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Seismic displacement analysis of embankment dams with reinforced cohesive shell
Soil Dynamics and Earthquake Engineering 30 (2010) 1149–1157
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Seismic displacement analysis of embankment dams with reinforced cohesive shell Reza Noorzad a,n, Mehdi Omidvar b a b
Faculty of Civil Engineering, Babol University of Technology, Iran Engineering Faculty, University of Golestan, Iran
a r t i c l e in fo
abstract
Article history: Received 19 February 2008 Received in revised form 22 April 2010 Accepted 27 April 2010
Suitable materials for use as shell of embankment dams are clean coarse-grained soils or natural rockfill. In some sites these materials may not be available at an economic distance from the dam axis. The use of in-situ cohesive soils reinforced with geotextiles as the shell is suggested in this study for such cases. Dynamic behavior of reinforced embankment dam is evaluated through fully coupled nonlinear effective stress dynamic analysis. A practical pore generation model has been employed to incorporate pore pressure build up during cyclic loading. Parametric analyses have been performed to study the effect of reinforcements on the seismic behavior of the reinforced dam. Results showed that reinforcements placed within the embankment reduce horizontal and vertical displacements of the dam as well as crest settlements. Maximum shear strains within the embankment also decreased as a result of reinforcing. Furthermore, it was observed that reinforcements cause amplification in maximum horizontal crest acceleration. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Dynamic analysis Embankment dam Reinforced soil Cohesive soil
1. Introduction Suitable materials for use as shell of embankment dams are clean, coarse-grained soils and natural or crushed rockfill, which may not be available at economic distances from the dam axis. Under such conditions, the use of in-situ cohesive soil in reinforced form may provide a practical alternative for construction of the shell. However, some concerns arise when cohesive soils are used in construction of reinforced soil structures, including: higher deformation characteristics due to lower shear modulus, higher creep potential compared to granular fills, potential for developing positive pore pressures during construction and possible weakness in soil–reinforcement interactions. Extensive research has been devoted in the past years to investigate the mentioned concerns regarding reinforced cohesive soil structures. Zornberg and Mitchell [1] gave a comprehensive review of the experimental research from the literature concerning cohesive soil–reinforcement interaction as well as drainage function of reinforcement elements in poorly draining soils. In a companion paper, Mitchell and Zornberg [2] gave a valuable assessment of the use of reinforced cohesive soils by reviewing the performance of such structures reported from numerous case histories. Numerical investigations have also been carried out to evaluate the behavior of reinforced cohesive soil structures [3,4].
n
Corresponding author. E-mail addresses: [email protected], [email protected] (R. Noorzad).
0267-7261/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2010.04.023
The available literature suggests that permeable reinforcements can be effectively used to reinforce cohesive soils [5–8], and have emphasized that several issues including seismic behavior and creep potential must be taken into account [1,2]. However, to date, no comprehensive design methodology has been developed for reinforced soil structures consisting of cohesive soils. Reports on the behavior of reinforced soil structures during seismic events emphasize a relatively small shaking-induced distress [9,10]. However, since design approaches are still based on traditional limit equilibrium methods, actual seismic behavior of reinforced soil structures during earthquake-induced shaking is often neglected. Study of the seismic behavior of reinforced cohesive soils has suffered from lack of reported field performance data. Realizing the merits of constructing reinforced cohesive soils as a possible design alternative, more research is needed to fully understand the behavior of these structures under different loading conditions, especially during seismic events. In this paper, the use of cohesive soils in reinforced form has been suggested as the shell of embankment dams. It should be noted that the first use of reinforced earth in dam construction dates back to 1972, in Vallon de Bimes dam in France, with a height of 9 m and a crest length of 36 m. Numerous other dams or parts of dams have been constructed by utilizing reinforced fills [11]. However, nearly all the reported cases involve the utilization of free draining rockfill in reinforced form, and there is very little knowledge available on the applicability of reinforced cohesive soils for dam construction, and the body of literature emphasizing the seismic behavior of such structures is scarce. In the lack of
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reported case histories, numerical analysis has been carried out to investigate the seismic response of these structures to earthquake loading. Results of the analyses are interpreted in order to better understand the seismic response of reinforced cohesive soils. In the consequent sections, the modeling procedures for static as well as dynamic analysis of the reinforced dam models are described, followed by an assessment of the results of the parametric analyses.
2. Analysis approach During a seismic event, stress waves propagate through soils and attenuate with distance. Energy dissipation, volume changes and stiffness degradation of the materials are factors which affect this attenuation. During shaking, soils exhibit continuous hysteresis modulus degradation resulting in increasing levels of damping, which in turn decrease the amplitudes of the stress waves. The representation of this material behavior is important in seismic analysis of embankment dams. Two approaches are conventionally used in simulation of inelastic characteristics of soils subjected to cyclic loading: equivalent linear methods (ELM) and nonlinear numerical methods [12]. In the ELM nonlinear soil behavior is simulated by adjusting the shear modulus and damping ratio as functions of maximum shear strain in the soil. On the other hand, nonlinear methods use nonlinear constitutive models to represent the nonlinear behavior during cyclic loading. Constitutive equations used in predicting inelastic cyclic behavior of soils can become quite complex and may require many material parameters. Alternatively, simple elastic–plastic constitutive models may be used with additional damping added to represent inelastic damping behavior [12]. The latter method has been adopted in the present study and will be described in next sections. Damping in soils is primarily hysteretic, since energy dissipation occurs when grains slide over one another [13]. In the present study, a bilinear, elastic-perfectly plastic stress–strain relationship with a Mohr–Coulomb failure criterion has been used in the dynamic analyses. In this model, energy dissipation is achieved by plastic flow when shear stresses reach the yield strength. For cycles generating shear stress levels remaining in the elastic range, energy dissipation is achieved by viscous damping. Rayleigh damping consisting of two viscous elements is conventionally used in the numerical analyses herein. The two elements of Rayleigh damping are both frequency dependent; one increases linearly with frequency (stiffness damping as a function of strain rate) and the other decreases exponentially with increase in frequency (mass damping as a function of particle velocity) [13]. By choosing a center frequency, at which the combined effects of the two elements cancel out, it is possible to have damping that is nearly independent of frequency over a fairly wide range of frequencies on either side of the center frequency [14]. The center frequency is usually chosen in the range between the natural frequency of the model and the predominant frequency of the input motion. Fast Lagrangian analysis of continua (FLAC) [14] explicit finite difference code has been employed to perform fully coupled nonlinear dynamic analysis on models of embankment dams with reinforced cohesive soil as the shell. A fully coupled analysis is one in which calculation of displacements and pore pressure is carried out by solving a coupled system of equations that includes the motion equation and the diffusion equation [15]. In the code used herein, saturated soil is treated as a two-phase material using Biot coupled equations for the soil and water phases. Pore pressure generation is incremental and fully integrated with the nonlinear dynamic analysis. During dynamic analysis pore fluid
simply responds to changes in pore volume caused by mechanical dynamic loading; the average pore pressure does not vary significantly in the analysis [14]. It is known, however, that pore pressure may build up considerably during cyclic shear loading. It is important to incorporate this physical process in the coupled nonlinear dynamic analysis. Martin et al. [16] proposed the following empirical equation that relates the increment of volume decrease, Devd, to the cyclic shear strain amplitude, g:
Devd ¼ c1 ðgc2 evd Þ þ
c3 e2vd gc4 evd
ð1Þ
where C1, C2, C3 and C4 are constants. It is noteworthy in Eq. (1) that the increment of volume strain decreases as volume strain is accumulated. Byrne [17] suggested the following simpler formula: Devd e ¼ c1 exp c2 vd ð2Þ
g
g
where C1 and C2 are constants with different interpretations from Eq. (1). C1 can be derived from relative density, Dr as follows: C1 ¼ 7600ðDr Þ2:5
ð3Þ
Further, using an empirical relation between Dr and normalized standard penetration test values, (N1)60 as Dr ¼ 15ðN1 Þ0:5 60
ð4Þ
Therefore, C1 ¼ 8:7ðN1 Þ1:25 and in many cases C2 ¼0.4/C1 [14]. 60 The mentioned formulation is available in FLAC as a built-in model and was adopted in this study along with a bilinear, elasticperfectly plastic stress–strain relationship and Rayleigh damping. Therefore during dynamic analysis, as effective stresses decrease with increase in pore pressure, the soil begins to yield and increments of permanent deformation are accumulated. The simultaneous coupling of pore pressure generation with nonlinear, plasticity based, stress analysis produces a more realistic dynamic response than can be achieved with the equivalent linear method [13]. The approach described above has been verified in the literature through analysis of well documented case histories [18,19] and was adopted herein for the dynamic analysis of embankment dams with shell of reinforced cohesive soil.
