformations and EPWP distribution rules in the liquefiable soils were only described by physical and numerical models under different shaking intensities. These conclusions may be helpful for understanding the failure mechanism of dyke on the liquefiable soils, and provide a basis for seismic design and seismic reinforcement. But further research should be conducted in order to develop rational seismic design method for the dyke on the liquefiable soils.
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Acknowledgements Financial supports provided by Science and Technological Fund of Anhui Province for Outstanding Youth (No. 08040106830) and National Natural Sciences Foundation of China (No. 41172274) are gratefully acknowledged. The authors also want to thank the reviewers and the editors for their thorough reviews and useful suggestions. References Cai YQ, Qian L, Ling DS, Wu SM. Seismic liquefaction and stability analysis of Qiantang river embankment. Journal of Hydraulic Engineering 2001(1):57–61 [in Chinese]. Iai S, Matsunaga Y, Kameoka T. Strain space plasticity model for cyclic mobility. Soils and Foundations 1992;32(2):1–15. Iai S, Ozutsumi O. Yield and cyclic behaviour of a strain space multiple mechanism model for granular materials. International Journal for Numerical and Analytical Methods in Geomechanics 2005;29(4):417–42. Ozutsumi O, Sawada S, Iai S, Takeshima Y, Sugiyama W, Shimazu T. Effective stress analyses of liquefaction-induced deformation in river dikes. Soil Dynamics and Earthquake Engineering 2002;22(9):1075–82. Shao SJ, Kojima K, Fukui T. Liquefaction numerical simulation of sand ground with embankment. Journal of Xi’an University of Technology 2001;17(2):138–42 [in Chinese]. Sharma JS, Bolton MD. Finite element analysis of centrifuge tests on reinforced embankments on soft clay. Computers and Geotechnics 1996;19(1): 1–22. Wang MW, Luo GY. Application of reliability analysis to assessment of sand liquefaction potential. Chinese Journal of Geotechnical Engineering 2000;22(5):542–4 [in Chinese]. Wang MW, Jin JL, Li L. Application of PP method based on RAGA to assessment of sand liquefaction potential. Chinese Journal of Rock Mechanics and Engineering 2004;23(4):631–4 [in Chinese]. Wang MW, Iai S, Tobita T. Numerical modelling for dynamic centrifuge model test of the seismic behaviors of pile-supported structure. Chinese Journal of Geotechnical Engineering 2005;27(7):738–41 [in Chinese]. Wang MW, Iai S, Tobita T. Centrifuge test and numerical analysis of seismic responses of dyke on liquefiable soils foundation. Journal of Hydraulic Engineering 2008;39(12):1346–52 [in Chinese]. Wang MW. Dynamic centrifuge tests and numerical modelling for geotechnical earthquake engineering in liquefiable soils. Beijing: Science Press; 2012 [in Chinese]. Wu CH, Ni CK, Ko HY. Seismic reaction of earth and rockfill dam: centrifuge modeling test and numerical simulation. Chinese Journal of Rock Mechanics and Engineering 2007;26(1):1–14 [in Chinese].
