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Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls
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Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls Majid Yazdandoust Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran Received 14 February 2017; received in revised form 3 November 2017; accepted 1 December 2017
Abstract To investigate the influence of the peak acceleration, the loading duration, and the strip length on the dynamic behavior of steel-strip reinforced soil walls (SSWs), in terms of the dynamic reinforcement load distribution and the dynamic lateral earth pressure behind the surface, a series of 1-g shaking table tests was performed on five reduced-scale reinforced soil wall models. It was observed that the maximum axial force of the strips (Tmax) is mobilized at the intersection of the failure plane with strips in all rows. It was also discovered that, in the upper half of the walls, the Tmax values decrease with a decreasing strip length, while this trend is reversed in the lower half of the walls. Additionally, a proper convergence was found between the Tmax/HcsSVSH and L/H0 ratio at different levels of acceleration and duration, so that Tmax/HcsSVSH can be defined as a function of the L/H0 ratio and the seismic parameters for different rows of strips. On the other hand, it was observed that the values of earth pressure predicted by conventional methods under static and seismic conditions are too conservative and these methods predict the position of the resultant lateral force higher than the actual point. Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.
Keywords: Steel-strip reinforced soil wall; Seismic earth pressure; Dynamic reinforcement load; 1-g shaking table test
1. Introduction In order to better understand the seismic performance of reinforced soil walls, the dynamic behavior of these structures has been investigated experimentally, including studies on full-scale models (Richardson et al., 1977; Futaki et al., 1996), large-scale models (Murata et al., 1994; Bathurst et al., 2000; Ling et al., 2005; Wang et al., 2015), and reduced-scale models (Koseki et al., 2003; ElEmam and Bathurst, 2007; Ling et al., 2009; Huang et al., 2011; Komak Panah et al., 2015). Although many studies on the seismic behavior of geosynthetic-reinforced soil walls (GRSWs) have been undertaken, little attention has been paid to retaining walls with metallic reinforcements, such that the seismic performance of these walls Peer review under responsibility of The Japanese Geotechnical Society. E-mail address: [email protected]
has been examined in only a few studies (Uezawa et al., 1974; Richardson et al., 1977; Futaki et al., 1996; Siddharthan et al., 2004; Anastasopoulos et al., 2010; Suzuki et al., 2015). The first seismic full-scale model test was performed by Richardson et al. (1977) on a 6-m-high steel-strip reinforced soil wall (SSW) with a discrete concrete block facing. The results indicated that the measured dynamic forces of the strips are considerably less than the forces calculated by the methods recommended for the seismic design, and the induced dynamic forces of the strips could be greatly reduced by decreasing the length of the strips. Futaki et al. (1996) studied the seismic performance of large-scale model walls with ribbed strips and segmental precast concrete panels by shaking table tests. They pointed out that the distribution of lateral earth pressure behind the facing is almost triangular and the coefficient of seismic earth pressure increases with an increasing
https://doi.org/10.1016/j.sandf.2018.02.016 0038-0806/Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.
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amplitude of base excitation. The results also showed that the measured seismic tensile forces of the strips are almost equal to the design values and the distribution trend of axial force along the strips is not constant among the different rows. Based on the large-scale shaking table tests on modular-block reinforced-soil retaining walls, Ling et al. (2005) showed that the magnitude and the location of the maximum tensile force change in each layer of reinforcement so that by reducing the height of the rows, the magnitude of Tmax increases and the location of Tmax becomes close to the blocks. In the field of reduced-scale models, the effect of earthquake motion parameters on the seismic behavior of GRSW models was investigated by Watanabe et al. (2003). Their model tests indicated that the values of the mobilized tensile forces along the reinforcement layers increase with an increasing magnitude of the input ground acceleration and with a decreasing height of the layers, such that this increase becomes more prominent in the bottom half of the walls. Wang et al. (2015) carried out a series of shaking table tests on reinforced soil models with a rigid facing. The results of model tests demonstrated that the maximum tensile force is mobilized at the reinforcement layer which is located in the middle of the wall height. In addition, for all layers, the maximum geogrid internal force is mobilized at the position of connection with the wall. Therefore, they concluded that the point of connection plays a key role in the seismic design of geogrid-reinforced rigid retaining walls. In the current study, the influence of the duration and the peak acceleration of the input excitation and the influence of the strip length on the seismic response of SSWs were investigated using a series of reduced-scale shaking table tests. Based on the simulation roles, five SSW models were constructed with different strip lengths and loaded to failure using variable-amplitude harmonic excitations with different durations and peak accelerations. The seismic response of the models to base shaking was measured in terms of the dynamic reinforcement load and the dynamic lateral earth pressure behind the surface and was then compared to the predictions made with conventional methods. 2. Physical model tests The SSW models were constructed and tested at the Centrifuge and Physical Modeling Center of Tehran University. This center is equipped with a uni-axial shaking table which is capable of shaking specimens of 5000 kg at accelerations up to 1.6g. As shown in Fig. 1(a), a rigid box container was used to construct the model walls. The box was 0.8 m in width, 1.82 m in length, and 1.23 m in height, and had been fabricated from transparent Plexiglas sheets to make the model deformations and the behavior visible. 2.1. Model configuration and construction Taking account of the dimensions of traditional segmental precast concrete panels (1.5 m 1.5 m) and the selected
Fig. 1. (a) Finished steel-strip reinforced-soil mode wall, (b) configuration of SSW model and arrangement of instrumentation.
scale factor for model test simulation (N = 10), and by considering the limitation in the height of the box container, 0.9 m was selected for the height of the models. With regard to the wall height (H = 0.9 m) and the limitation in the height of the box (1.2 m), a thickness of 0.15 m was selected for the foundation. As recommended by FHWA (2009) for mechanically stabilized earth walls and the erection of facing panels, a leveling pad with a width of 0.03 m and a thickness of 0.015 m was used. Moreover, to prevent the retaining wall from sliding, a minimum embedment depth of 0.6 (in full scale) was recommended for walls from the adjoining finished grade to the top of the leveling pad. Thus, in the reduced-scale models, a thickness of 0.1 m was considered for the embedment. Also, as recommended by Bhattacharya et al. (2011), a 40-mmthick conventional foam sheet was placed on the internal side of the end-models to reduce the reflection of waves from the rigid boundaries. The configuration of the experimental reinforced wall model for the present study is shown in Fig. 1(b). In order to construct reduced-scale SSW models in accordance with the real conditions of the prototype, the
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body of models was divided into three zones of soil mass with different relative densities. The retained backfill and foundation zones were constructed with the same relative density of 56% (cd = 16.11 kN/m3) and, as recommended by FHWA (2009) for SSWs, a relative density of 85% (cd = 17.01 kN/m3) was selected to construct the reinforced zone. To prepare the aforementioned zones, a uniformly graded silty sand (SP-SM) with a coefficient of curvature Cc = 1.18 and a coefficient of uniformity Cu = 2.28 was selected as the soil material and used at a moisture content of 6%. This silty sand was a silica synthetic soil composed of angular particles with a specific gravity of 2.66 that had maximum and minimum void ratios of 0.78 and 0.49, respectively. To define the shear strength characteristics of the silty sand with different relative densities, a series of monotonic undrained triaxial tests were carried out on specimens with Dr = 56% and Dr = 85% that the obtained resulting curves of the effective stress paths are presented in Fig. 2. Given the importance of selecting the reinforcement element in reduced-scale tests and the impossibility of simulating all the characteristics of the reinforcement, the most influential characteristics should be used for the simulation. Therefore, as recommended by Viswanadham and Mahajan (2007), by considering the tensile strength and the pull-out capacity as the similarity criteria for selecting the strip element for use in reduced-scaled SSW models and by taking the scaling relationships proposed by Iai (1989) for pullout resistance ((FP)prototype = N2(FP)model) and tensile strengh of reinforcment ((T)prototype = N(T)model), a longitudinal smooth strip made of Phosphor Bronze, with a width of 5 mm and a thickness of 0.4 mm, was selected to reinforce the SSW models. More details on the properties of Phosphor Bronze strips can be found in Yazdandoust (2017a). In addition, the results of flexural tests performed on the selected strip demonstrated that due to the insignificance of bending strain generated on the strip at curvatures less than 90°, the bending effect of strips on the measured tensile forces can be ignored during the tests.
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The physical models were prepared by following the real construction sequence of steel-stripe reinforced soilretaining walls. For this purpose, a row of cruciform concrete panels made of lightweight concrete, with dimensions of 0.15 m 0.15 m 0.015 m, was firstly placed on the leveling pad. Then, a soil layer was compacted behind the panels, using the control volume method, and the corresponding reinforcement row was installed, followed by the next soil layer, and the next reinforcement, and so on, until reaching the top. Black colored sand was poured at discrete horizontal and vertical intervals close to the window of the box to investigate the deformation mechanism at the end of each loading sequence. To investigate only the effects of the strip length, the models were reinforced with the uniform arrangement of strips and different values for L/H0 (0.5, 0.6, 0.7, 0.8, and 0.9). A summary of the model configurations and the arrangement of the strips are presented in Table 1 and Fig. 3(a), respectively. 2.2. Instrumentation A illustrated in Fig. 1(b), four different types of instruments were installed in each model to monitor the dynamic respons of the models. To measure the lateral movements of the surface and the lateral earth pressure behind the panels, four displacement transducers (LVDT sensors) and four pressure sensors were installed in the models, respectively. While undertaking the layer-by-layer construction, two accelerometers were placed at the predetermined positions. After the completion of the model, one accelerometer was also attached to the rigid box to measure the input acceleration. As shown in Fig. 3(b), to measure the axial force distribution on the strips, five strain gauges were bonded to the surface of four strips. The strain values were converted to axial forces using the results of tensile tests. Data from the instruments were collected by a high-speed data acquisition system with the ability to record 100 pieces of datum per second per channel. 2.3. Dynamic loading and testing sequence In order to investigate the effects of the peak acceleration and the loading duration on the seismic behavior of the SSW models, SSW models were subjected to the variableamplitude harmonic excitations with a constant frequency in two main stages such that each was applied after the termination of the previous motion. As illustrated in Table 1 Summary of model configurations and testing sequence.
Fig. 2. The resulting curves for effective stress paths from undrained triaxial tests on silty sand for a variety of relative densities.
Name
L/H0
SH & SVa (cm)
Testing sequence
SSW-01 SSW-02 SSW-03 SSW-04 SSW-05
0.9 0.8 0.7 0.6 0.5
7.5 & 7.5
Test-01 Test-01 Test-01 Test-01 Test-01
a
to to to to to
Test-10 Test-10 Test-09 Test-09 Test-08
Horizontal and vertical spacing of steel strips
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3.1. Distribution of strip tensile forces
Fig. 3. Arrangement of (a) strips and (b) strain gauges.