3. Numerical model and material properties 3.1. Model geometry and soil properties Two-dimensional plane strain models of the reinforced embankment dam were considered in the parametric analyses of this study. The geometry of the base model is shown in Fig. 1. The embankment dam is constructed of clay with physical and mechanical properties typical of compacted in-situ clay soils. Based on previous experience in actual embankment dam projects, the reinforced dam was assumed to be constructed on an alluvial foundation. Physical and mechanical properties of the embankment and foundation soil used in the numerical models are given in Table 1. The embankment consists of an upstream and downstream shell of cohesive soil reinforced with non-woven geotextile layers. The central core of the embankment was left unreinforced in order to act as a seepage barrier, since the permeable horizontal reinforcements promote seepage through the embankment. Three dam heights of 15, 25 and 40 m were considered in the parametric analyses in order to assess the effect of dam height on the seismic behavior of the reinforced dam. The stable side slopes for each height were determined through performing trial analyses, in which reinforced upstream and downstream slopes were constructed following an approach
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3m
H 3H
3H
Quiet boundary
Inputt motion
H
0.5H
Free field
Free field
Fig. 1. Schematic view of the base model used for performing the dynamic analyses.
Table 1 Material properties of embankment and foundation soils. Parameter
Foundation
Embankment
Dry unit weight (kg/m3) Elastic modulus (MPa) Poisson’s ratio Drained internal friction angle (1) Drained cohesion (KPa) Porosity Permeability (m/s) Normalized SPT number (Blows)
1900 50 0.3 35 3 0.3 10 8 —
1660 7 0.35 28 10 0.37 10 9 25
described below, and the side slopes were altered in consecutive analyses while monitoring the displacements of the crest. For each height, once the horizontal and vertical crest displacements were confined within tolerable limits, the resulting side slopes were adopted for that height in the parametric analysis. Stable side slopes obtained through the aforementioned procedure were 2.5, 3 and 3.5 (horizontal, to one vertical) for the three dam heights of 15, 25 and 40 m, respectively. The finite difference grid dimensions were selected taking into account the maximum frequency, f, of the shear wave that the model could respond to during earthquake loading. This frequency is determined by the following equation [20]: f¼
Cs 10Dl
ð5Þ
where Cs is the shear wave velocity of the soil and Dl is the largest grid zone size in the model. Referring to Eq. (5), a uniform zone size of 0.5 m 0.5 m was selected and since the lowest shear wave velocity in the model belongs to the embankment soil, the highest admissible frequency for a propagating shear wave is 7.9 Hz. Therefore the input earthquake record will have to be filtered by a low pass filter to remove frequency components higher than 7.9 Hz. A frequency of 5 Hz was ultimately selected for the low pass filter to account for the reduction in shear wave velocity that may occur due to plastic flow during seismic loading. Although optimal design of the reinforcement configuration was not intended, the proposed configuration was checked for adequate embedment length. The method suggested by Federal highway Administration (FHWA) [21] for minimum embedment length of reinforced soil slopes was followed. Stability analyses were performed using RSS limit equilibrium code developed by FHWA. The calculations performed showed that the proposed design provides adequate embedment lengths against pullout in all the models considered. 3.2. Reinforcement modeling and properties The geotextile layers were modeled using the one-dimensional linear, elastic–plastic cable elements readily available in the finite
difference code. Cable elements were originally designed to model structural elements in which tensile capacity is important and the bending resistance is negligible. There are several reports available in the literature regarding the successful employment of cable elements as geotextile reinforcements [22–24]. Since the original formulation was intended for nails and bolts, some adjustments to the input properties of cable elements are necessary in order to match manufacturer-provided specifications of geotextiles with the physical and mechanical input parameters in the numerical code. The behavior of the cable element and the required input parameters are described in the next section. Cable behavior is characterized by two distinct properties, which include axial behavior of the reinforcement element and the constitutive behavior of the soil–reinforcement interface. Both aforementioned properties must be specified in order to achieve a realistic model of the actual reinforcement behavior. Cable elements are assumed to follow a linear elastic behavior both in tension and compression, with tensile and compression yielding limits specified, beyond which a perfectly plastic yield occurs. The axial stiffness of cable elements is described in terms of its crosssectional area, A, and Young’s modulus, E. The geotextile reinforcement stiffness obtained from wide width tensile test may be employed to specify the Young’s modulus of the cable element in the finite difference modeling. In doing so, the Young’s modulus is obtained by dividing the manufacturer-provided tensile stiffness of the geotextile by its thickness. A thickness value in the range of 1–5 mm is typical for geotextiles as specified by manufacturers. The value of the ultimate tensile strength of the reinforcement is taken the same as the tensile yield strength of the cable element, and a small compression limit is also usually specified. The interface between the geotextile and the base soil is modeled using grout elements available in the finite difference code, which was initially supplied for the modeling of concrete grouts in soil nail and rock bolt modeling. Grout elements are characterized by shear and normal behavior. The shear behavior of the grout annulus is represented by a spring-slider system attached to the nodal points of the reinforcement. Grout shear stiffness governs the magnitude of the relative displacements between geotextile and the base soil. The maximum shear force mobilized in the grout annulus follows a Mohr–Coulomb failure criterion. The above-described formulation of the interface system allows for relative shear displacements between the reinforcement and the base soil to occur, hence permitting pullout of geotextile to be modeled. In the normal direction, however, the nodes of the geotextile are slaved to the base soil and will therefore deform as the finite difference grid representing the base soil deforms. The horizontal geotextile layers placed within the upstream and downstream shells of the embankment dam were modeled using linear, elastic–plastic cable elements with the abovedescribed properties. In order for the conceptual study of this research to be representative of actual conditions, several geotextile specifications provided by different manufacturers