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Journal of Rock Mechanics and Geotechnical Engineering journal homepage: www.rockgeotech.org
Seismic performances of dyke on liquefiable soils Mingwu Wang a,∗ , Guangyi Chen a , Susumu Iai b a b
School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China Disaster Prevention Research Institute, Kyoto University, Kyoto 611-0011, Japan
a r t i c l e
i n f o
Article history: Received 15 July 2012 Received in revised form 26 March 2013 Accepted 23 April 2013 Keywords: Dyke Dynamic centrifuge test Effective stress analysis Liquefaction Seismic design Seismic responses
a b s t r a c t Various field investigations of earthquake disaster cases have confirmed that earthquake-induced liquefaction is a main factor causing significant damage to dyke, research on seismic performances of dyke is thus of great importance. In this paper, seismic responses of dyke on liquefiable soils were investigated by means of dynamic centrifuge model tests and three-dimensional (3D) effective stress analysis method which is based on a multiple shear mechanism model and a liquefaction front. For the prototype scale centrifuge tests, sine wave input motions with peak accelerations 0.806 m/s2 , 1.790 m/s2 and 3.133 m/s2 of varied amplitudes were adopted to study the seismic performances of dyke on the saturated soil layer foundation with relative density of approximately 30%. Then, corresponding numerical simulations were conducted to investigate the distribution and variations of deformation, acceleration, excess pore-water pressure (EPWP), and behaviors of shear dilatancy in the dyke and the liquefiable soil foundation. Moreover, detailed discussions and comparisons between numerical simulations and centrifuge tests were also presented. It is concluded that the computed results have a good agreement with the measured results by centrifuge tests. The physical and numerical models both indicate that the dyke hosted on liquefiable soils subjected to earthquake motions has exhibited larger settlement and lateral spread: the stronger the motion is, the larger the dyke deformation is. Compared to soils in the deep ground under the dyke and the free field, the EPWP ratio is much smaller in the shallow liquefiable soil beneath the dyke in spite of large deformation produced. For the same overburden depth soil from free site and the liquefiable foundation beneath dyke, the characteristics of effective stress path and stress–strain relations are different. All these results may be of theoretical and practical significance for seismic design of the dyke on liquefiable soils. © 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved.
1. Introduction According to results of field investigations of earthquake disasters in various countries, the earthquake-induced liquefaction is one of the most important factors that cause serious damage to dykes due to the sharp increase of excess pore-water pressure (EPWP) during strong earthquake (Wang and Luo, 2000; Wang et al., 2004), followed by effective stress reduction or even lost. Dyke safety is a major concern in human life and property, social economy, and cultural security. Consequently, research on
∗ Corresponding author. Tel.: +86 551 62901434. E-mail address: [email protected] (M. Wang). Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.
1674-7755 © 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jrmge.2013.06.001
seismic response and damage mechanism of dyke on the liquefiable soils is critically important in structure operation, dyke earthquake prevention, and disaster reduction. Evaluation of dyke seismic performances is basically carried out through laboratory tests and numerical simulations. Sharma and Bolton (1996), Wu et al. (2007) and Wang et al. (2008) discussed the seismic responses of the reinforced embankments, earth-rockfill dam and dyke on liquefiable soils by dynamic centrifuge tests, and some valuable results were obtained. Cai et al. (2001) studied the liquefaction characteristics of silty soil through the dynamic triaxial test and the resonant column test. Shao et al. (2001) and Wang et al. (2005) conducted a two-dimensional (2D) numerical analysis of seismic responses of the dyke on liquefiable soils. Ozutsumi et al. (2002) simulated the representative damaged river dykes during earthquakes in Japan. It is noted that the effective stress analysis method is widely used in analyses of numerous practical problems for evaluating seismic performances of dykes. However, most of the work was limited to the 2D boundary value problems. Up to now, there is no consensus on the damage mechanism of dyke hosted on the liquefiable soils subjected to strong motions yet. By means of three-dimensional (3D) effective stress numerical analysis method and centrifuge tests results, the paper attempts to
0 −4
get insights into the responses of dyke subjected to strong motions which include the deformation and acceleration of dyke, the variation of the EPWP and the evolution of effective stress path in liquefiable soils, for the purpose of providing a basis for seismic design.
0
10
0
10
0
10
Time (s) (a) Case 1.
20
30
20
30
20
30
4
0
−4
Input acceleration (m/s2)
Fig. 1. Dynamic centrifuge test model (unit: mm).
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Input acceleration (m/s2)
Input acceleration (m/s2)
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Time (s) (b) Case 2.
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0
−4
Time (s) (c) Case 3.
Fig. 2. Input motion of each centrifuge model.