Fig. 4, in the first stage (Test-01 to Test-06), the models were shaken in six steps at a constant peak acceleration of 0.5 g and by increasing the duration at each step. In the second stage (Test-07 to Test-10), the models were shaken for a constant duration of 15 s and by increasing the acceleration amplitude at each step until the model reached the failure conditions. To avoid the resonance phenomenon during seismic loading, the harmonic excitation frequency should be selected in a range distant from the natural frequency (fn) of the reduced-scale models. For this purpose, with regards to the obtained value of the natural frequency of the models (about 18 Hz), bearing in mind the typical predominant frequencies of strong earthquake motions (1–3 Hz), and based on the scaling relationship proposed by Iai (1989) for the frequency ((f)prototype =1/N1-k/2(f)model where k is a governing parameter which is considered equal to 0.5 for sands), the frequency value of 6 Hz was selected for the harmonic excitation. The testing sequence for all models is summarized in Table 1. 3. Response of reinforced soil-retaining wall models to input ground motion Based on the obtained data through instrumentation during the seismic loadings, the seismic response of the wall models was determined in terms of the dynamic reinforcement load and the dynamic lateral earth pressure behind the surface.
To determine the distribution of tensile forces along the selected strips, the local strains in each strip were measured continuously at five points on each strip during the defined seismic excitations. The strip forces were calculated from the measured average strains using the force-strain relationship determined from tensile tests on the strip elements. In order to reduce the effects of the lateral boundaries on the results, the strips which had been located in the middle of the wall width were used (Fig. 3(b)). In order to evaluate the effects of the seismic loading parameters (PGA and duration), the strip length, and the strip location on the distribution of tensile forces along the strips, the values of the mobilized tensile forces along the selected strips were measured at the end of each loading sequence. Based on the obtained values, the distribution of the tensile forces along the selected strips, corresponding to different values of duration and peak acceleration of excitation, are presented in Fig. 5(a) and (b), respectively, for models with different strip lengths. It was observed that the distribution of tensile forces along the strips is nonlinear and the distribution trend is not constant among the different rows. In the top-row strips, the distribution of mobilized tensile forces along the strips depicts a triangular shape with a certain maximum point (Tmax) which is located near the end of the strips (approximately 0.75L behind the wall facing). By reducing the height of the rows, the location of Tmax approaches the wall facing, so that the maximum tensile force is mobilized in the lower half of the walls at the position of the connection with the facing (strip head, T0 = Tmax). By investigating the distribution of tensile forces along the strips in all the rows and by considering the location of the potential failure surface (Fig. 5(c), (d), and (e)), it can be concluded that the maximum tensile force in each instrumented strip corresponds to the trace of potential failure surface in the model. In the other words, the location of Tmax is approximately at the intersection of the failure plane and the strips. Moreover, by considering the anchoring mechanism of the strips located in the lower half of the SSW models (Fig. 5(c), (d), and (e)), it can be expected that increasing the horizontal
Fig. 4. Loading sequence applied to model SSW-01. Please cite this article in press as: Yazdandoust, M., Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls, Soils Found. (2018), https://doi.org/10.1016/j.sandf.2018.02.016
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Fig. 5. Distribution of tensile forces along the selected strips under seismic excitation with different values for (a) duration and (b) peak acceleration, and the failure mechanism at the end of the tests for the model including strips with lengths of (c) 0.9H0 , (d) 0.7H0 , and (e) 0.5H0 .
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displacements in the walls with shorter strips will lead to an increase in the mobilized tensile forces in the strips located in the bottom half of SSW systems. On the other hand, with regard to the role of the upper strips in maintaining the internal stability of SSWs (Fig. 5(c), (d), and (e)), it can be expected that increasing the dimension of the upper portion of the failure wedge in the walls with longer strips will lead to an increase in the mobilized tensile forces in the strips located in the upper half of SSW systems. These trends are clearly seen in the graphs of Fig. 5(a) and (b). Therefore, it can be concluded that, in the upper half of the walls, the Tmax values decrease with a decrease in the strip length, while this trend is reversed in the bottom half of the walls. This can also be seen in Figs. 6 and 7. Furthermore, it was found that the values for the mobilized tensile forces along the strips increase with a decreasing height of the rows, so that this increase becomes more prominent in the bottom half of the walls. This observation is consistent with that of Watanabe et al. (2003), who reported that the distribution of axial forces along the reinforcement layers is not uniform and that the maximum tensile force is mobilized in the reinforcement layers located in the bottom portion of the GRSWs. With regard to the position of the strips located in the bottom half of the walls relative to the fail surface (Fig. 5(c), (d), and (e)) and also the significant increase in the values of the mobilized tensile forces in the strips located in the bottom half of the walls (Fig. 5(a) and (b)), it can be concluded that at the moment of formation of internal failure, the strips located in the bottom half of the walls act predominantly as an anchoring mechanism and their pullout capacity plays a significant role in the internal stability of SSW systems. Therefore, the strips located in the lower rows should be given more attention under earthquake conditions. The importance of lower reinforcements under seismic conditions has also been emphasized for other reinforced earth systems (Tufenkjian and Vucetic, 2000; Yazdandoust, 2018). On the other hand, by comparing the curves of force distribution presented in Fig. 5(a) and (b), it can be concluded that among the seismic loading parameters, the influence of the peak acceleration is significantly greater than the influence of the loading duration on the mobilized tensile forces along the strips. It can also be seen that, the values for the mobilized tensile forces along the strips increase with increasing loading duration and peak acceleration, so that this increase becomes more prominent in the bottom half of the walls and in the walls with shorter strips. To investigate the effects of the input motion parameters (PGA and duration) on the maximum mobilized tensile forces of the strips, the magnitude of the measured maximum forces at the end of each loading sequence were normalized to the soil unit weight (cs), the strip vertical and horizontal intervals (SV and SH), and the wall height (H), and the Tmax/HcsSVSH values at different levels of PGA and loading duration were plotted versus the L/H0 ratio for the selected rows of strips (Fig. 7). The results presented in Fig. 7 show that there is a proper convergence
Fig. 6. (a) Time history of input motion in Test-06, and time histories of tensile force on strips located in (b) bottom half of the models (S1) and (c) upper half of the models (S3).
between the Tmax/HcsSVSH and L/H0 ratios at different levels of acceleration and duration, so that Tmax/HcsSVSH can be defined as a function of the L/H0 ratio and the seismic parameters for different rows of strip. Thus, the maximum tensile forces of the strips under seismic conditions can be estimated using the normalized plots shown in Fig. 7 and by considering areas of influence around individual strips (SV SH), the soil unit weight, and the wall height. This method has also been proposed by Yazdandoust (2017b) for soil-nailed walls to estimate the maximum mobilized axial forces along the nails under seismic conditions. 3.2. Distribution of lateral earth pressure The determination of the actual variation in lateral earth pressure is one of the most important factors in the optimized design of reinforced soil structures. In reinforced soil structures, an accurate estimate of the location of the
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0.06
Duration = 5s Duration = 9s Duration = 13s
0.04
Duration = 7s Duration = 11s Duration = 15s
Peak Acc. = 0.6g Peak Acc. = 0.8g
0.10
Normalized Maximum Strip Force (Tmax/H. s.SV.SH)
Normalized Maximum Strip Force (Tmax/H. s.SV.SH)
Peak Acc. = 0.5g Peak Acc. = 0.7g
0.15
0.02 0.00 0.06
0.04
0.02
0.00 0.18 0.12 0.06 0.00 0.18
0.05 0.00 0.15 0.10 0.05 0.00 0.30
0.20
0.10
0.00 0.30
0.12
0.20
0.06
0.10
0.00
0.00
0.4
(a)
7
0.5
0.6
0.7
0.8
0.9
Strip length to wall height ratio (L/H')
1
0.4
(b)
0.5
0.6
0.7
0.8
0.9
1
Strip length to wall height ratio (L/H')
Fig. 7. Variation in normalized maximum strip force with L/H0 ratio under seismic excitations with different values of (a) duration and (b) peak acceleration.