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were observed, and the geotextile properties were extracted from these specifications to represent a low to medium strength nonwoven geotextile product. The main reason for selecting non-woven geotextiles was to take advantage of its lower stiffness, which allows it to conform with the soil as it deforms. Moreover, as reported in the literature, the in-plane drainage characteristics of the non-woven geotextile prevents pore pressure build up during staged construction of the embankment [1,2,8,25,26]. Accordingly, the reinforcement stiffness was taken as 25 kN/m. The tensile yield strength of the reinforcement was set to 15 kN/m, which is also a typical value for non-woven geotextiles. The relatively lower value for the tensile strength means that reinforcement rupture will be an anticipated failure mechanism in the analyses. The interface between the reinforcement and the soil was modeled by the grout annulus described above. The grout was considered to have negligible thickness. The mechanical properties of the interface are usually specified in terms of the properties of the base soil. In the absence of experimental data, results of previous studies were consulted in determining realistic properties for the clay–nonwoven geotextile interface. Athanasopoulos [27] performed direct shear tests on silty clay samples reinforced with non-woven geotextiles, and presented the interface properties in terms of an efficiency ratio, defined as the ratio of the interface properties to those of the base soil. Comparing the geotextile strength selected in the present study with the different geotextiles used by Athanasopoulos [27], it was observed that an approximate average efficiency ratio of 0.8 (considering tests performed on Terram 1500 geotextile) could be representative for the clay-geotextile interface properties of the present study. The interface properties of the grout, as described above, were determined by reducing base soil properties by a factor of 0.8. An equivalent thickness of 2 mm was adopted as the reinforcement thickness, which yields an equivalent cross-sectional area of 0.002 m2. In order to take into account the beneficial effects of the drainage properties of the non-woven geotextile reinforcements, the horizontal permeability of the reinforced zone was increased by a factor of one hundred [28]. Three vertical spacings of 0.5, 1 and 1.5 m were considered between geotextile layers in order to assess the effects of reinforcement spacing on the seismic behavior of the composite structure. 3.3. Dam construction and dynamic loading The technique of layered construction was employed in the static stress analyses. Since pore pressure generation during construction was a concern, the following procedures were used to model the static effective stress conditions: (a) The foundation was first placed as submerged soil and was forced to equilibrium.
(b) Embankment soil materials were divided into ten layers and were placed sequentially. Following the placement of each layer, reinforcement layers were added to the layer and the model was set to run for a time period equal to the estimated time required for actual construction of the layer under field conditions. The time needed was calculated by assuming an embankment construction speed of 1000 m3/day and multiplying this by the total fill volume of each layer. The fill volume was obtained by considering a crest length of 100, 200 and 300 m for the three dam heights of 15, 25 and 40 m, respectively. (c) The water level was then raised to full pool. Boundary water pressures were applied along the interior dam surface and the reservoir bed to account for water pressures. (d) Seepage analysis was performed to achieve steady state conditions within the embankment and the foundation. (e) Mechanical adjustment of stresses was allowed by performing mechanical calculations with flow calculations turned off, and forcing the model to equilibrium. During the process of layered construction, pore pressures within the embankment were monitored and when needed, embankment construction was halted and the model was run under coupled conditions for a six month period in order to allow for consolidation and dissipation of excess pore pressures. Once initial stresses for the steady state condition were achieved, the following steps were taken to prepare the model for dynamic analysis: (a) Apply dynamic boundary conditions: In order to enforce free field conditions in the numerical boundaries of the discretized half space foundation, free field boundary conditions available in the code were adopted for the lateral boundaries. As for the horizontal boundary, the simulation of outward propagating waves in the foundation was achieved by employing the absorbing boundary conditions also available in the finite difference code. Absorbing boundaries have been shown to be effective in absorbing outward propagating waves, and hence simulating half space conditions [29]. The viscous boundaries developed by Lysmer and Kuhlemeyer [30] are adopted in the finite difference code, and were employed in the analyses herein. One restriction in applying absorbing boundaries to numerical boundaries in a dynamic analysis is that such boundary conditions cannot be simultaneously applied to a boundary where acceleration or velocity input is applied, as prescribing acceleration or velocities to a boundary would nullify the effect of the absorbing boundary. In such situations it is necessary to convert acceleration or velocity inputs into stress waves, as described below. (b) Prepare input motion and apply seismic loading to the numerical model. Horizontal component of the acceleration record from Tabas earthquake was applied to the base of
Fig. 2. Acceleration time history of Tabas earthquake—horizontal component.
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Fig. 3. Displacement history at center of crest for 25 m dam with 1.5 m reinforcement spacing.