2. Centrifuge tests 2.1. Centrifuge model Three centrifuge models of different sine input motions were carried out to investigate the seismic performances of dyke during earthquakes. Model configuration is depicted in Fig. 1. The peaks of prototype input motions in the centrifuge tests (Cases 1, 2 and 3) are 0.806 m/s2 , 1.790 m/s2 , and 3.133 m/s2 , respectively. The programmed motion was excited parallel to the base of the container. The sinusoidal prototype input motions applied on the base of each model were shown in Fig. 2.
of 1.8 and mean grain size of 0.15 mm. The specific gravity of the sand is Gs = 2.63. The maximum and minimum void ratios are 1.11 and 0.7, respectively. The viscosity of the saturated sand consists of silica sand and de-aired methyl cellulose solution is 50 times larger than that of water. The groundwater table, as shown in Fig. 1, is considered as the surface of the liquefiable soil. 2.4. Model preparation and test procedure
All centrifuge tests were conducted by the DPRI Centrifuge, and the rigid container box and silica sand were used. The DPRI Centrifuge has an effective radius of 2.5 m, and its maximum centrifugal acceleration for static test is 200 g, and 50 g for dynamic test. Three centrifuge tests (acceleration 50 g) were conducted. A rigid rectangular container with internal dimensions of 150 mm × 450 mm × 300 mm (W × L × H) was applied on the centrifuge tests. For each test, a series of complete time histories were recorded, during and after shaking, by 4 accelerometers, 1 pore pressure transducer, and 1 vertical displacement transducer at the top of dyke surface (see Fig. 1). A data acquisition system was installed on the centrifuge to minimize electric noise. Digitals signals were transferred to the computer in control room via wireless communications.
The preparation and test procedure of the saturated centrifuge models presented in the study are basically described as follows: At first, weigh the soil container, install the accelerometers and pore pressure transducers at the proper orientation and locations, and pour the degassed metolose to the designated height of the container. Then, flow the dry soil into soil bin by a hopper to ensure the designed relative density. After making the test model, a vacuum system is used to remove air from the model. The height of sand surface is measured at 12 points and the initial height responding to the location is taken as the average height. After that, the container is moved onto the centrifuge platform and soil model is normally consolidated for 5 min. Next, make the dyke model by dry sand and install laser displacement sensor at the dyke model top. Finally, check the whole measuring system and start the test to reach a centrifugal acceleration of 50 g. The horizontal accelerations in the liquefiable soil and the container base, dyke horizontal accelerations and its top settlement, and EPWP are measured.
2.3. Soils
3. Numerical modeling
In prototype scale, the soil foundation, about 5.0 m in thickness and relative density of roughly 30%, is mainly comprised of silica sand resting on stiff bedrock. The dyke is constructed by the dry sand. The sand has a good gradation with uniformity coefficient
3.1. Outline of the effective stress analysis method
2.2. Instrumentations
A program FLIP3D (Finite element analysis program for LIquefaction Program) based on the effective stress analysis method,
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developed by Iai and Ozutsumi (2005) and Ozutsumi et al. (2002), was used to conduct numerical analysis. The constitutive model used in the program is a multiple shear mechanism model, proposed by Towhata and Ishihara (Shao et al., 2001). This model can reproduce the effect of the periodic principal stress axes deflection (Iai et al., 1992; Ozutsumi et al., 2002; Iai and Ozutsumi, 2005; Wang et al., 2005, 2008; Wang, 2012). The incremental stress–strain relationship was incorporated in the program, and it can be written in the vector-matrix notation as T
(j)
KL/U {m(0j) }{m(0j) } ({dε} − {dεp }) +
j=1
j=1
1 V I
(j)
KL/U =
i=1
(ij)
GL/U =
1 V
J I
T
GL/U {m(i j) }{m(i j) } {dε} (ij)
(1)
i=1
Fig. 3. Half computed mesh and output nodes and output elements (unit: m).