resultant force and the variation in earth pressure distribution along the wall play an important role in evaluating the internal stability. Based on the limit equilibrium approach and the limit state analysis, and by assuming the rigidity of the soil mass, various methods have been developed to determine the static and seismic earth pressure on rigid retaining walls, which are also used to reinforce soil structures. Since the reinforced soil mass is a flexible structure, the above-mentioned methods are not capable of determining the actual variation in lateral earth pressure on these structures. Therefore, in the following sections, the distribution of lateral earth pressure on a steel-strip reinforced soil-retaining wall, the resultant force, and its point of application are investigated under static and seismic conditions and the results are also compared to those of conventional methods. 3.2.1. Distribution of lateral earth pressure under static conditions The first analytical solution for the problem of lateral static earth pressure on retaining structures is attributed to Coulomb. Based on Coulomb’s theory, the total active earth force can be expressed as
1 P A ¼ K A cH 2 2
ð1Þ
where KA = active earth pressure coefficient given by KA ¼
cos2 ðu hÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 sinðdþuÞ: sinðuaÞ g cos2 h:cosb: cosðd þ hÞf1 þ cosðdþhÞ: cosðhaÞ
ð2Þ
Considering the interaction parameter between the soil mass and the wall (d) causes the results obtained with Coulomb’s theory to be more realistic than those obtained with other methods. This has caused that a particular attention is paid to Coulomb’s earth pressure theory in the current limit equilibrium-based static analysis, as far as this method is routinely used to estimate the earth forces to be carried by the reinforcement. To evaluate the qualitative and quantitative variations in lateral earth pressure on the SSWs under static conditions, the values for lateral earth pressure were measured after the completion of the construction process of the models and before seismic loading, using pressure sensors which had been installed behind the panels. Fig. 8(a) and (b) present the variations in normalized horizontal displacement profiles of the wall facing and the normalized
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distribution of lateral earth pressure behind the facing under static conditions, respectively. The results show that a non-linear distribution of active earth pressure forms behind the surface of the SSW systems. It seems that this shape of pressure distribution which was also observed by Paik and Salgado (2003), occurs due to arching effects in the retained soil, which result from the frictional resistance between the wall and the soil. The distribution of active earth pressure changes from non-linear to trapezoidal as the strip length decreases from 0.7H0 . This observation is consistent with the earth pressure diagrams presented by Sabatini et al. (1999) for tied-back retaining walls. By investigating the results in Fig. 8(a) and (b), it can be concluded that the values for the active earth pressure and the deformability of SSW systems, as two interdependent parameters, are affected by the strip length, so that reducing the L/H0 ratio from 0.9 to 0.5 results in an increase in deformability of the SSW by 42% and a decrease in the lateral active pressure by 15%. Thus, it can be concluded that the decline in lateral pressure in SSW systems with shorter strips is due to the changing wall state, from at-rest to active. In order to determine the actual value of the friction angle between the reinforced zone materials and the wall facing (d) to use in the Coulomb method, a series of direct shear tests was carried out. For this purpose, the specimens were prepared in the direct shear box by compacting a layer of reinforced zone materials with a relative density of 85% on the facing sample. The range in normal stress used in the direct shear tests was selected based on the minimum and maximum horizontal earth pressure levels which had been measured in the model tests. Based on the obtained results, a range in friction angle (d) between 22° and 30° was calculated, so that with regard to the values of the internal friction angles of the reinforced zone materials (obtained from triaxial tests), the value of d can be defined as a function of ures.(d = 0.62ures.). In Fig. 9, the values for the lateral earth pressure coefficient and the positions of the resultant lateral force, as obtained from experimental models with different strip lengths, are compared to the predictions by Coulomb’s
theory under the active state. The comparison shows that the predicted coefficients of lateral earth pressure, ka, are too conservative, so that the overestimation approaches 240%. It can also be seen that, the elevation of the line of action of the resultant lateral force R varies from about 0.24H to 0.28H above the toe, while this elevation is predicted by Coulomb’s theory to be about 0.33H. Moreover, the measured data in Fig. 9(b) show that the coefficient of active lateral pressure and the position of the resultant lateral force are significantly affected by the strip length. It is evident that the ka and R values increase regularly with an increasing strip length, such that the values for ka and R can be defined as a function of the L/H0 ratio. 3.2.2. Distribution of lateral earth pressure under seismic conditions The dynamic active earth pressure on retaining structures due to seismic loading is commonly obtained by using the modified Coulomb’s approach which is known as the Mononobe-Okabe method and can be expressed as 1 P AE ¼ K AE cH 2 ð1 k v Þ 2
ð3Þ
The total (static + dynamic) earth pressure coefficient, KAE, is calculated using the following equation: K AE ¼
cos2 ðu h bÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 sinðdþuÞ: sinðuabÞ g cos2 h:cosb: cosðd þ h þ bÞf1 þ cosðdþhþbÞ: cosðhaÞ ð4Þ
where u = soil friction angle, a = backfill surface slope angle from the horizontal, d = wall–soil interface friction angle, and b = seismic inertial angle given by b = tan1(kh/ (1 kv)). For practical purposes, Seed and Whitman (1970) proposed the separation of the total (static and dynamic) active lateral force, PAE, into two components, namely, the initial static component, PA, and the dynamic increment due to the base motion, DPAE, where PAE = PA + DPAE, KAE = KA + DKAE, and DKAE = 0.75kh. They also recommended that the resultant dynamic thrust be applied
(b)
(a)
Measured data Predicted data using Coulomb theory
L/H' = 0.9 L/H' = 0.7 L/H' = 0.5
0.08
0.06
0.04
x/H' (%)
0.02
0
0
0.05
0.1
0.15
Normalized lateral earth pressure, (
0.2 H
0.25
/ H)
Fig. 8. Variation in (a) normalized horizontal displacement and (b) normalized distribution of lateral earth pressure behind the facing under the active state. Please cite this article in press as: Yazdandoust, M., Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls, Soils Found. (2018), https://doi.org/10.1016/j.sandf.2018.02.016
0.50
PA H R
Measured data Predicted data using Coulomb theory
R/H
0.40
Normalized resultant force of active pressure PA /½ H² = KA
Normalized resultant elevation
M. Yazdandoust / Soils and Foundations xxx (2018) xxx–xxx
0.30
0.20 0.50
Distribution of active earth pressure in static conditions
PA
0.40
0.30
0.20
0.10
0.00 0.4
0.5
0.6
0.7
0.8
0.9
1
L/H' ratio Fig. 9. Variation in lateral earth pressure coefficient and position of the resultant lateral force versus the L/H0 ratio in the active state.
at 0.6H above the base of the wall. Therefore, the point of application of the resultant total force under seismic conditions is calculated using the following equation: P A H3 þ DP AE ð0:6H Þ ð5Þ h¼ P AE To investigate the effects of the seismic loading parameters (PGA and duration) and the strip length on the lateral earth pressure, the values of the lateral earth pressure were measured at the end of each loading sequence using pressure sensors installed at different heights. Based on the obtained values, the distribution of incremental dynamic earth pressure along the wall height (DrAE) corresponding to different values of duration and peak acceleration of excitation are presented in Figs. 10 and 11, respectively, for models with different strip lengths. The results show that the distribution of incremental dynamic earth pressure along the wall height depicts a curved shape with a certain maximum point. The elevation of this point is constant with changes in the duration of excitation and decreases with an increasing peak acceleration amplitude, so that the decreasing trend becomes more prominent with a decreasing strip length. By comparing Figs. 10 and 11, it
9
can be concluded that despite an increasing incremental dynamic earth pressure, due to an increase in the values of acceleration and duration of excitation, DrAE is significantly more affected by the changes in acceleration amplitude than the duration of excitation. A noteworthy observation is that increasing the length of strips leads to a significant reduction in DrAE around 53% and 45% for seismic loadings with amax 0.5 g and amax > 0.5 g, respectively. In this regard, a similar evidence has also been reported by Futaki et al. (1996) from shaking table tests on reinforced soil wall models. Furthermore, it can be clearly seen in Figs. 10 and 11 that under the same seismic conditions, SSWs with shorter strips experience more movement. It is completely obvious that this movement occurs due to larger inertia forces which are applied to the retained soil. Therefore, it can be concluded that the inertia forces applied to retained soil increase with a decreasing length of the strips, so that this increase leads to an increase in the seismic earth pressure in SSWs with shorter strips. In Fig. 12, a comparison is made of the results obtained from the SSW models and the results predicted by the current pseudo-static seismic analysis approach. The distribution of total earth pressure (rAE) is compared to the predictions of the Mononobe-Okabe and Seed and Whitman earth pressure methods for different values of peak acceleration in models with different lengths of strips. To select the initial assumptions for these methods, the recommendations presented by FHWA (2009) (u = upeak and kh = 0.5amax/g) and the value of the interface frictional angle obtained from direct shear tests (d = 0.62ures.) were used. With the exception of the results for the failure stage of models with long strips (L/H0 > 0.7), the predicted total earth pressure is too conservative, such that the overestimation increases from about 200% to 240% by reducing the L/H0 ratio from 0.9 to 0.5. In Figs. 13 and 14, the variations in normalized resultant force of the total earth pressure (PAE/½cH2), the normalized resultant force of the incremental dynamic earth pressure (DPAE/½cH2) and the position of the resultant lateral forces (R) versus the values of peak acceleration and duration of excitation are compared to the predictions of the Mononobe-Okabe and Seed and Whitman earth pressure methods for different values of the L/H0 ratio. The results show that the values for the total and incremental dynamic earth pressure coefficients, KAE and DKAE, increase regularly and nonlinearly with an increasing peak acceleration in all models. Hence, the values for KAE and DKAE can be defined as functions of the peak input base acceleration and strip length. Moreover, a comparison of the obtained and predicated data shows that the predicated data are too conservative, especially for KAE, so that the overestimation decreases with an increasing peak acceleration and a decreasing strip length. It can also be seen that the measured points of action for the resultant earth force (R) are much lower than the predicated points for the
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(a)
(b)
(c)
Test-01 (Duration = 5s) Test-02 (Duration = 7s) Test-03 (Duration = 9s) Test-04 (Duration = 11s) Test-05 (Duration = 13s) Test-06 (Duration = 15s)
0
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Normalized dynamic increment earth pressure, (Δ
0
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/ H)
AE
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Normalized dynamic increment earth pressure, (Δ
/ H)
AE
/ H)
AE
x H'
Test-01 (Duration = 5s) Test-02 (Duration = 7s) Test-03 (Duration = 9s) Test-04 (Duration = 11s) Test-05 (Duration = 13s) Test-06 (Duration = 15s)
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0
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x/H' (%)
0.12
0.16
0
0.04
0.08
(f)
x/H' (%)
0.12
0.16
x/H' (%)
Fig. 10. Distribution of incremental dynamic earth pressure on SSW models with strip lengths of (a) 0.9H0 , (b) 0.7H0 , and (c) 0.5H0 , and profiles of normalized horizontal displacement of models with strip lengths of (d) 0.9H0 , (e) 0.7H0 , and (f) 0.5H0 under seismic loading with different values of duration.
(a)
(b)
(c) Test-06 (PGA=0.5g) Test-07 (PGA=0.6g) Test-08 (PGA=0.7g) Test-09 (PGA=0.8g) Test-10 (PGA=0.9g)
The stage of wall failure
The stage of wall failure
0
0.05
0.1
0.15
0
0.2
Normalized dynamic increment earth pressure, (Δ
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0.1
0.15
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Normalized dynamic increment earth pressure, (Δ
/ H)
AE
The stage of wall failure
0
0.05
0.1
0.15
0.2
Normalized dynamic increment earth pressure, (Δ
/ H)
AE
/ H)
AE
x H'
Test-06 (PGA=0.5g) Test-07 (PGA=0.6g) Test-08 (PGA=0.7g) Test-09 (PGA=0.8g) Test-10 (PGA=0.9g)
0
(d)
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4
x/H' (%)
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14
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0.4
(e)
0.8
4
x/H' (%)
9
14
0
(f)
0.4
0.8
4
9
14
x/H' (%)
Fig. 11. Distribution of incremental dynamic earth pressure on SSW models with strip lengths of (a) 0.9H0 , (b) 0.7H0 , and (c) 0.5H0 , and profiles of normalized horizontal displacement of models with strip lengths of (d) 0.9H0 , (e) 0.7H0 , and (f) 0.5H0 under seismic loading with different values of peak acceleration.
incremental dynamic earth pressure, while a good agreement between the measurements and the predictions for R was observed for the total pressure. From the results observed in Fig. 13(b), it can be noted that for the incremental dynamic earth pressure, R is significantly affected by the strip length and the peak ground acceleration value, as it decreases with increasing peak acceleration values and with decreasing strip length. It was observed that the position of the resultant earth force above the toe varies from
about 0.42H to 0.34H and from about 0.37H to 0.31H for models with L/H0 = 0.9 and 0.5, respectively. On the other hand, it is evident from Fig. 14 that the values for the total and incremental dynamic earth pressure coefficients, KAE and DKAE, are not influenced by the loading duration and the predicated data are too conservative, especially for DKAE, as the overestimation approaches about 355% and 480% for KAE and DKAE, respectively. Meanwhile, a good agreement between the measurements
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(a)
11
(c)
(b)
Measured data Predicted data using Mononabe–Okabe method (kh = 0.5 PGA) Predicted data using Seed & Whitman method (kh = 0.5 PGA)
Test-06 (PGA=0.5g) Test-07 (PGA=0.6g) Test-08 (PGA=0.7g) Test-09 (PGA=0.8g) Test-10 (PGA=0.9g)
failure 0
0.1
failure
failure
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Normalized total earth pressure, (
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/ H)
AE
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Normalized total earth pressure, (
/ H)
AE
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/ H)
AE
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Distribution of total (i.e. dynamic and static) earth pressure
PAE
H
R
0.60
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The stages of wall failure 0.00
(a)
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0.6
0.7
0.8
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Peak input base acceleration amplitude (g)
0.55
1
L/H' = 0.9 L/H' = 0.7 L/H' = 0.5
0.45
0.35
0.25
Normalized resultant force of incremental dynamic pressure, ΔPAE /½ H² = ΔKAE
0.25
0.65
R/H
Measured data Predicted data using Mononabe–Okabe method (kh = 0.5 PGA) Predicted data using Seed & Whitman method (kh = 0.5 PGA)
0.55
R/H
Normalized resultant elevation
0.65
Normalized resultant force of total pressure PAE /½ H² = KAE
Normalized resultant elevation
Fig. 12. Measured and predicted total earth pressure on SSW models with strip lengths of (a) 0.9H0 , (b) 0.7H0 , and (c) 0.5H0 under seismic loading with different values of peak acceleration.