the model. Since quiet boundaries were already attributed to the horizontal boundary, the acceleration time history of the input motion was converted to shear stress waves, as described above. The process of converting an acceleration time history into a shear wave time history has been described elsewhere (Itasca [14]), and was verified by monitoring the acceleration time history of the horizontal boundary where the seismic input was applied. A nearly perfect match between the input acceleration time history and the time history recorded after applying the shear wave time history confirmed the validation of the process employed. There is a limit to the rate at which waves can be accurately transmitted through a grid. Kuhlemeyer and Lysmer [20] have suggested that for accurate wave transmission, the spatial element size should be less than eight to ten times the wavelength associated with the highest frequency content of the input motion (after Itasca [14]). Therefore, since the finite difference grid was chosen to have a grid spacing of 0.5 m, by the aforementioned suggestion, the input motion would have to be filtered by a low pass filter to remove frequency components exceeding 5 Hz. The horizontal acceleration component of Tabas earthquake after applying the aforementioned low pass filter is shown in Fig. 2. It can be seen that the filtered acceleration time history has a peak ground acceleration (PGA) of 6.8 m/s2. After preparing the input motion by filtering the acceleration time history and converting it to a shear stress time history, the resulting shear stress time history was prescribed to each of the grid points at the horizontal boundary where absorbent boundary conditions were previously prescribed. (c) Rayleigh damping was assigned to each element of the model in the mid-range between the natural frequency of the model and the predominant frequency of the input motion. The value of Rayleigh damping was chosen based on shear strains recorded from undamped analysis, by taking 65% of the peak recorded strain. The damping ratios obtained by this procedure ranged from 4% to 15%. (d) Dynamic analysis was performed for the duration of the earthquake, and results were extracted for interpretation and further assessment. It should be mentioned that for simplification purposes, the hydrodynamic interaction effects of the dam reservoir were neglected. Furthermore, the vertical component of the seismic input was not considered in the seismic loading, since the present study aims to provide qualitative results of the behavior of a reinforced dam under seismic loading conditions. In a real case, however, the horizontal and vertical components of the seismic motion would have to be applied to the dam simultaneously. Several studies have been performed to evaluate the effect of
30 1.5 1 0.5 Nonreinforced 25
20
15 0.00
0.05
0.10
0.15
0.25
0.20
0.30
0.35
30
25
20 1.5 1 0.5
15 0
0.1
0.2
0.3
0.4
0.5
0.6
Fig. 4. Distribution of displacement along height of 15 m high dam: (a) relative horizontal displacements and (b) relative vertical displacements.
vertical acceleration on reinforced earth structures including Ling and Leshchinsky [31] and Wolfe et al. [32]. It can be interpreted from these studies that the effect of vertical acceleration on the seismic response of reinforced earth structures depends on the magnitude of the horizontal and vertical peak acceleration.
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The effect of the vertical acceleration has been mentioned to mainly increase the required geotextile length, and to increase the required tensile reinforcement and the permanent displacements in some cases [31]. Although it is important to consider the simultaneous effect of horizontal and vertical components of earthquake motions in seismic design of earth dams as specified by design codes, in the present conceptual study, only the horizontal component has been considered in order to prevent modeling complications, and to reduce analysis time.
4. Results of dynamic analysis The computed deformation time history at crest level for one of the models consisting of a 25 m high dam with 1.5 m geotextile spacing is shown in Fig. 3. Results of the parametric analyses showed that reinforcing the dam decreases both horizontal and vertical crest displacements. Fig. 4 depicts the patterns of the relative displacements along the dam axis for 15 m dam height. Relative displacements were calculated as the difference between the displacements at the crest level and that of the base of the dam. It can be noted that all the reinforced dams show the same
Fig. 5. Displacements recorded at the end of shaking for 1.5 m reinforcement spacing: (a) horizontal displacement and (b) vertical displacement.
qualitative trend of displacements along the dam axis as the reinforced dam. As described by Gazetas [33], the trends observed in the dam models are representative of a second mode response of a shear beam, with the reinforced models showing a stiffer response in the reinforced zone as compared to the nonreinforced dam. Similar patterns were observed in the models with 25 and 40 m heights. Maximum displacements obtained at the end of earthquake loading for reinforced and non-reinforced models are also presented in Fig. 5. Displacements at the crest level were recorded as the difference between displacements of a node on the central axis at crest level and displacements of a node along the same axis at the base of the model. Maximum horizontal crest displacements in the unreinforced models of 15, 25 and 40 m dam height were 0.69, 0.76 and 0.89 m, respectively, while maximum recorded horizontal crest displacements of the reinforced dam with 0.5 m reinforcement spacing were 0.20, 0.21 and 0.44 m, respectively, for the same three heights considered. Moreover, maximum vertical crest displacements in the
Fig. 6. Shear strain reduction due to reinforcement. (a) Distribution along height of 15 m dam. (b) Variation with dam height and reinforcement spacing for three dam heights considered.
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unreinforced dam models with three heights of 15, 25 and 40 m were 0.38, 0.50 and 0.94 m, respectively, whereas in the reinforced dams with 0.5 m reinforcement spacing, these values reduced to 0.17, 0.18 and 0.42 m, respectively. Displacement values from models with geotextile spacing of 1 and 1.5 m showed similar trends. It can be deduced form Fig. 5 and the mentioned values, that maximum reductions of horizontal displacements due to reinforcing for the three dam heights of 15, 25 and 40 m were 3.35%, 2.09% and 1.15% of dam height, respectively, while maximum vertical displacements diminished by 2.18%, 1.55% and 1.30% of dam height, respectively. These values show that beneficial effects of reinforcing the dam decrease as the dam height increases. Fig. 6a compares shear strain distribution along dam height of non-reinforced dam with dams having different reinforcement spacing. In general, peak shear strains decreased as a result of reinforcement. Reduction of peak shear strain for three dam heights and three geotextile spacing considered is summarized in Fig. 6b. Peak shear strain reduction due to reinforcement was generally higher in dams with lower heights and less reinforcement spacing. Maximum reductions of peak shear
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strain due to reinforcement of the shell obtained at the end of shaking were 19.7%, 18.5% and 12.8% for three dam heights of 15, 25 and 40 m, respectively. Shear stress history from one of the models is shown in Fig. 7. Shear stress history consists of higher frequencies and amplitudes in the initial portion of the shaking, both decreasing as shaking continues. This behavior is a result of gradual decrease in soil stiffness and shear strength due to buildup of excess pore pressure, an important mechanism affecting the dynamic response. This recorded response shows that the coupled nonlinear model used in the dynamic analyses was able to appropriately capture the basic response behavior of soil under seismic loading. Acceleration time history obtained at the crest of 15 m high dam height with 1.5 m geotextile spacing is plotted in Fig. 8. There is a clear amplification of the response for low amplitude cycles of the input motion, especially towards the end of shaking. It is known that amplification is a result of elastic response. Higher amplitude cycles cause yield of embankment material which in turn dissipates input energy and prevents amplification of the response. This behavior is evident from the plot of crest
Acceleration (m/sec 2)
Fig. 7. Shear stress history at point A of 15 m high dam with 1.5 m reinforcement spacing.
6 4 2 0 -2 -4 -6 0
4
8
12
16
20
24
28
20
24
28
Time (sec)
Acceleration (m/sec 2)
6 4 2 0 -2 -4 -6 -8 0
4
8
12
16
Time (sec) Fig. 8. Acceleration time history recorded at the base and crest of 15 m high dam with 1.5 m reinforcement spacing—(a) base acceleration and (b) crest acceleration.