2 (j) (j)
(r (j) ) kF cF
2 (−/2)(j) (−/2)(j) cF
{[r (−/2)(j) ] kF
2 (j) (j)
+ (r (j) ) kS cS } (3)
R(ij)
(j)
(ij)
where KL/U and GL/U are the tangential bulk moduli for the virtual plane strain mechanism and the shear mechanism, respectively; the subscripts ‘L’ and ‘U’ denote loading and unloading in the jth plane, respectively; {m(0j) } and {m(i j) } are the stress direction vectors for the 2D volumetric mechanism and the ith virtual simple shear mechanism in the jth plane; r (j) is the radius of a sphere that has a contact normal along the direction with the jth plane; V is (j) (j) the volume of the representative volume element; kF and kS are the normal and tangential contact stiffness with contact normal in (j) (j) the direction within the jth plane; cF and cS are the correction (i j) factors; R is a class of contacts of which contact force and contact normal are parallel to the jth plane, having the direction between ( i − /2)/2 and ( i + /2)/2, relative to the {x(j)} axis within the jth plane and the relevant quantities specifying the direction are given by i = (i − 1)
I
(i = 1, 2, . . . , I, sets of zones)
(4)
The EPWP generation due to dilatancy is modeled by the concept of liquefaction front. In the normalized stress space defined with the isotropic stress ratio S = p/p0 and the deviatoric stress ratio r = /(−p0 ), where = ( 1 − 3 )/2, the liquefaction front is specified by
S=
⎧ S0 (for r ≤ 0.67 sin ϕp ) ⎪ ⎪ ⎪
⎪ ⎨ 2 S0 + ⎪ ⎪ ⎪ ⎪ ⎩
0
(2)
R(ij)
0.33 sin ϕp sin ϕf
+
(r − 0.67 sin ϕp ) sin ϕf
Residual settlement (mm)
J
Measured Computed −500
−1000
−1500 0
1 2 3 Acceleration (m/s2)
4
(a) Residual settlement. Maximum lateral displacement (mm)
{d } =
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400 300 200 100 0 0
1 2 3 Acceleration (m/s2)
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(b) Maximum lateral displacement.
2 (5)
Fig. 4. Deformations at dyke top.
(for r > 0.67 sin ϕp )
w p1 ⎧ ⎪ ⎨ 1 − 0.6 w 1 S0 = ⎪ w p2 ⎩ +S (0.4 − S ) 1
w1
1
(for w ≤ w1 )
3.2. Simulation model (6)
(for w > w1 )
where the normal shear work w is defined as a ratio of cumulative plastic shear work to equivalent elastic energy. The parameters S1 , w1 , p1 and p2 characterize the cyclic accumulation of the excess water pressure ratio obtained by laboratory tests. ϕf , ϕp and r are the internal friction angle, phase transformation angle and deviatoric stress ratio, respectively. More details on this numerical analysis method can be found in Iai et al. (1992) and Wang (2012).
Based on the 50 g centrifuge tests, corresponding numerical models of different earthquake intensities were carried out to investigate seismic performances of the dyke on liquefiable soils. The numerical models were constructed according to the dimensions of the centrifuge tests. The half model mesh behind the middle section of the X–Y plane crossing the coordinate point (0, 0, 3.75 m) used in the analysis was shown in Fig. 3. The finite element model consists of 2761 nodes and 3480 elements. The locations of the output elements A, B and C, the output nodes D, E, F, G and H were illustrated in Fig. 3. Pore-water element and multi-spring
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Table 1 Soil parameters for numerical analysis. Soil
(g/cm3 )
Gma (MPa)
Kma (MPa)
ϕf (◦ )
ϕp (◦ )
Liquefiable foundation Dry sand in the dyke
2.00 1.67
53.02 212.7
138.3 554.7
38.37 44.02
28 –
S1
w1
p1
p2
c1
0.005 –
1.413 –
0.6 –
1.112 –
1.566 –
Notes: Kma , rebound modulus; Gma , shear modulus; ϕf , angle of internal friction; ϕp , phase transformation angle; S1 , w1 , p1 , p2 , c1 , dilatancy parameters.