0.90
Distribution of incremental dynamic earth pressure
ΔPAE
H
R
0.60
0.30
0.00
(b)
0.4
0.5
0.6
0.7
0.8
0.9
1
Peak input base acceleration amplitude (g)
Fig. 13. Variation in normalized resultant force of (a) total earth pressure and (b) incremental dynamic earth pressure and the positions of the resultant lateral force with peak input base acceleration.
and the predictions was observed in term of the position of the resultant force of total pressure, while the measured and the predicated values for R in the case of the incremental dynamic pressure were very different. 4. Conclusions In the work at hand, the dynamic response of steel-strip reinforced soil-retaining walls was investigated using reduced-scale physical models. For this purpose, uni-axial shaking table tests on 0.9-m-high models with different strip lengths were performed to investigate the influence of the peak ground acceleration, the loading duration,
and the strip length on the seismic response of the SSWs in terms of the dynamic reinforcement load and the dynamic lateral earth pressure behind the surface. Some results from the physical models have been compared to those of conventional methods as described in FHWA (2009). The following points summarize the major findings of this research: (1) During seismic excitation with different peak accelerations and durations, the non-linear distribution of the tensile force along the strips was observed, such that the distribution trend was not constant among the different rows. In the top-row strips, the distribution of
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H
R/H
R 0.45
0.35
0.25 0.39
0.26
Distribution of total / incremental dynamic earth pressure
PAE or ΔPAE
0.13
0.00
(a)
3
5
7
9
11
13
15
17
Loading duration (s)
0.55
R/H
L/H' = 0.9 L/H' = 0.7 L/H' = 0.5
0.65
0.45
0.35
0.25
Normalized resultant force of incremental dynamic pressure, ΔPAE /½ H² = ΔKAE
0.55
PAE or Δ PAE
Normalized resultant elevation
0.65
Normalized resultant force of total pressure PAE /½ H² = KAE
Normalized resultant elevation
12
0.39
Measured data Predicted data using Mononabe–Okabe method (kh = 0.5 PGA) Predicted data using Seed & Whitman method (kh = 0.5 PGA)
0.26
0.13
0.00
(b)
3
5
7
9
11
13
15
17
Loading duration (s)
Fig. 14. Variation in normalized resultant force of (a) total earth pressure and (b) incremental dynamic earth pressure and the positions of the resultant lateral force with loading duration.
mobilized tensile forces along the strips depicted a triangular shape with a certain maximum point (Tmax), which was located near the end of the strips, while with a decrease in the height of the rows, the location of Tmax became close to the facing, so that in the bottom half of the walls, the maximum mobilized tension was generated at the strip head (T0 = Tmax). It was also discovered that the maximum tensile force in each instrumented strip is mobilized approximately at the intersection of the failure plane and the strip. (2) In the upper half of the walls, the Tmax values decreased with a decreasing strip length, while this trend was reversed in the bottom half of the walls. Furthermore, it was found that the values of the mobilized tensile forces along the strips increase with a decreasing height of the rows, such that this increase become more prominent in the bottom half of the walls. It was discovered that strips located in the bottom half of wall play a significant role in the internal stability of SSW systems, and thus, should be given more attention under earthquake conditions. (3) A proper convergence was observed between the Tmax/HcsSVSH and L/H0 ratio at different levels of acceleration and duration, so that Tmax/HcsSVSH can be defined as a function of the L/H0 ratio and seismic parameters for different rows of strip.
(4) It was discovered that the values of the predicated earth pressure by conventional methods under static and seismic conditions are too conservative and these methods predict the position of the resultant lateral force as being higher than the actual point. (5) It was concluded that the values for active earth pressure and the deformability of SSW systems under static conditions, as two interdependent parameters, are affected by the strip length, so that reducing the L/H0 ratio from 0.9 to 0.5 will result in an increase in the deformability of the SSW by 42% and a decrease in the lateral active pressure by 15%. (6) The distribution of incremental dynamic earth pressure (DrAE) along the wall height depicted a curved shape, with a certain maximum point. The elevation of this point was constant with changes in the duration of the excitation and decreased with an increasing peak acceleration amplitude, so that the decreasing trend became more prominent with a decreasing strip length. (7) Despite the increasing DrAE, due to an increase in the values of acceleration and the duration of excitation, DrAE is significantly more affected by changes in acceleration amplitude than by changes in the duration of excitation. On the other hand, an increase in the length of the strips led to a significant reduction
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in DrAE by about 53% and 45% for seismic loadings with amax 0.5 g and amax > 0.5 g, respectively. (8) It was found that the values for the total and the incremental dynamic earth pressure coefficients (KAE and DKAE) were not influenced by the loading duration, although these coefficients were strongly influenced by the peak input base acceleration. Acknowledgements The author would like to express his appreciation to Dr. A. Komak Panah and Dr. A. Ghalandarzadeh for their valuable assistance in the construction of the physical models and also gratefully acknowledges the encouragement and guidance of Mrs. Z. Jenab Isfahani throughout this research effort. References Anastasopoulos, I., Georgarakos, T., Georgiannou, V., Drosos, V., Kourkoulis, R., 2010. Seismic performance of bar-mat reinforced-soil retaining wall: shaking table testing versus numerical analysis with modified kinematic hardening constitutive model. Soil Dyn. Earthquake Eng. 30 (10), 1089–1105. Bathurst, R.J., Walters, D., Vlachopoulos, N., Burgess, P., Allen, T.M., 2000. Full scale testing of geosynthetic reinforced walls. Geotech. Geoenviron. Eng. 291 (14), 201–217. Bhattacharya, S., Lombardi, D., Dihoru, L., Dietz, M., Crewe, A.J., Taylor, C.A., 2011. Model container design for soil-structure interaction studies. Role Seismic Test. Facil. Perform.-Earthquake Eng. 22, 135–158. El-Emam, M.M., Bathurst, R.J., 2007. Influence of reinforcement parameters on the seismic response of reduced-scale reinforced soil retaining walls. Geotext. Geomembr. 25 (1), 33–49. FHWA, 2009. Design and Construction of Mechanically Stabilized Earth Walls and Reinforced Soil Slopes, vol. I. Federal Highway Administration and National Highway Institute, Washington DC. NHI-10-024. Futaki, M., Ogawa, N., Sato, M., Kumada, T., Natsume, S., 1996. Experiments about seismic performance of reinforced earth retaining wall. In: Proceedings of the 11th World Conference on Earthquake Engineering, Paper no. 1083. Huang, C.-C., Horng, J.-C., Chang, W.-J., Chiou, J.-S., Chen, C.-H., 2011. Dynamic behavior of reinforced walls - horizontal displacement response. Geotext. Geomembr. 29, 257–267. Iai, S., 1989. Similitude for shaking table tests on soil-structure-fluid models in 1g gravitational field. Soils Found. 29 (1), 105–118. Komak Panah, A., Yazdi, M., Ghalandarzadeh, A., 2015. Shaking table tests on soil retaining walls reinforced by polymeric strips. Geotext. Geomembr. 43 (2), 148–161. Koseki, J., Tatsuoka, F., Watanabe, K., Tateyama, M., Kojima, K., Munaf, Y., 2003. Model tests of seismic stability of several types of soil retaining walls. In: Ling, H., Leshchinsky, D., Tatsuoka, F. (Eds.),
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Reinforced Soil Engineering Advances in Research and Practice. Marcel Dekker, New York, pp. 378–385. Ling, H.I., Mohri, I., Leshchinsky, D., Burke, C., Matsushima, K., Liu, H., 2005. Large-scale shaking table tests on modular-block reinforced soil retaining walls. Geotech. Geoenviron. Eng. 131 (4), 465–476. Ling, H.I., Leshchinsky, D., Wang, J.P., Mohri, Y., Rosen, A., 2009. Seismic response of geocell retaining walls: experimental studies. Geotech. Geoenviron. Eng. 135 (4), 515–524. Murata, O., Tateyama, M.M., Tatsuoka, F., 1994. Shaking Table Tests on a Large Geosynthetic-reinforced Soil Retaining Wall Model. In: Tatsuoka, F., Leshchinsky, D. (Eds.), Proceedings of Recent Case History of Permanent Geosynthetic- Reinforced Soil Retaining Wall. Balkema, Rotterdam, pp. 259–264. Paik, K.H., Salgado, R., 2003. Estimation of active earth pressure against rigid retaining walls considering arching effects. Geomethod 53 (7), 643–653. Richardson, G.N., Feger, A., Lee, K.L., 1977. Seismic testing of reinforced earth walls. Geotech. Geoenviron. Eng. 103 (1), 1–17. Sabatini, P.J., Pass, D.G., Bachus, R.C., 1999. Ground anchors and anchored systems, Geotechnical Circular. No. 4, FHWA-IF-99-015, Federal Highway Administration, Department of Transportation, Washington DC. Seed, H.B., Whitman, R.V., 1970. Design of earth retaining structures for dynamic loads. Proc. Special Conf. Later. Stresses Ground and Design Earth Retain. Struct., 103–147 Siddharthan, R.V., Ganeshwara, V., Kutter, B.L., El-Desouky, M., Whitman, R.V., 2004. Seismic deformation of bar mat mechanically stabilized earth walls, I: centrifuge tests. Geotech. Geoenviron. Eng. 130 (1), 14–25. Suzuki, M., Shimura, N., Fukumura, T., Yoneda, O., Tasaka, Y., 2015. Seismic performance of reinforced soil wall with untreated and cementtreated soils as backfill using a 1-g shaking table. Soils Found. 55 (3), 626–636. Tufenkjian, M.R., Vucetic, M., 2000. Dynamic failure mechanism of soilnailed excavation models in centrifuge. J. Geotech. Geoenviron. Eng. 126 (3), 227–235. Uezawa, H., Yasuda, Y., Menjo, S., 1974. Experiment and analysis of the failure of model reinforced earth (Terre Arme´e) Railway Technical Research Report. 889. The Railway Technical Research Institute, Jpn. Nat. Railways 1–16 (in Japanese). Viswanadham, B.V.S., Mahajan, R.R., 2007. Centrifuge model tests on geotextile reinforced slopes. Geosynth. Int. 14 (6), 365–379. Watanabe, K., Munaf, Y., Koseki, J., Tateyama, M., Kojima, K., 2003. Behavior of several types of model retaining walls subjected to irregular exaction. Soils Found. 43 (5), 13–27. Wang, L., Chen, G., Chen, S., 2015. Experimental study on seismic response of geogrid reinforced rigid retaining walls with saturated backfill sand. Geotext. Geomembr. 43 (1), 35–45. Yazdandoust, M., 2017a. Investigation on the seismic performance of steel-strip reinforced-soil retaining walls using shaking table test. Soil Dyn. Earthquake Eng. 97, 216–232. Yazdandoust, M., 2017b. Experimental study on seismic response of soilnailed walls with permanent facing. Soil Dyn. Earthquake Eng. 98, 101–119. Yazdandoust, M., 2018. Seismic performance of soil-nailed walls using a 1g shaking table. Can. Geotech. J. 55 (1), 1–18.