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Fig. 9. Variation of amplification factor for reinforced and non-reinforced models.
acceleration time history shown in Fig. 8, and can be supported by the plot of displacement time history from Fig. 3, where significant displacements occur as a result of intense shaking. It can be seen that from seconds 8 to 12 of the earthquake loading, where the peak acceleration pulse is observed, less amplification of peak acceleration is observed at crest level, which is due to yielding of the embankment soil. Fig. 9 compares amplification values for the different models considered in the parametric analyses. It can be seen that as the vertical reinforcement spacing decreases in the embankment, amplification of the input motion increases. Once again, this behavior can be attributed to the tendency for elastic response in the reinforced dam as a result of decrease in shaking-induced displacements. The distribution and magnitudes of maximum recoded geotextile load, Tmax, in the upstream and downstream section of each dam at the end of shaking are plotted in Fig. 10. Maximum load value recorded at each level corresponds to the maximum tensile load recorded along the entire reinforcement length at that level. Different patterns were observed in the upstream and downstream reinforcements. The peak reinforcement load along the upstream occurs at nearly one third of the height of the reinforced zone. This pattern becomes more evident as the dam height increases, where the ratio of maximum to minimum reinforcement load exceeds 5. In the downstream reinforcements, however, a more uniform distribution of maximum load with height was observed, especially in the upper half of the reinforced zone. Comparison of the maximum mobilized reinforcement load with the tensile strength of the reinforcements indicates that the rupture of the geotextile layers did not occur during the seismic loading. Since relatively large deformations were recorded after the shaking, it is postulated the weak geotextile–soil interface properties resulted in slippage at the interface, preventing full mobilization of the reinforcement strength.
5. Conclusions The results of parametric seismic analyses of embankment dam with shells of reinforced cohesive soil have been reported. Three dam heights of 15, 25 and 40 m, as well as three vertical reinforcement spacing of 0.5, 1 and 1.5 m were considered in the analyses. Several features of the dynamic response to actual acceleration time history are summarized below:
Fig. 10. Distribution of maximum reinforcement load along height of the embankment. (a) Upstream and (b) downstream.
1- Reinforcement of the dam decreased both crest displacements and displacements along the height of the dam. Amount of decrease in horizontal displacements for three heights of 15, 25 and 40 m were 3.35%, 2.09% and 1.15% of dam height, respectively, while maximum vertical displacements reduced at 2.18%, 1.55% and 1.30% of dam height, respectively. 2- Strain distribution along height of the dam decreased as a result of reinforcement. It was observed that maximum reduction in shear strains due to reinforcement increased when reinforcement arrangements with lower vertical spacing were considered. Moreover, beneficial effects of reinforcement diminished as dam height increased. 3- Input acceleration was amplified at the crest level due to reinforcement. The amplification factor ranged between 1.05 and 1.48. The low amplification factors observed were attributed mainly to the high amount of damping due to yielding of embankment material. Reinforcing the embankment increased the elastic response and resulted in higher amplification as compared to the non-reinforced dam. 4- Different patterns of maximum tensile load distribution were observed along the upstream and downstream reinforcements.
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Maximum tensile load along the upstream occurred at around one third of the reinforced zone height, while relatively uniform distribution was observed along the downstream.
References [1] Zornberg JG, Mitchell JK. Reinforced soil structures with poorly draining backfills. Part I: reinforcement interactions and functions. Geosynthetics International 1994;1(2):103–47. [2] Mitchell JK, Zornberg JG. Reinforced soil structures with poorly draining backfills. Part II: case histories and applications. Geosynthetics International 1994;1(2):265–307. [3] Kobayashi M, Porbaha A. Numerical simulation of scaled steep reinforced slopes. In: Computer methods and advances in geomechanics, Balkema, Rotterdam; 1997. [4] Lindquist DD. Seismic modeling of geosynthetic-reinforced slopes. MS Thesis, University of Washington, 1998. [5] Fourie AB, Fabian KJ. Laboratory determination of clay geotextile interaction. Geotextiles and Geomembranes 1987;6(4):275–94. [6] Ling HI, Tatsuoka F. Laboratory evaluation of a nonwoven geotextile for reinforcing on-site soil. In: Proceedings of geosynthetics 0 93, 2, Vancouver, Canada; 1993. p. 533–46. [7] Mohiuddin A. Analysis of laboratory and field pull-out tests of geosynthetics in clayey soils. M.S. Thesis, Louisiana State University, Baton Rouge, L.A.; 2003. [8] Yunoki Y, Nagao A. An application of non-woven fabrics to embankment of cohesive soil. Theory and Practice of Earth Reinforcement. In: Proceedings of symposium held in Fukuoka, Japan; 1988 p. 491–6 . [9] Tatsuoka F, Tateyama M, Koseki J. Performance of geogrid reinforced soil retaining walls during the Great Hanshin-Awaji earthquake. In: First international symposium on earthquake geotechnical engineering, Tokyo; 1995. [10] White DM, Holtz RD. Performance of geosynthetic reinforced slopes and walls during the Northridge California earthquake of 17 January, 1994. Report. University of Washington, Seattle, 1995. [11] ICOLD Bulletin No. 89: Reinforced Rockfill and Reinforced Fill for Dams, 1993. [12] Han Y, Hart R. Application of a simple hysteretic damping formulation in dynamic continuum simulations. In: Varona P, Hart R, editors. Proceedings of the fourth international FLAC symposium on numerical modeling in geomechanics, Madrid, Spain; 2006. [13] Zhai E, Roth W, Dawson E, Davis C. Seismic deformation analysis of an earth dam—a comparison study between equivalent-linear and nonlinear effective-stress approaches. In: Proceedings of the 13th world conference on earthquake engineering, Vancouver, BC, Canada; 2004. [14 Itasca Consulting Group. FLAC, Fast Lagrangian Analysis of Continua, Version 4.0, Itasca Consulting Group, Minneapolis, Minnesota, 2001. [15] Wang ZL, Makdisi FI, Egan J. Practical applications of a nonlinear approach to analysis of earthquake-induced liquefaction and deformation of earth structures. Soil Dynamics and Earthquake Engineering 2005;26(2–4):231–52. [16] Martin GR, Finn WDL, Seed HB. Fundamentals of liquefaction under cyclic loading. Soil Mechanics and Foundation Engineering Division, ASCE 1975;101(GT5). 423–438.