300 Dyke bottom Liquefiable soil
0
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0
1
2 3 Acceleration (m/s2) (a) Residual lateral displacement.
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Liquefiable soil 150
0
- 150 0
1
2
3
4
Acceleration (m/s2) (a) Lateral displacement.
Dyke bottom
0
Liquefiable soil −200
Maximum settlement (mm)
Residual settlement (mm)
0
Dyke bottom
Maximum lateral displacement (mm)
Residual lateral displacement (mm)
100
−400
−600
−800
0
1
2 3 Acceleration (m/s2)
- 200
- 400
Dyke bottom Liquefiable soil
- 600
4
- 800
(b) Residual settlement.
0
1
Fig. 5. Residual deformations at dyke bottom and in liquefiable soil.
2 3 Acceleration (m/s2)
4
(b) Settlement. Fig. 6. Maximum deformations at dyke bottom and in liquefiable soil.
element were used to simulate the excess pore-water and soils, respectively. Input waves shown in Fig. 2 at prototype scale were adopted to measure the motions on the base of container box in the centrifuge tests. The seismic response analysis was performed for the duration of 30 s. To simulate the actual conditions of centrifuge test, the bottom boundary of the analytical domain was set at the base of liquefiable soil layer. The ground motions were applied on the fixed bottom boundary. A vertical roller condition was assigned for both sides, behind and front boundaries. Before the dynamic response analysis under undrained condition, a static analysis was performed considering gravity to simulate the initial stress in site. The numerical integral is done by Wilson- method ( = 1.4) at time step of 0.01 s. Also, Rayleigh damping (˛ = 0.000, ˇ = 0.004) was used to ensure the stability of the numerical solution process.
3.3. Model parameters The parameters of soil layer used for the numerical analysis were listed in Table 1. The parameters were determined from the soil layer used for centrifuge tests and from laboratory test results. The shear modulus was specified from the relative density. Table 2 The residual settlements at the dyke top (at prototype scale). Case
Measured values (mm)
Computed values from 3D numerical modeling (mm)
Case 1 Case 2 Case 3
11 1001 1402
18 1112 1324
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Fig. 7. Comparisons of settlement time histories between centrifuge tests and simulations.
Fig. 8. Computed and measured settlements in the dyke and the liquefiable soil.
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Fig. 9. Comparison of time histories of lateral deformation.
The angles of internal friction were estimated by referring to the drained shear strength obtained from the results of triaxial consolidated-undrained (CU) shear test. The shear dilatancy parameters were specified by a simple method (Iai et al., 1992). 4. Results and discussions The results from prototype scale tests and numerical predications are presented and comparative analyses are elucidated in the below. 4.1. Deformations The residual deformations for the dyke top after 30 s shaking were depicted in Fig. 4 and the corresponding results were listed in Table 2. The deformation at dyke top represented by the crest settlement was compared with that measured after shaking (Fig. 4). The computed residual and the maximum deformations in dyke bottom soil and liquefiable soil during earthquake are depicted in Figs. 5 and 6, respectively. It can be observed that the motion intensity has a minor effect on the residual lateral displacement of soil at dyke bottom and in liquefiable soil. But the residual settlement increased with the increase of motion intensity. It is also found that the maximum deformation increased with the increase of motion intensity, and the value at dyke bottom was much larger than that in liquefiable soil. The comparison of settlement responses between the centrifuge tests and numerical simulations was illustrated in Fig. 7. In Cases 2 and 3, where the soils were liquefied, the deformations were