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Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls Majid Yazdandoust Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran Received 14 February 2017; received in revised form 3 November 2017; accepted 1 December 2017
Abstract To investigate the influence of the peak acceleration, the loading duration, and the strip length on the dynamic behavior of steel-strip reinforced soil walls (SSWs), in terms of the dynamic reinforcement load distribution and the dynamic lateral earth pressure behind the surface, a series of 1-g shaking table tests was performed on five reduced-scale reinforced soil wall models. It was observed that the maximum axial force of the strips (Tmax) is mobilized at the intersection of the failure plane with strips in all rows. It was also discovered that, in the upper half of the walls, the Tmax values decrease with a decreasing strip length, while this trend is reversed in the lower half of the walls. Additionally, a proper convergence was found between the Tmax/HcsSVSH and L/H0 ratio at different levels of acceleration and duration, so that Tmax/HcsSVSH can be defined as a function of the L/H0 ratio and the seismic parameters for different rows of strips. On the other hand, it was observed that the values of earth pressure predicted by conventional methods under static and seismic conditions are too conservative and these methods predict the position of the resultant lateral force higher than the actual point. Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.
Keywords: Steel-strip reinforced soil wall; Seismic earth pressure; Dynamic reinforcement load; 1-g shaking table test
1. Introduction In order to better understand the seismic performance of reinforced soil walls, the dynamic behavior of these structures has been investigated experimentally, including studies on full-scale models (Richardson et al., 1977; Futaki et al., 1996), large-scale models (Murata et al., 1994; Bathurst et al., 2000; Ling et al., 2005; Wang et al., 2015), and reduced-scale models (Koseki et al., 2003; ElEmam and Bathurst, 2007; Ling et al., 2009; Huang et al., 2011; Komak Panah et al., 2015). Although many studies on the seismic behavior of geosynthetic-reinforced soil walls (GRSWs) have been undertaken, little attention has been paid to retaining walls with metallic reinforcements, such that the seismic performance of these walls Peer review under responsibility of The Japanese Geotechnical Society. E-mail address: [email protected]
has been examined in only a few studies (Uezawa et al., 1974; Richardson et al., 1977; Futaki et al., 1996; Siddharthan et al., 2004; Anastasopoulos et al., 2010; Suzuki et al., 2015). The first seismic full-scale model test was performed by Richardson et al. (1977) on a 6-m-high steel-strip reinforced soil wall (SSW) with a discrete concrete block facing. The results indicated that the measured dynamic forces of the strips are considerably less than the forces calculated by the methods recommended for the seismic design, and the induced dynamic forces of the strips could be greatly reduced by decreasing the length of the strips. Futaki et al. (1996) studied the seismic performance of large-scale model walls with ribbed strips and segmental precast concrete panels by shaking table tests. They pointed out that the distribution of lateral earth pressure behind the facing is almost triangular and the coefficient of seismic earth pressure increases with an increasing
https://doi.org/10.1016/j.sandf.2018.02.016 0038-0806/Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.
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amplitude of base excitation. The results also showed that the measured seismic tensile forces of the strips are almost equal to the design values and the distribution trend of axial force along the strips is not constant among the different rows. Based on the large-scale shaking table tests on modular-block reinforced-soil retaining walls, Ling et al. (2005) showed that the magnitude and the location of the maximum tensile force change in each layer of reinforcement so that by reducing the height of the rows, the magnitude of Tmax increases and the location of Tmax becomes close to the blocks. In the field of reduced-scale models, the effect of earthquake motion parameters on the seismic behavior of GRSW models was investigated by Watanabe et al. (2003). Their model tests indicated that the values of the mobilized tensile forces along the reinforcement layers increase with an increasing magnitude of the input ground acceleration and with a decreasing height of the layers, such that this increase becomes more prominent in the bottom half of the walls. Wang et al. (2015) carried out a series of shaking table tests on reinforced soil models with a rigid facing. The results of model tests demonstrated that the maximum tensile force is mobilized at the reinforcement layer which is located in the middle of the wall height. In addition, for all layers, the maximum geogrid internal force is mobilized at the position of connection with the wall. Therefore, they concluded that the point of connection plays a key role in the seismic design of geogrid-reinforced rigid retaining walls. In the current study, the influence of the duration and the peak acceleration of the input excitation and the influence of the strip length on the seismic response of SSWs were investigated using a series of reduced-scale shaking table tests. Based on the simulation roles, five SSW models were constructed with different strip lengths and loaded to failure using variable-amplitude harmonic excitations with different durations and peak accelerations. The seismic response of the models to base shaking was measured in terms of the dynamic reinforcement load and the dynamic lateral earth pressure behind the surface and was then compared to the predictions made with conventional methods. 2. Physical model tests The SSW models were constructed and tested at the Centrifuge and Physical Modeling Center of Tehran University. This center is equipped with a uni-axial shaking table which is capable of shaking specimens of 5000 kg at accelerations up to 1.6g. As shown in Fig. 1(a), a rigid box container was used to construct the model walls. The box was 0.8 m in width, 1.82 m in length, and 1.23 m in height, and had been fabricated from transparent Plexiglas sheets to make the model deformations and the behavior visible. 2.1. Model configuration and construction Taking account of the dimensions of traditional segmental precast concrete panels (1.5 m 1.5 m) and the selected
Fig. 1. (a) Finished steel-strip reinforced-soil mode wall, (b) configuration of SSW model and arrangement of instrumentation.
scale factor for model test simulation (N = 10), and by considering the limitation in the height of the box container, 0.9 m was selected for the height of the models. With regard to the wall height (H = 0.9 m) and the limitation in the height of the box (1.2 m), a thickness of 0.15 m was selected for the foundation. As recommended by FHWA (2009) for mechanically stabilized earth walls and the erection of facing panels, a leveling pad with a width of 0.03 m and a thickness of 0.015 m was used. Moreover, to prevent the retaining wall from sliding, a minimum embedment depth of 0.6 (in full scale) was recommended for walls from the adjoining finished grade to the top of the leveling pad. Thus, in the reduced-scale models, a thickness of 0.1 m was considered for the embedment. Also, as recommended by Bhattacharya et al. (2011), a 40-mmthick conventional foam sheet was placed on the internal side of the end-models to reduce the reflection of waves from the rigid boundaries. The configuration of the experimental reinforced wall model for the present study is shown in Fig. 1(b). In order to construct reduced-scale SSW models in accordance with the real conditions of the prototype, the
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body of models was divided into three zones of soil mass with different relative densities. The retained backfill and foundation zones were constructed with the same relative density of 56% (cd = 16.11 kN/m3) and, as recommended by FHWA (2009) for SSWs, a relative density of 85% (cd = 17.01 kN/m3) was selected to construct the reinforced zone. To prepare the aforementioned zones, a uniformly graded silty sand (SP-SM) with a coefficient of curvature Cc = 1.18 and a coefficient of uniformity Cu = 2.28 was selected as the soil material and used at a moisture content of 6%. This silty sand was a silica synthetic soil composed of angular particles with a specific gravity of 2.66 that had maximum and minimum void ratios of 0.78 and 0.49, respectively. To define the shear strength characteristics of the silty sand with different relative densities, a series of monotonic undrained triaxial tests were carried out on specimens with Dr = 56% and Dr = 85% that the obtained resulting curves of the effective stress paths are presented in Fig. 2. Given the importance of selecting the reinforcement element in reduced-scale tests and the impossibility of simulating all the characteristics of the reinforcement, the most influential characteristics should be used for the simulation. Therefore, as recommended by Viswanadham and Mahajan (2007), by considering the tensile strength and the pull-out capacity as the similarity criteria for selecting the strip element for use in reduced-scaled SSW models and by taking the scaling relationships proposed by Iai (1989) for pullout resistance ((FP)prototype = N2(FP)model) and tensile strengh of reinforcment ((T)prototype = N(T)model), a longitudinal smooth strip made of Phosphor Bronze, with a width of 5 mm and a thickness of 0.4 mm, was selected to reinforce the SSW models. More details on the properties of Phosphor Bronze strips can be found in Yazdandoust (2017a). In addition, the results of flexural tests performed on the selected strip demonstrated that due to the insignificance of bending strain generated on the strip at curvatures less than 90°, the bending effect of strips on the measured tensile forces can be ignored during the tests.