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[17] Byrne PA. Cyclic shear-volume coupling and pore pressure model for sand. In: Proceedings of the second international conference on recent advances in geotechnical earthquake engineering and soil dynamics, St. Louis, Missouri; 1991. [18] Roth WH, Dawson E, Somerville P, Davis C, Plumb CC. Evaluating the seismic performance of Stone Canyon Dam with 2-D and 3-D analyses. In: Proceedings of the 13th world conference on earthquake engineering, Vancouver, BC, Canada; 2004. [19] Roth WH, Scott RF, Cundall, PA. Nonlinear dynamic analysis of a centrifuge model embankment. In: Proceedings of the third US national conference on earthquake engineering, August 23–28, Charleston, South Carolina; 1986, vol. 1. [20] Kuhlemeyer RL, Lysmer J. Finite element method accuracy for wave propagation problems. Journal of Soil Mechanics and Foundation Engineering Division, ASCE 1973;99(SM5):421–7. [21] Elias V, Christopher BR, Berg, RR. Mechanically stabilized earth walls and reinforced soil slopes design and construction guidelines. Report No. FHWANHI-00-043, FHWA-US Department of Transportation, Washington, DC, 2001. [22] Bathurst RJ, Hatami K. Seismic response analysis of a geosynthetic-reinforced soil retaining wall. Geosynthetics International 1998;5(1–2):127–66. [23] Mendonca AA, Lurdes Lopes M. Role of reinforcement density on the behavior of geogrid reinforced systems. In: Varona P, Hart R, editors. In: Proceedings of the fourth international FLAC symposium on numerical modeling in geomechanics, Madrid, Spain; 2006. [24] Viera CS, Lopes ML. Caldeira LMMS. Seismic response of a geosynthetic reinforced steep slope using FLAC. In: Varona P, Hart R, editors. Proceedings of the fourth international FLAC symposium on numerical modeling in geomechanics, Madrid, Spain; 2006. [25] Tatsuoka F, Murata O, Tateyama M, Nakamura K, Tamura Y, Ling HI, Iwasaki K, Yamauchi H. Reinforcing steep clay slopes with a non-woven geotextile, performance of reinforced soil structures. In: McGown A, Yeo K, Andrews KZ, editors, Thomas Telford, 1991. Proceedings of the international reinforced soil conference held in Glasgow. Scotland, September 1990. p. 141–6. [26] Abu-Farsakh MY, Coronel J. Characterization of cohesive soil-geotextile interactions from large direct shear tests. Transportation Research Board. TRB 2006 Annual Meeting Report, 2006 p. 9. [27] Athanasopoulos GA. Results of direct shear tests on geotextile reinforced cohesive soil. Geotextiles and Geomembranes 1996;14:619–44. [28] Dolezalova IH, Zemanova V. Stability analysis of a motorway embankment on soft subsoil using FEM, FLAC and limit equilibrium methods. In: Proceedings of the second international FLAC symposium on numerical modeling in geomechanics, Lyon, France; 2001. [29] White W, Walther H. Unified boundary for finite dynamic models. Journal of Engineering Mechanics 1977;103:949–64. [30] Lysmer J, Kuhlemeyer RL. Finite dynamic model for infinite media. Journal of Engineering Mechanics 1969;95(EM4):859–77. [31] Ling HI, Leshchinsky D. Effects of vertical acceleration on seismic design of geosynthetic-reinforced soil structures. Geotechnique 1998;48(3):347–73. [32] Wolfe WE, Lee KL, Rea D, Yourman AM. The effect of vertical motion on the stability of reinforced earth walls. In: Proceedings of the international symposium on earth reinforcement, ASCE, p. 856–79. [33] Gazetas G. Shear vibration of vertically inhomogeneous earth dams. International Journal for Numerical and Analytical Methods in Geomechnics 1982;6:219–41.
Contents lists available at ScienceDirect
Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Seismic displacement analysis of embankment dams with reinforced cohesive shell Reza Noorzad a,n, Mehdi Omidvar b a b
Faculty of Civil Engineering, Babol University of Technology, Iran Engineering Faculty, University of Golestan, Iran
a r t i c l e in fo
abstract
Article history: Received 19 February 2008 Received in revised form 22 April 2010 Accepted 27 April 2010
Suitable materials for use as shell of embankment dams are clean coarse-grained soils or natural rockfill. In some sites these materials may not be available at an economic distance from the dam axis. The use of in-situ cohesive soils reinforced with geotextiles as the shell is suggested in this study for such cases. Dynamic behavior of reinforced embankment dam is evaluated through fully coupled nonlinear effective stress dynamic analysis. A practical pore generation model has been employed to incorporate pore pressure build up during cyclic loading. Parametric analyses have been performed to study the effect of reinforcements on the seismic behavior of the reinforced dam. Results showed that reinforcements placed within the embankment reduce horizontal and vertical displacements of the dam as well as crest settlements. Maximum shear strains within the embankment also decreased as a result of reinforcing. Furthermore, it was observed that reinforcements cause amplification in maximum horizontal crest acceleration. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Dynamic analysis Embankment dam Reinforced soil Cohesive soil
1. Introduction Suitable materials for use as shell of embankment dams are clean, coarse-grained soils and natural or crushed rockfill, which may not be available at economic distances from the dam axis. Under such conditions, the use of in-situ cohesive soil in reinforced form may provide a practical alternative for construction of the shell. However, some concerns arise when cohesive soils are used in construction of reinforced soil structures, including: higher deformation characteristics due to lower shear modulus, higher creep potential compared to granular fills, potential for developing positive pore pressures during construction and possible weakness in soil–reinforcement interactions. Extensive research has been devoted in the past years to investigate the mentioned concerns regarding reinforced cohesive soil structures. Zornberg and Mitchell [1] gave a comprehensive review of the experimental research from the literature concerning cohesive soil–reinforcement interaction as well as drainage function of reinforcement elements in poorly draining soils. In a companion paper, Mitchell and Zornberg [2] gave a valuable assessment of the use of reinforced cohesive soils by reviewing the performance of such structures reported from numerous case histories. Numerical investigations have also been carried out to evaluate the behavior of reinforced cohesive soil structures [3,4].
n
Corresponding author. E-mail addresses: [email protected], [email protected] (R. Noorzad).
0267-7261/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2010.04.023
The available literature suggests that permeable reinforcements can be effectively used to reinforce cohesive soils [5–8], and have emphasized that several issues including seismic behavior and creep potential must be taken into account [1,2]. However, to date, no comprehensive design methodology has been developed for reinforced soil structures consisting of cohesive soils. Reports on the behavior of reinforced soil structures during seismic events emphasize a relatively small shaking-induced distress [9,10]. However, since design approaches are still based on traditional limit equilibrium methods, actual seismic behavior of reinforced soil structures during earthquake-induced shaking is often neglected. Study of the seismic behavior of reinforced cohesive soils has suffered from lack of reported field performance data. Realizing the merits of constructing reinforced cohesive soils as a possible design alternative, more research is needed to fully understand the behavior of these structures under different loading conditions, especially during seismic events. In this paper, the use of cohesive soils in reinforced form has been suggested as the shell of embankment dams. It should be noted that the first use of reinforced earth in dam construction dates back to 1972, in Vallon de Bimes dam in France, with a height of 9 m and a crest length of 36 m. Numerous other dams or parts of dams have been constructed by utilizing reinforced fills [11]. However, nearly all the reported cases involve the utilization of free draining rockfill in reinforced form, and there is very little knowledge available on the applicability of reinforced cohesive soils for dam construction, and the body of literature emphasizing the seismic behavior of such structures is scarce. In the lack of
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reported case histories, numerical analysis has been carried out to investigate the seismic response of these structures to earthquake loading. Results of the analyses are interpreted in order to better understand the seismic response of reinforced cohesive soils. In the consequent sections, the modeling procedures for static as well as dynamic analysis of the reinforced dam models are described, followed by an assessment of the results of the parametric analyses.