1.001 m and 1.402 m, respectively, significantly larger than that in the Case 1 (0.011 m), where the soil is not liquefied during shaking. It is clear that, the stronger the motion was, the larger the deformation of dyke was. There was a good agreement in computed and measured settlements (see Fig. 7). And the lateral displacement was less than that at the dyke top. The results also matched with the observed phenomena of larger deformation and serious damage for the dyke on the liquefiable soils after earthquake. Fig. 8 illustrates settlement time histories at the dyke bottom and the liquefiable foundation under dyke (at depth of 2.5 m). It is shown that the settlement at the dyke axis increased with the shaking intensity. The residual settlement at the dyke bottom for Cases 1, 2, and 3 were 3.9 mm, 679.6 mm, and 819.1 mm, respectively (see Fig. 8a, c, and e), and for the liquefiable soil under dyke, the corresponding settlements were 0.8 mm, 251.5 mm, and 299.3 mm, respectively (node G) (see Fig. 8b, d, and f). The predicted lateral displacement time histories at the dyke top, the dyke bottom and the middle of the liquefiable foundation for three numerical models were depicted in Fig. 9. It can be found that the maximum lateral displacements at the dyke top, the dyke bottom, and the middle of foundation in Case 1 were 7.1 mm, 5.1 mm, and 2.1 mm, respectively. And the residual lateral displacements were all less than 0.5 mm (see Fig. 9a, d, and g). However, in Case 3, the maximum lateral displacements were 291.3 mm, 280.0 mm, and 151.3 mm, respectively. The corresponding residual lateral displacements were 101.0 mm, 6.5 mm, and 1.0 mm, respectively (see Fig. 9c, f, and i). It is concluded that the lateral displacement increased significantly, and the residual deformation at the upper dyke was also increased
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Fig. 10. Comparison of horizontal acceleration responses between centrifuge tests and simulations for Case 1.
for Cases 2 and 3 when the foundation was liquefied. While for Case 1 of low earthquake intensity, the lateral displacement and residual deformation for the dyke and the liquefiable soil were much smaller. It is also seen that the subsidence value was much larger than lateral displacement value. The residual settlement at the dyke top was 14 times the residual lateral displacement in Case 3. 4.2. Accelerations The computed and measured horizontal acceleration responses of the dyke and the liquefiable soil were depicted in Figs. 10–12. The time histories of vertical acceleration were illustrated in Fig. 13. For Case 1, the computed peaks of horizontal acceleration were 0.8273 m/s2 , 0.8207 m/s2 , 0.8193 m/s2 , and 0.7956 m/s2 at the dyke top, the dyke bottom, in the liquefiable soil under dyke, and in the liquefiable soil of the free site, respectively. And the amplification
coefficients associated with input waves were 1.027, 1.019, 1.017 and 0.988, respectively (see Fig. 10a, c, e, and g). The measured values with respect to input motions were 1.039, 1.072, 1.037, and 1.124, respectively. However, the peak values of horizontal acceleration in Case 3 were 0.6409 m/s2 , 0.6112 m/s2 , 0.6997 m/s2 , and 1.2302 m/s2 , respectively. And the amplification coefficients in Case 3 were 0.2046, 0.1951, 0.2233 and 0.3927, respectively (see Fig. 12b, d, f, and h). It is indicated that for Case 1, the horizontal acceleration behaved similar waveform with minor change, because the maximum amplitude at the dyke top only increased by 3.9% with respect to the input motion, and decreased by 3.1%, compared with the measured value of the dyke bottom. For Cases 2 and 3, the peaks of horizontal acceleration at the dyke bottom and in the middle of dyke decreased significantly, while they only increased by 0.3% and 4.9% respectively with reference to that of dyke bottom. It can be concluded that the horizontal acceleration decreased sharply when the saturated foundation
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301
Fig. 11. Comparison of horizontal acceleration responses between centrifuge tests and simulations for Case 2.
was liquefied. Besides, the waveform of horizontal acceleration in the liquefiable soil was different from that in the dyke with a longer vibration period (see Fig. 12). The computed horizontal acceleration responses had a good agreement with the measured values. The predicted vertical accelerations in the dyke and the liquefiable soil were shown in Fig. 13. It is observed that the vertical accelerations of soil in the vicinity of the dyke central axis decreased with the increase of buried depth, but were smaller than the value of horizontal accelerations at the same location. The vertical accelerations at the dyke top were up to 0.0363 m/s2 , 0.7706 m/s2 , and 0.2967 m/s2 for Cases 1, 2, and 3, respectively.