3
The physical models were prepared by following the real construction sequence of steel-stripe reinforced soilretaining walls. For this purpose, a row of cruciform concrete panels made of lightweight concrete, with dimensions of 0.15 m 0.15 m 0.015 m, was firstly placed on the leveling pad. Then, a soil layer was compacted behind the panels, using the control volume method, and the corresponding reinforcement row was installed, followed by the next soil layer, and the next reinforcement, and so on, until reaching the top. Black colored sand was poured at discrete horizontal and vertical intervals close to the window of the box to investigate the deformation mechanism at the end of each loading sequence. To investigate only the effects of the strip length, the models were reinforced with the uniform arrangement of strips and different values for L/H0 (0.5, 0.6, 0.7, 0.8, and 0.9). A summary of the model configurations and the arrangement of the strips are presented in Table 1 and Fig. 3(a), respectively. 2.2. Instrumentation A illustrated in Fig. 1(b), four different types of instruments were installed in each model to monitor the dynamic respons of the models. To measure the lateral movements of the surface and the lateral earth pressure behind the panels, four displacement transducers (LVDT sensors) and four pressure sensors were installed in the models, respectively. While undertaking the layer-by-layer construction, two accelerometers were placed at the predetermined positions. After the completion of the model, one accelerometer was also attached to the rigid box to measure the input acceleration. As shown in Fig. 3(b), to measure the axial force distribution on the strips, five strain gauges were bonded to the surface of four strips. The strain values were converted to axial forces using the results of tensile tests. Data from the instruments were collected by a high-speed data acquisition system with the ability to record 100 pieces of datum per second per channel. 2.3. Dynamic loading and testing sequence In order to investigate the effects of the peak acceleration and the loading duration on the seismic behavior of the SSW models, SSW models were subjected to the variableamplitude harmonic excitations with a constant frequency in two main stages such that each was applied after the termination of the previous motion. As illustrated in Table 1 Summary of model configurations and testing sequence.
Fig. 2. The resulting curves for effective stress paths from undrained triaxial tests on silty sand for a variety of relative densities.
Name
L/H0
SH & SVa (cm)
Testing sequence
SSW-01 SSW-02 SSW-03 SSW-04 SSW-05
0.9 0.8 0.7 0.6 0.5
7.5 & 7.5
Test-01 Test-01 Test-01 Test-01 Test-01
a
to to to to to
Test-10 Test-10 Test-09 Test-09 Test-08
Horizontal and vertical spacing of steel strips
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3.1. Distribution of strip tensile forces
Fig. 3. Arrangement of (a) strips and (b) strain gauges.
Fig. 4, in the first stage (Test-01 to Test-06), the models were shaken in six steps at a constant peak acceleration of 0.5 g and by increasing the duration at each step. In the second stage (Test-07 to Test-10), the models were shaken for a constant duration of 15 s and by increasing the acceleration amplitude at each step until the model reached the failure conditions. To avoid the resonance phenomenon during seismic loading, the harmonic excitation frequency should be selected in a range distant from the natural frequency (fn) of the reduced-scale models. For this purpose, with regards to the obtained value of the natural frequency of the models (about 18 Hz), bearing in mind the typical predominant frequencies of strong earthquake motions (1–3 Hz), and based on the scaling relationship proposed by Iai (1989) for the frequency ((f)prototype =1/N1-k/2(f)model where k is a governing parameter which is considered equal to 0.5 for sands), the frequency value of 6 Hz was selected for the harmonic excitation. The testing sequence for all models is summarized in Table 1. 3. Response of reinforced soil-retaining wall models to input ground motion Based on the obtained data through instrumentation during the seismic loadings, the seismic response of the wall models was determined in terms of the dynamic reinforcement load and the dynamic lateral earth pressure behind the surface.
To determine the distribution of tensile forces along the selected strips, the local strains in each strip were measured continuously at five points on each strip during the defined seismic excitations. The strip forces were calculated from the measured average strains using the force-strain relationship determined from tensile tests on the strip elements. In order to reduce the effects of the lateral boundaries on the results, the strips which had been located in the middle of the wall width were used (Fig. 3(b)). In order to evaluate the effects of the seismic loading parameters (PGA and duration), the strip length, and the strip location on the distribution of tensile forces along the strips, the values of the mobilized tensile forces along the selected strips were measured at the end of each loading sequence. Based on the obtained values, the distribution of the tensile forces along the selected strips, corresponding to different values of duration and peak acceleration of excitation, are presented in Fig. 5(a) and (b), respectively, for models with different strip lengths. It was observed that the distribution of tensile forces along the strips is nonlinear and the distribution trend is not constant among the different rows. In the top-row strips, the distribution of mobilized tensile forces along the strips depicts a triangular shape with a certain maximum point (Tmax) which is located near the end of the strips (approximately 0.75L behind the wall facing). By reducing the height of the rows, the location of Tmax approaches the wall facing, so that the maximum tensile force is mobilized in the lower half of the walls at the position of the connection with the facing (strip head, T0 = Tmax). By investigating the distribution of tensile forces along the strips in all the rows and by considering the location of the potential failure surface (Fig. 5(c), (d), and (e)), it can be concluded that the maximum tensile force in each instrumented strip corresponds to the trace of potential failure surface in the model. In the other words, the location of Tmax is approximately at the intersection of the failure plane and the strips. Moreover, by considering the anchoring mechanism of the strips located in the lower half of the SSW models (Fig. 5(c), (d), and (e)), it can be expected that increasing the horizontal
Fig. 4. Loading sequence applied to model SSW-01. Please cite this article in press as: Yazdandoust, M., Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls, Soils Found. (2018), https://doi.org/10.1016/j.sandf.2018.02.016
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Fig. 5. Distribution of tensile forces along the selected strips under seismic excitation with different values for (a) duration and (b) peak acceleration, and the failure mechanism at the end of the tests for the model including strips with lengths of (c) 0.9H0 , (d) 0.7H0 , and (e) 0.5H0 .
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displacements in the walls with shorter strips will lead to an increase in the mobilized tensile forces in the strips located in the bottom half of SSW systems. On the other hand, with regard to the role of the upper strips in maintaining the internal stability of SSWs (Fig. 5(c), (d), and (e)), it can be expected that increasing the dimension of the upper portion of the failure wedge in the walls with longer strips will lead to an increase in the mobilized tensile forces in the strips located in the upper half of SSW systems. These trends are clearly seen in the graphs of Fig. 5(a) and (b). Therefore, it can be concluded that, in the upper half of the walls, the Tmax values decrease with a decrease in the strip length, while this trend is reversed in the bottom half of the walls. This can also be seen in Figs. 6 and 7. Furthermore, it was found that the values for the mobilized tensile forces along the strips increase with a decreasing height of the rows, so that this increase becomes more prominent in the bottom half of the walls. This observation is consistent with that of Watanabe et al. (2003), who reported that the distribution of axial forces along the reinforcement layers is not uniform and that the maximum tensile force is mobilized in the reinforcement layers located in the bottom portion of the GRSWs. With regard to the position of the strips located in the bottom half of the walls relative to the fail surface (Fig. 5(c), (d), and (e)) and also the significant increase in the values of the mobilized tensile forces in the strips located in the bottom half of the walls (Fig. 5(a) and (b)), it can be concluded that at the moment of formation of internal failure, the strips located in the bottom half of the walls act predominantly as an anchoring mechanism and their pullout capacity plays a significant role in the internal stability of SSW systems. Therefore, the strips located in the lower rows should be given more attention under earthquake conditions. The importance of lower reinforcements under seismic conditions has also been emphasized for other reinforced earth systems (Tufenkjian and Vucetic, 2000; Yazdandoust, 2018). On the other hand, by comparing the curves of force distribution presented in Fig. 5(a) and (b), it can be concluded that among the seismic loading parameters, the influence of the peak acceleration is significantly greater than the influence of the loading duration on the mobilized tensile forces along the strips. It can also be seen that, the values for the mobilized tensile forces along the strips increase with increasing loading duration and peak acceleration, so that this increase becomes more prominent in the bottom half of the walls and in the walls with shorter strips. To investigate the effects of the input motion parameters (PGA and duration) on the maximum mobilized tensile forces of the strips, the magnitude of the measured maximum forces at the end of each loading sequence were normalized to the soil unit weight (cs), the strip vertical and horizontal intervals (SV and SH), and the wall height (H), and the Tmax/HcsSVSH values at different levels of PGA and loading duration were plotted versus the L/H0 ratio for the selected rows of strips (Fig. 7). The results presented in Fig. 7 show that there is a proper convergence
Fig. 6. (a) Time history of input motion in Test-06, and time histories of tensile force on strips located in (b) bottom half of the models (S1) and (c) upper half of the models (S3).
between the Tmax/HcsSVSH and L/H0 ratios at different levels of acceleration and duration, so that Tmax/HcsSVSH can be defined as a function of the L/H0 ratio and the seismic parameters for different rows of strip. Thus, the maximum tensile forces of the strips under seismic conditions can be estimated using the normalized plots shown in Fig. 7 and by considering areas of influence around individual strips (SV SH), the soil unit weight, and the wall height. This method has also been proposed by Yazdandoust (2017b) for soil-nailed walls to estimate the maximum mobilized axial forces along the nails under seismic conditions. 3.2. Distribution of lateral earth pressure The determination of the actual variation in lateral earth pressure is one of the most important factors in the optimized design of reinforced soil structures. In reinforced soil structures, an accurate estimate of the location of the
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0.06
Duration = 5s Duration = 9s Duration = 13s
0.04
Duration = 7s Duration = 11s Duration = 15s
Peak Acc. = 0.6g Peak Acc. = 0.8g
0.10
Normalized Maximum Strip Force (Tmax/H. s.SV.SH)
Normalized Maximum Strip Force (Tmax/H. s.SV.SH)
Peak Acc. = 0.5g Peak Acc. = 0.7g
0.15
0.02 0.00 0.06
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0.00 0.18 0.12 0.06 0.00 0.18
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0.00 0.30
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0.00
0.00
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(a)
7
0.5
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0.9
Strip length to wall height ratio (L/H')
1
0.4
(b)
0.5
0.6
0.7
0.8
0.9
1
Strip length to wall height ratio (L/H')
Fig. 7. Variation in normalized maximum strip force with L/H0 ratio under seismic excitations with different values of (a) duration and (b) peak acceleration.