2. Analysis approach During a seismic event, stress waves propagate through soils and attenuate with distance. Energy dissipation, volume changes and stiffness degradation of the materials are factors which affect this attenuation. During shaking, soils exhibit continuous hysteresis modulus degradation resulting in increasing levels of damping, which in turn decrease the amplitudes of the stress waves. The representation of this material behavior is important in seismic analysis of embankment dams. Two approaches are conventionally used in simulation of inelastic characteristics of soils subjected to cyclic loading: equivalent linear methods (ELM) and nonlinear numerical methods [12]. In the ELM nonlinear soil behavior is simulated by adjusting the shear modulus and damping ratio as functions of maximum shear strain in the soil. On the other hand, nonlinear methods use nonlinear constitutive models to represent the nonlinear behavior during cyclic loading. Constitutive equations used in predicting inelastic cyclic behavior of soils can become quite complex and may require many material parameters. Alternatively, simple elastic–plastic constitutive models may be used with additional damping added to represent inelastic damping behavior [12]. The latter method has been adopted in the present study and will be described in next sections. Damping in soils is primarily hysteretic, since energy dissipation occurs when grains slide over one another [13]. In the present study, a bilinear, elastic-perfectly plastic stress–strain relationship with a Mohr–Coulomb failure criterion has been used in the dynamic analyses. In this model, energy dissipation is achieved by plastic flow when shear stresses reach the yield strength. For cycles generating shear stress levels remaining in the elastic range, energy dissipation is achieved by viscous damping. Rayleigh damping consisting of two viscous elements is conventionally used in the numerical analyses herein. The two elements of Rayleigh damping are both frequency dependent; one increases linearly with frequency (stiffness damping as a function of strain rate) and the other decreases exponentially with increase in frequency (mass damping as a function of particle velocity) [13]. By choosing a center frequency, at which the combined effects of the two elements cancel out, it is possible to have damping that is nearly independent of frequency over a fairly wide range of frequencies on either side of the center frequency [14]. The center frequency is usually chosen in the range between the natural frequency of the model and the predominant frequency of the input motion. Fast Lagrangian analysis of continua (FLAC) [14] explicit finite difference code has been employed to perform fully coupled nonlinear dynamic analysis on models of embankment dams with reinforced cohesive soil as the shell. A fully coupled analysis is one in which calculation of displacements and pore pressure is carried out by solving a coupled system of equations that includes the motion equation and the diffusion equation [15]. In the code used herein, saturated soil is treated as a two-phase material using Biot coupled equations for the soil and water phases. Pore pressure generation is incremental and fully integrated with the nonlinear dynamic analysis. During dynamic analysis pore fluid
simply responds to changes in pore volume caused by mechanical dynamic loading; the average pore pressure does not vary significantly in the analysis [14]. It is known, however, that pore pressure may build up considerably during cyclic shear loading. It is important to incorporate this physical process in the coupled nonlinear dynamic analysis. Martin et al. [16] proposed the following empirical equation that relates the increment of volume decrease, Devd, to the cyclic shear strain amplitude, g:
Devd ¼ c1 ðgc2 evd Þ þ
c3 e2vd gc4 evd
ð1Þ
where C1, C2, C3 and C4 are constants. It is noteworthy in Eq. (1) that the increment of volume strain decreases as volume strain is accumulated. Byrne [17] suggested the following simpler formula: Devd e ¼ c1 exp c2 vd ð2Þ
g
g
where C1 and C2 are constants with different interpretations from Eq. (1). C1 can be derived from relative density, Dr as follows: C1 ¼ 7600ðDr Þ2:5
ð3Þ
Further, using an empirical relation between Dr and normalized standard penetration test values, (N1)60 as Dr ¼ 15ðN1 Þ0:5 60
ð4Þ
Therefore, C1 ¼ 8:7ðN1 Þ1:25 and in many cases C2 ¼0.4/C1 [14]. 60 The mentioned formulation is available in FLAC as a built-in model and was adopted in this study along with a bilinear, elasticperfectly plastic stress–strain relationship and Rayleigh damping. Therefore during dynamic analysis, as effective stresses decrease with increase in pore pressure, the soil begins to yield and increments of permanent deformation are accumulated. The simultaneous coupling of pore pressure generation with nonlinear, plasticity based, stress analysis produces a more realistic dynamic response than can be achieved with the equivalent linear method [13]. The approach described above has been verified in the literature through analysis of well documented case histories [18,19] and was adopted herein for the dynamic analysis of embankment dams with shell of reinforced cohesive soil.
3. Numerical model and material properties 3.1. Model geometry and soil properties Two-dimensional plane strain models of the reinforced embankment dam were considered in the parametric analyses of this study. The geometry of the base model is shown in Fig. 1. The embankment dam is constructed of clay with physical and mechanical properties typical of compacted in-situ clay soils. Based on previous experience in actual embankment dam projects, the reinforced dam was assumed to be constructed on an alluvial foundation. Physical and mechanical properties of the embankment and foundation soil used in the numerical models are given in Table 1. The embankment consists of an upstream and downstream shell of cohesive soil reinforced with non-woven geotextile layers. The central core of the embankment was left unreinforced in order to act as a seepage barrier, since the permeable horizontal reinforcements promote seepage through the embankment. Three dam heights of 15, 25 and 40 m were considered in the parametric analyses in order to assess the effect of dam height on the seismic behavior of the reinforced dam. The stable side slopes for each height were determined through performing trial analyses, in which reinforced upstream and downstream slopes were constructed following an approach
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3m
H 3H
3H
Quiet boundary
Inputt motion
H
0.5H
Free field
Free field
Fig. 1. Schematic view of the base model used for performing the dynamic analyses.