4.3. Excess pore-water pressure The measured and computed time histories of EPWPs in the ground at depth of 3.75 m were illustrated in Fig. 14. The computed EPWP ratio at different depths and different distances to
the dyke central axis were shown in Fig. 15, with locations shown in Fig. 3. It can be seen that, the soil at depth of 3.75 m for Case 1 did not liquefy, while Cases 2 and Case 3 did. The computed values were in agreement with the measured values. In Fig. 15a, for the soil at depth of 1.125 m (element A), the EPWP ratio first increased up to 0.883, then quickly decreased with shaking intensity, because the EPWP in the shallow soil was easy to dissipate. However, for Case 3 its EPWP in the soil at depth of 3.75 m (element C) increased sharply and reached a high and stable value with the shaking intensity (see Fig. 15c). Its EPWP ratio increased up to 0.964 after the seismic duration of 3.02 s, which indicates that the soil was liquefied in Case 3. Therefore, it may be concluded from the computed results that the overlying stress in the soil at depth of 3.75 m was bigger than that at depth of 1.125 m, and the deep soil was easier to liquefy than the shallow soil. The EPWP in the soil at depth of 1.125 m (element B) in free field with no constraints of overburden stress was bigger than that in the soils at same depth under the dyke (element A), and wide variation
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Fig. 12. Comparison of horizontal acceleration responses between centrifuge tests and simulations for Case 3.
range of EPWP is seen in Fig. 15a and b. These were in a good agreement with the observed phenomena in the centrifuge tests. However, in Case 1 the ratio of EPWP in soil was almost zero (see Fig. 15d), which suggests that the soils did not liquefy. These results agree with the previous discussions regarding deformation and acceleration. 4.4. Behaviors of shear dilatancy The behaviors of shear dilatancy of liquefiable soil during shaking were illustrated in Fig. 16. The locations of output elements were shown in Fig. 3. It is seen that the residual shear strains in Cases 2 and 3 were much larger than that in Case 1 at the same location. Soil residual shear strain in free field (element B) is larger than that under the dyke (element A). The soil residual shear strain (element B) at depth of 1.125 m in Case 3 increased up to 13.9%, but in Case 1 it was only 0.2% (see Fig. 16b and e). It is concluded that
the soils under the dyke behaved different characteristics of stress paths compared with soils in free field. In Case 3, the soil shear strain during each cycle showed plastic deformation due to the liquefaction lateral spread, while the residual shear strain in free field developed along increase direction, and the effective stress path under the dyke appeared symmetrically due to the overlying stress. For element C at depth of 3.75 m, residual shear strain was smaller than that in the element A. It can be seen that at the first segment of stress path, the shear stress increased with shaking for the first two cases, but in Case 3 its shear stress decreased sharply when soil was liquefied; while in Case 1 the peak value almost kept constant. This agreed with the previous discussions of EPWP. The shearing power under the dyke was bigger than that in free field at the same depth. Besides, the shearing capacity induced by the shear stress and the shear strain was a dominant factor of soil liquefaction under the dyke, but in free field the axial stress difference and the axial strain difference were the major factors. These
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Fig. 13. Computed vertical acceleration responses in the dyke and the liquefiable soil.
Fig. 14. Excess pore-water pressure curves in the liquefiable soil.
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Fig. 15. Ratio of excess pore-water pressure curves in the liquefiable soil.
Fig. 16. Shear dilatancy behaviors in liquefiable foundation.