resultant force and the variation in earth pressure distribution along the wall play an important role in evaluating the internal stability. Based on the limit equilibrium approach and the limit state analysis, and by assuming the rigidity of the soil mass, various methods have been developed to determine the static and seismic earth pressure on rigid retaining walls, which are also used to reinforce soil structures. Since the reinforced soil mass is a flexible structure, the above-mentioned methods are not capable of determining the actual variation in lateral earth pressure on these structures. Therefore, in the following sections, the distribution of lateral earth pressure on a steel-strip reinforced soil-retaining wall, the resultant force, and its point of application are investigated under static and seismic conditions and the results are also compared to those of conventional methods. 3.2.1. Distribution of lateral earth pressure under static conditions The first analytical solution for the problem of lateral static earth pressure on retaining structures is attributed to Coulomb. Based on Coulomb’s theory, the total active earth force can be expressed as
1 P A ¼ K A cH 2 2
ð1Þ
where KA = active earth pressure coefficient given by KA ¼
cos2 ðu hÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 sinðdþuÞ: sinðuaÞ g cos2 h:cosb: cosðd þ hÞf1 þ cosðdþhÞ: cosðhaÞ
ð2Þ
Considering the interaction parameter between the soil mass and the wall (d) causes the results obtained with Coulomb’s theory to be more realistic than those obtained with other methods. This has caused that a particular attention is paid to Coulomb’s earth pressure theory in the current limit equilibrium-based static analysis, as far as this method is routinely used to estimate the earth forces to be carried by the reinforcement. To evaluate the qualitative and quantitative variations in lateral earth pressure on the SSWs under static conditions, the values for lateral earth pressure were measured after the completion of the construction process of the models and before seismic loading, using pressure sensors which had been installed behind the panels. Fig. 8(a) and (b) present the variations in normalized horizontal displacement profiles of the wall facing and the normalized
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M. Yazdandoust / Soils and Foundations xxx (2018) xxx–xxx
distribution of lateral earth pressure behind the facing under static conditions, respectively. The results show that a non-linear distribution of active earth pressure forms behind the surface of the SSW systems. It seems that this shape of pressure distribution which was also observed by Paik and Salgado (2003), occurs due to arching effects in the retained soil, which result from the frictional resistance between the wall and the soil. The distribution of active earth pressure changes from non-linear to trapezoidal as the strip length decreases from 0.7H0 . This observation is consistent with the earth pressure diagrams presented by Sabatini et al. (1999) for tied-back retaining walls. By investigating the results in Fig. 8(a) and (b), it can be concluded that the values for the active earth pressure and the deformability of SSW systems, as two interdependent parameters, are affected by the strip length, so that reducing the L/H0 ratio from 0.9 to 0.5 results in an increase in deformability of the SSW by 42% and a decrease in the lateral active pressure by 15%. Thus, it can be concluded that the decline in lateral pressure in SSW systems with shorter strips is due to the changing wall state, from at-rest to active. In order to determine the actual value of the friction angle between the reinforced zone materials and the wall facing (d) to use in the Coulomb method, a series of direct shear tests was carried out. For this purpose, the specimens were prepared in the direct shear box by compacting a layer of reinforced zone materials with a relative density of 85% on the facing sample. The range in normal stress used in the direct shear tests was selected based on the minimum and maximum horizontal earth pressure levels which had been measured in the model tests. Based on the obtained results, a range in friction angle (d) between 22° and 30° was calculated, so that with regard to the values of the internal friction angles of the reinforced zone materials (obtained from triaxial tests), the value of d can be defined as a function of ures.(d = 0.62ures.). In Fig. 9, the values for the lateral earth pressure coefficient and the positions of the resultant lateral force, as obtained from experimental models with different strip lengths, are compared to the predictions by Coulomb’s
theory under the active state. The comparison shows that the predicted coefficients of lateral earth pressure, ka, are too conservative, so that the overestimation approaches 240%. It can also be seen that, the elevation of the line of action of the resultant lateral force R varies from about 0.24H to 0.28H above the toe, while this elevation is predicted by Coulomb’s theory to be about 0.33H. Moreover, the measured data in Fig. 9(b) show that the coefficient of active lateral pressure and the position of the resultant lateral force are significantly affected by the strip length. It is evident that the ka and R values increase regularly with an increasing strip length, such that the values for ka and R can be defined as a function of the L/H0 ratio. 3.2.2. Distribution of lateral earth pressure under seismic conditions The dynamic active earth pressure on retaining structures due to seismic loading is commonly obtained by using the modified Coulomb’s approach which is known as the Mononobe-Okabe method and can be expressed as 1 P AE ¼ K AE cH 2 ð1 k v Þ 2
ð3Þ
The total (static + dynamic) earth pressure coefficient, KAE, is calculated using the following equation: K AE ¼
cos2 ðu h bÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 sinðdþuÞ: sinðuabÞ g cos2 h:cosb: cosðd þ h þ bÞf1 þ cosðdþhþbÞ: cosðhaÞ ð4Þ
where u = soil friction angle, a = backfill surface slope angle from the horizontal, d = wall–soil interface friction angle, and b = seismic inertial angle given by b = tan1(kh/ (1 kv)). For practical purposes, Seed and Whitman (1970) proposed the separation of the total (static and dynamic) active lateral force, PAE, into two components, namely, the initial static component, PA, and the dynamic increment due to the base motion, DPAE, where PAE = PA + DPAE, KAE = KA + DKAE, and DKAE = 0.75kh. They also recommended that the resultant dynamic thrust be applied
(b)
(a)
Measured data Predicted data using Coulomb theory
L/H' = 0.9 L/H' = 0.7 L/H' = 0.5
0.08
0.06
0.04
x/H' (%)
0.02
0
0
0.05
0.1
0.15
Normalized lateral earth pressure, (
0.2 H
0.25
/ H)
Fig. 8. Variation in (a) normalized horizontal displacement and (b) normalized distribution of lateral earth pressure behind the facing under the active state. Please cite this article in press as: Yazdandoust, M., Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls, Soils Found. (2018), https://doi.org/10.1016/j.sandf.2018.02.016
0.50
PA H R
Measured data Predicted data using Coulomb theory
R/H
0.40
Normalized resultant force of active pressure PA /½ H² = KA
Normalized resultant elevation
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0.30
0.20 0.50
Distribution of active earth pressure in static conditions
PA
0.40
0.30
0.20
0.10
0.00 0.4
0.5
0.6
0.7
0.8
0.9
1
L/H' ratio Fig. 9. Variation in lateral earth pressure coefficient and position of the resultant lateral force versus the L/H0 ratio in the active state.
at 0.6H above the base of the wall. Therefore, the point of application of the resultant total force under seismic conditions is calculated using the following equation: P A H3 þ DP AE ð0:6H Þ ð5Þ h¼ P AE To investigate the effects of the seismic loading parameters (PGA and duration) and the strip length on the lateral earth pressure, the values of the lateral earth pressure were measured at the end of each loading sequence using pressure sensors installed at different heights. Based on the obtained values, the distribution of incremental dynamic earth pressure along the wall height (DrAE) corresponding to different values of duration and peak acceleration of excitation are presented in Figs. 10 and 11, respectively, for models with different strip lengths. The results show that the distribution of incremental dynamic earth pressure along the wall height depicts a curved shape with a certain maximum point. The elevation of this point is constant with changes in the duration of excitation and decreases with an increasing peak acceleration amplitude, so that the decreasing trend becomes more prominent with a decreasing strip length. By comparing Figs. 10 and 11, it
9
can be concluded that despite an increasing incremental dynamic earth pressure, due to an increase in the values of acceleration and duration of excitation, DrAE is significantly more affected by the changes in acceleration amplitude than the duration of excitation. A noteworthy observation is that increasing the length of strips leads to a significant reduction in DrAE around 53% and 45% for seismic loadings with amax 0.5 g and amax > 0.5 g, respectively. In this regard, a similar evidence has also been reported by Futaki et al. (1996) from shaking table tests on reinforced soil wall models. Furthermore, it can be clearly seen in Figs. 10 and 11 that under the same seismic conditions, SSWs with shorter strips experience more movement. It is completely obvious that this movement occurs due to larger inertia forces which are applied to the retained soil. Therefore, it can be concluded that the inertia forces applied to retained soil increase with a decreasing length of the strips, so that this increase leads to an increase in the seismic earth pressure in SSWs with shorter strips. In Fig. 12, a comparison is made of the results obtained from the SSW models and the results predicted by the current pseudo-static seismic analysis approach. The distribution of total earth pressure (rAE) is compared to the predictions of the Mononobe-Okabe and Seed and Whitman earth pressure methods for different values of peak acceleration in models with different lengths of strips. To select the initial assumptions for these methods, the recommendations presented by FHWA (2009) (u = upeak and kh = 0.5amax/g) and the value of the interface frictional angle obtained from direct shear tests (d = 0.62ures.) were used. With the exception of the results for the failure stage of models with long strips (L/H0 > 0.7), the predicted total earth pressure is too conservative, such that the overestimation increases from about 200% to 240% by reducing the L/H0 ratio from 0.9 to 0.5. In Figs. 13 and 14, the variations in normalized resultant force of the total earth pressure (PAE/½cH2), the normalized resultant force of the incremental dynamic earth pressure (DPAE/½cH2) and the position of the resultant lateral forces (R) versus the values of peak acceleration and duration of excitation are compared to the predictions of the Mononobe-Okabe and Seed and Whitman earth pressure methods for different values of the L/H0 ratio. The results show that the values for the total and incremental dynamic earth pressure coefficients, KAE and DKAE, increase regularly and nonlinearly with an increasing peak acceleration in all models. Hence, the values for KAE and DKAE can be defined as functions of the peak input base acceleration and strip length. Moreover, a comparison of the obtained and predicated data shows that the predicated data are too conservative, especially for KAE, so that the overestimation decreases with an increasing peak acceleration and a decreasing strip length. It can also be seen that the measured points of action for the resultant earth force (R) are much lower than the predicated points for the
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(a)
(b)
(c)
Test-01 (Duration = 5s) Test-02 (Duration = 7s) Test-03 (Duration = 9s) Test-04 (Duration = 11s) Test-05 (Duration = 13s) Test-06 (Duration = 15s)
0
0.005
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Normalized dynamic increment earth pressure, (Δ
0
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Normalized dynamic increment earth pressure, (Δ
/ H)
AE
0
0.005
0.01
0.015
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Normalized dynamic increment earth pressure, (Δ
/ H)
AE
/ H)
AE
x H'
Test-01 (Duration = 5s) Test-02 (Duration = 7s) Test-03 (Duration = 9s) Test-04 (Duration = 11s) Test-05 (Duration = 13s) Test-06 (Duration = 15s)
0
0.04
0.08
(d)
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0
0.04
0.08
(e)
x/H' (%)
0.12
0.16
0
0.04
0.08
(f)
x/H' (%)
0.12
0.16
x/H' (%)
Fig. 10. Distribution of incremental dynamic earth pressure on SSW models with strip lengths of (a) 0.9H0 , (b) 0.7H0 , and (c) 0.5H0 , and profiles of normalized horizontal displacement of models with strip lengths of (d) 0.9H0 , (e) 0.7H0 , and (f) 0.5H0 under seismic loading with different values of duration.
(a)
(b)
(c) Test-06 (PGA=0.5g) Test-07 (PGA=0.6g) Test-08 (PGA=0.7g) Test-09 (PGA=0.8g) Test-10 (PGA=0.9g)
The stage of wall failure
The stage of wall failure
0
0.05
0.1
0.15
0
0.2
Normalized dynamic increment earth pressure, (Δ
0.05
0.1
0.15
0.2
Normalized dynamic increment earth pressure, (Δ
/ H)
AE
The stage of wall failure
0
0.05
0.1
0.15
0.2
Normalized dynamic increment earth pressure, (Δ
/ H)
AE
/ H)
AE
x H'
Test-06 (PGA=0.5g) Test-07 (PGA=0.6g) Test-08 (PGA=0.7g) Test-09 (PGA=0.8g) Test-10 (PGA=0.9g)
0
(d)
0.4
0.8
4
x/H' (%)
9
14
0
0.4
(e)
0.8
4
x/H' (%)
9
14
0
(f)
0.4
0.8
4
9
14
x/H' (%)
Fig. 11. Distribution of incremental dynamic earth pressure on SSW models with strip lengths of (a) 0.9H0 , (b) 0.7H0 , and (c) 0.5H0 , and profiles of normalized horizontal displacement of models with strip lengths of (d) 0.9H0 , (e) 0.7H0 , and (f) 0.5H0 under seismic loading with different values of peak acceleration.
incremental dynamic earth pressure, while a good agreement between the measurements and the predictions for R was observed for the total pressure. From the results observed in Fig. 13(b), it can be noted that for the incremental dynamic earth pressure, R is significantly affected by the strip length and the peak ground acceleration value, as it decreases with increasing peak acceleration values and with decreasing strip length. It was observed that the position of the resultant earth force above the toe varies from
about 0.42H to 0.34H and from about 0.37H to 0.31H for models with L/H0 = 0.9 and 0.5, respectively. On the other hand, it is evident from Fig. 14 that the values for the total and incremental dynamic earth pressure coefficients, KAE and DKAE, are not influenced by the loading duration and the predicated data are too conservative, especially for DKAE, as the overestimation approaches about 355% and 480% for KAE and DKAE, respectively. Meanwhile, a good agreement between the measurements
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(a)
11
(c)
(b)
Measured data Predicted data using Mononabe–Okabe method (kh = 0.5 PGA) Predicted data using Seed & Whitman method (kh = 0.5 PGA)
Test-06 (PGA=0.5g) Test-07 (PGA=0.6g) Test-08 (PGA=0.7g) Test-09 (PGA=0.8g) Test-10 (PGA=0.9g)
failure 0
0.1
failure
failure
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Normalized total earth pressure, (
0.5
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0
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Normalized total earth pressure, (
/ H)
AE
0.6
0
0.1
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0.5
Normalized total earth pressure, (
/ H)
AE
0.6
/ H)
AE
0.45
0.35
0.90
Distribution of total (i.e. dynamic and static) earth pressure
PAE
H
R
0.60
0.30
The stages of wall failure 0.00
(a)
0.4
0.5
0.6
0.7
0.8
0.9
Peak input base acceleration amplitude (g)
0.55
1
L/H' = 0.9 L/H' = 0.7 L/H' = 0.5
0.45
0.35
0.25
Normalized resultant force of incremental dynamic pressure, ΔPAE /½ H² = ΔKAE
0.25
0.65
R/H
Measured data Predicted data using Mononabe–Okabe method (kh = 0.5 PGA) Predicted data using Seed & Whitman method (kh = 0.5 PGA)
0.55
R/H
Normalized resultant elevation
0.65
Normalized resultant force of total pressure PAE /½ H² = KAE
Normalized resultant elevation
Fig. 12. Measured and predicted total earth pressure on SSW models with strip lengths of (a) 0.9H0 , (b) 0.7H0 , and (c) 0.5H0 under seismic loading with different values of peak acceleration.
0.90
Distribution of incremental dynamic earth pressure
ΔPAE
H
R
0.60
0.30
0.00
(b)
0.4
0.5
0.6
0.7
0.8
0.9
1
Peak input base acceleration amplitude (g)
Fig. 13. Variation in normalized resultant force of (a) total earth pressure and (b) incremental dynamic earth pressure and the positions of the resultant lateral force with peak input base acceleration.
and the predictions was observed in term of the position of the resultant force of total pressure, while the measured and the predicated values for R in the case of the incremental dynamic pressure were very different. 4. Conclusions In the work at hand, the dynamic response of steel-strip reinforced soil-retaining walls was investigated using reduced-scale physical models. For this purpose, uni-axial shaking table tests on 0.9-m-high models with different strip lengths were performed to investigate the influence of the peak ground acceleration, the loading duration,
and the strip length on the seismic response of the SSWs in terms of the dynamic reinforcement load and the dynamic lateral earth pressure behind the surface. Some results from the physical models have been compared to those of conventional methods as described in FHWA (2009). The following points summarize the major findings of this research: (1) During seismic excitation with different peak accelerations and durations, the non-linear distribution of the tensile force along the strips was observed, such that the distribution trend was not constant among the different rows. In the top-row strips, the distribution of
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H
R/H
R 0.45
0.35
0.25 0.39
0.26
Distribution of total / incremental dynamic earth pressure
PAE or ΔPAE
0.13
0.00
(a)
3
5
7
9
11
13
15
17
Loading duration (s)
0.55
R/H
L/H' = 0.9 L/H' = 0.7 L/H' = 0.5
0.65
0.45
0.35
0.25
Normalized resultant force of incremental dynamic pressure, ΔPAE /½ H² = ΔKAE
0.55
PAE or Δ PAE
Normalized resultant elevation
0.65
Normalized resultant force of total pressure PAE /½ H² = KAE
Normalized resultant elevation
12
0.39
Measured data Predicted data using Mononabe–Okabe method (kh = 0.5 PGA) Predicted data using Seed & Whitman method (kh = 0.5 PGA)
0.26
0.13
0.00
(b)
3
5
7
9
11
13
15
17
Loading duration (s)
Fig. 14. Variation in normalized resultant force of (a) total earth pressure and (b) incremental dynamic earth pressure and the positions of the resultant lateral force with loading duration.
mobilized tensile forces along the strips depicted a triangular shape with a certain maximum point (Tmax), which was located near the end of the strips, while with a decrease in the height of the rows, the location of Tmax became close to the facing, so that in the bottom half of the walls, the maximum mobilized tension was generated at the strip head (T0 = Tmax). It was also discovered that the maximum tensile force in each instrumented strip is mobilized approximately at the intersection of the failure plane and the strip. (2) In the upper half of the walls, the Tmax values decreased with a decreasing strip length, while this trend was reversed in the bottom half of the walls. Furthermore, it was found that the values of the mobilized tensile forces along the strips increase with a decreasing height of the rows, such that this increase become more prominent in the bottom half of the walls. It was discovered that strips located in the bottom half of wall play a significant role in the internal stability of SSW systems, and thus, should be given more attention under earthquake conditions. (3) A proper convergence was observed between the Tmax/HcsSVSH and L/H0 ratio at different levels of acceleration and duration, so that Tmax/HcsSVSH can be defined as a function of the L/H0 ratio and seismic parameters for different rows of strip.
(4) It was discovered that the values of the predicated earth pressure by conventional methods under static and seismic conditions are too conservative and these methods predict the position of the resultant lateral force as being higher than the actual point. (5) It was concluded that the values for active earth pressure and the deformability of SSW systems under static conditions, as two interdependent parameters, are affected by the strip length, so that reducing the L/H0 ratio from 0.9 to 0.5 will result in an increase in the deformability of the SSW by 42% and a decrease in the lateral active pressure by 15%. (6) The distribution of incremental dynamic earth pressure (DrAE) along the wall height depicted a curved shape, with a certain maximum point. The elevation of this point was constant with changes in the duration of the excitation and decreased with an increasing peak acceleration amplitude, so that the decreasing trend became more prominent with a decreasing strip length. (7) Despite the increasing DrAE, due to an increase in the values of acceleration and the duration of excitation, DrAE is significantly more affected by changes in acceleration amplitude than by changes in the duration of excitation. On the other hand, an increase in the length of the strips led to a significant reduction
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in DrAE by about 53% and 45% for seismic loadings with amax 0.5 g and amax > 0.5 g, respectively. (8) It was found that the values for the total and the incremental dynamic earth pressure coefficients (KAE and DKAE) were not influenced by the loading duration, although these coefficients were strongly influenced by the peak input base acceleration. Acknowledgements The author would like to express his appreciation to Dr. A. Komak Panah and Dr. A. Ghalandarzadeh for their valuable assistance in the construction of the physical models and also gratefully acknowledges the encouragement and guidance of Mrs. Z. Jenab Isfahani throughout this research effort. References Anastasopoulos, I., Georgarakos, T., Georgiannou, V., Drosos, V., Kourkoulis, R., 2010. Seismic performance of bar-mat reinforced-soil retaining wall: shaking table testing versus numerical analysis with modified kinematic hardening constitutive model. Soil Dyn. Earthquake Eng. 30 (10), 1089–1105. Bathurst, R.J., Walters, D., Vlachopoulos, N., Burgess, P., Allen, T.M., 2000. Full scale testing of geosynthetic reinforced walls. Geotech. Geoenviron. Eng. 291 (14), 201–217. Bhattacharya, S., Lombardi, D., Dihoru, L., Dietz, M., Crewe, A.J., Taylor, C.A., 2011. Model container design for soil-structure interaction studies. Role Seismic Test. Facil. Perform.-Earthquake Eng. 22, 135–158. El-Emam, M.M., Bathurst, R.J., 2007. Influence of reinforcement parameters on the seismic response of reduced-scale reinforced soil retaining walls. Geotext. Geomembr. 25 (1), 33–49. FHWA, 2009. Design and Construction of Mechanically Stabilized Earth Walls and Reinforced Soil Slopes, vol. I. Federal Highway Administration and National Highway Institute, Washington DC. NHI-10-024. Futaki, M., Ogawa, N., Sato, M., Kumada, T., Natsume, S., 1996. Experiments about seismic performance of reinforced earth retaining wall. In: Proceedings of the 11th World Conference on Earthquake Engineering, Paper no. 1083. Huang, C.-C., Horng, J.-C., Chang, W.-J., Chiou, J.-S., Chen, C.-H., 2011. Dynamic behavior of reinforced walls - horizontal displacement response. Geotext. Geomembr. 29, 257–267. Iai, S., 1989. Similitude for shaking table tests on soil-structure-fluid models in 1g gravitational field. Soils Found. 29 (1), 105–118. Komak Panah, A., Yazdi, M., Ghalandarzadeh, A., 2015. Shaking table tests on soil retaining walls reinforced by polymeric strips. Geotext. Geomembr. 43 (2), 148–161. Koseki, J., Tatsuoka, F., Watanabe, K., Tateyama, M., Kojima, K., Munaf, Y., 2003. Model tests of seismic stability of several types of soil retaining walls. In: Ling, H., Leshchinsky, D., Tatsuoka, F. (Eds.),
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Please cite this article in press as: Yazdandoust, M., Laboratory evaluation of dynamic behavior of steel-strip mechanically stabilized earth walls, Soils Found. (2018), https://doi.org/10.1016/j.sandf.2018.02.016