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soils underwent shear failure rather than liquefaction because of the constantly applied deviator stresses due to gravity before and during the earthquake shaking. 5. Conclusions In this paper, the seismic performances of dyke on liquefiable soils subjected to different motion intensities were discussed by means of centrifuge tests and the 3D effective stress analysis incorporated with a multiple shear mechanism model, and some major conclusions can be drawn as follows: (1) The predicted results obtained from the numerical simulations are in good agreement with that from centrifuge tests, which suggests that the proposed numerical models used to analyze the seismic performances of dyke on the liquefiable soils are effective and reliable. (2) The vertical and the lateral displacements of soil at the top of dyke central axis are larger than those at the bottom, and the vertical displacement is higher than the lateral one. The vertical deformation increases with the increase of earthquake intensity, especially when the dyke foundation is liquefied. Much attention should be paid to the seismic design and rational countermeasures. (3) The deep liquefiable soil under the dyke is much easier to liquefy than the shallow soil, and the EPWP in free field is larger than that under the dyke at the same depth. The liquefiable soils in free field and under dyke bottom present different behaviors of shear dilatancy during shaking. (4) The problem of seismic performances of dyke on the liquefiable soils is a complex problem. The dyke deformations and EPWP distribution rules in the liquefiable soils were only described by physical and numerical models under different shaking intensities. These conclusions may be helpful for understanding the failure mechanism of dyke on the liquefiable soils, and provide a basis for seismic design and seismic reinforcement. But further research should be conducted in order to develop rational seismic design method for the dyke on the liquefiable soils.
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Acknowledgements Financial supports provided by Science and Technological Fund of Anhui Province for Outstanding Youth (No. 08040106830) and National Natural Sciences Foundation of China (No. 41172274) are gratefully acknowledged. The authors also want to thank the reviewers and the editors for their thorough reviews and useful suggestions. References Cai YQ, Qian L, Ling DS, Wu SM. Seismic liquefaction and stability analysis of Qiantang river embankment. Journal of Hydraulic Engineering 2001(1):57–61 [in Chinese]. Iai S, Matsunaga Y, Kameoka T. Strain space plasticity model for cyclic mobility. Soils and Foundations 1992;32(2):1–15. Iai S, Ozutsumi O. Yield and cyclic behaviour of a strain space multiple mechanism model for granular materials. International Journal for Numerical and Analytical Methods in Geomechanics 2005;29(4):417–42. Ozutsumi O, Sawada S, Iai S, Takeshima Y, Sugiyama W, Shimazu T. Effective stress analyses of liquefaction-induced deformation in river dikes. Soil Dynamics and Earthquake Engineering 2002;22(9):1075–82. Shao SJ, Kojima K, Fukui T. Liquefaction numerical simulation of sand ground with embankment. Journal of Xi’an University of Technology 2001;17(2):138–42 [in Chinese]. Sharma JS, Bolton MD. Finite element analysis of centrifuge tests on reinforced embankments on soft clay. Computers and Geotechnics 1996;19(1): 1–22. Wang MW, Luo GY. Application of reliability analysis to assessment of sand liquefaction potential. Chinese Journal of Geotechnical Engineering 2000;22(5):542–4 [in Chinese]. Wang MW, Jin JL, Li L. Application of PP method based on RAGA to assessment of sand liquefaction potential. Chinese Journal of Rock Mechanics and Engineering 2004;23(4):631–4 [in Chinese]. Wang MW, Iai S, Tobita T. Numerical modelling for dynamic centrifuge model test of the seismic behaviors of pile-supported structure. Chinese Journal of Geotechnical Engineering 2005;27(7):738–41 [in Chinese]. Wang MW, Iai S, Tobita T. Centrifuge test and numerical analysis of seismic responses of dyke on liquefiable soils foundation. Journal of Hydraulic Engineering 2008;39(12):1346–52 [in Chinese]. Wang MW. Dynamic centrifuge tests and numerical modelling for geotechnical earthquake engineering in liquefiable soils. Beijing: Science Press; 2012 [in Chinese]. Wu CH, Ni CK, Ko HY. Seismic reaction of earth and rockfill dam: centrifuge modeling test and numerical simulation. Chinese Journal of Rock Mechanics and Engineering 2007;26(1):1–14 [in Chinese].