Table 1 Material properties of embankment and foundation soils. Parameter
Foundation
Embankment
Dry unit weight (kg/m3) Elastic modulus (MPa) Poisson’s ratio Drained internal friction angle (1) Drained cohesion (KPa) Porosity Permeability (m/s) Normalized SPT number (Blows)
1900 50 0.3 35 3 0.3 10 8 —
1660 7 0.35 28 10 0.37 10 9 25
described below, and the side slopes were altered in consecutive analyses while monitoring the displacements of the crest. For each height, once the horizontal and vertical crest displacements were confined within tolerable limits, the resulting side slopes were adopted for that height in the parametric analysis. Stable side slopes obtained through the aforementioned procedure were 2.5, 3 and 3.5 (horizontal, to one vertical) for the three dam heights of 15, 25 and 40 m, respectively. The finite difference grid dimensions were selected taking into account the maximum frequency, f, of the shear wave that the model could respond to during earthquake loading. This frequency is determined by the following equation [20]: f¼
Cs 10Dl
ð5Þ
where Cs is the shear wave velocity of the soil and Dl is the largest grid zone size in the model. Referring to Eq. (5), a uniform zone size of 0.5 m 0.5 m was selected and since the lowest shear wave velocity in the model belongs to the embankment soil, the highest admissible frequency for a propagating shear wave is 7.9 Hz. Therefore the input earthquake record will have to be filtered by a low pass filter to remove frequency components higher than 7.9 Hz. A frequency of 5 Hz was ultimately selected for the low pass filter to account for the reduction in shear wave velocity that may occur due to plastic flow during seismic loading. Although optimal design of the reinforcement configuration was not intended, the proposed configuration was checked for adequate embedment length. The method suggested by Federal highway Administration (FHWA) [21] for minimum embedment length of reinforced soil slopes was followed. Stability analyses were performed using RSS limit equilibrium code developed by FHWA. The calculations performed showed that the proposed design provides adequate embedment lengths against pullout in all the models considered. 3.2. Reinforcement modeling and properties The geotextile layers were modeled using the one-dimensional linear, elastic–plastic cable elements readily available in the finite
difference code. Cable elements were originally designed to model structural elements in which tensile capacity is important and the bending resistance is negligible. There are several reports available in the literature regarding the successful employment of cable elements as geotextile reinforcements [22–24]. Since the original formulation was intended for nails and bolts, some adjustments to the input properties of cable elements are necessary in order to match manufacturer-provided specifications of geotextiles with the physical and mechanical input parameters in the numerical code. The behavior of the cable element and the required input parameters are described in the next section. Cable behavior is characterized by two distinct properties, which include axial behavior of the reinforcement element and the constitutive behavior of the soil–reinforcement interface. Both aforementioned properties must be specified in order to achieve a realistic model of the actual reinforcement behavior. Cable elements are assumed to follow a linear elastic behavior both in tension and compression, with tensile and compression yielding limits specified, beyond which a perfectly plastic yield occurs. The axial stiffness of cable elements is described in terms of its crosssectional area, A, and Young’s modulus, E. The geotextile reinforcement stiffness obtained from wide width tensile test may be employed to specify the Young’s modulus of the cable element in the finite difference modeling. In doing so, the Young’s modulus is obtained by dividing the manufacturer-provided tensile stiffness of the geotextile by its thickness. A thickness value in the range of 1–5 mm is typical for geotextiles as specified by manufacturers. The value of the ultimate tensile strength of the reinforcement is taken the same as the tensile yield strength of the cable element, and a small compression limit is also usually specified. The interface between the geotextile and the base soil is modeled using grout elements available in the finite difference code, which was initially supplied for the modeling of concrete grouts in soil nail and rock bolt modeling. Grout elements are characterized by shear and normal behavior. The shear behavior of the grout annulus is represented by a spring-slider system attached to the nodal points of the reinforcement. Grout shear stiffness governs the magnitude of the relative displacements between geotextile and the base soil. The maximum shear force mobilized in the grout annulus follows a Mohr–Coulomb failure criterion. The above-described formulation of the interface system allows for relative shear displacements between the reinforcement and the base soil to occur, hence permitting pullout of geotextile to be modeled. In the normal direction, however, the nodes of the geotextile are slaved to the base soil and will therefore deform as the finite difference grid representing the base soil deforms. The horizontal geotextile layers placed within the upstream and downstream shells of the embankment dam were modeled using linear, elastic–plastic cable elements with the abovedescribed properties. In order for the conceptual study of this research to be representative of actual conditions, several geotextile specifications provided by different manufacturers
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were observed, and the geotextile properties were extracted from these specifications to represent a low to medium strength nonwoven geotextile product. The main reason for selecting non-woven geotextiles was to take advantage of its lower stiffness, which allows it to conform with the soil as it deforms. Moreover, as reported in the literature, the in-plane drainage characteristics of the non-woven geotextile prevents pore pressure build up during staged construction of the embankment [1,2,8,25,26]. Accordingly, the reinforcement stiffness was taken as 25 kN/m. The tensile yield strength of the reinforcement was set to 15 kN/m, which is also a typical value for non-woven geotextiles. The relatively lower value for the tensile strength means that reinforcement rupture will be an anticipated failure mechanism in the analyses. The interface between the reinforcement and the soil was modeled by the grout annulus described above. The grout was considered to have negligible thickness. The mechanical properties of the interface are usually specified in terms of the properties of the base soil. In the absence of experimental data, results of previous studies were consulted in determining realistic properties for the clay–nonwoven geotextile interface. Athanasopoulos [27] performed direct shear tests on silty clay samples reinforced with non-woven geotextiles, and presented the interface properties in terms of an efficiency ratio, defined as the ratio of the interface properties to those of the base soil. Comparing the geotextile strength selected in the present study with the different geotextiles used by Athanasopoulos [27], it was observed that an approximate average efficiency ratio of 0.8 (considering tests performed on Terram 1500 geotextile) could be representative for the clay-geotextile interface properties of the present study. The interface properties of the grout, as described above, were determined by reducing base soil properties by a factor of 0.8. An equivalent thickness of 2 mm was adopted as the reinforcement thickness, which yields an equivalent cross-sectional area of 0.002 m2. In order to take into account the beneficial effects of the drainage properties of the non-woven geotextile reinforcements, the horizontal permeability of the reinforced zone was increased by a factor of one hundred [28]. Three vertical spacings of 0.5, 1 and 1.5 m were considered between geotextile layers in order to assess the effects of reinforcement spacing on the seismic behavior of the composite structure. 3.3. Dam construction and dynamic loading The technique of layered construction was employed in the static stress analyses. Since pore pressure generation during construction was a concern, the following procedures were used to model the static effective stress conditions: (a) The foundation was first placed as submerged soil and was forced to equilibrium.
(b) Embankment soil materials were divided into ten layers and were placed sequentially. Following the placement of each layer, reinforcement layers were added to the layer and the model was set to run for a time period equal to the estimated time required for actual construction of the layer under field conditions. The time needed was calculated by assuming an embankment construction speed of 1000 m3/day and multiplying this by the total fill volume of each layer. The fill volume was obtained by considering a crest length of 100, 200 and 300 m for the three dam heights of 15, 25 and 40 m, respectively. (c) The water level was then raised to full pool. Boundary water pressures were applied along the interior dam surface and the reservoir bed to account for water pressures. (d) Seepage analysis was performed to achieve steady state conditions within the embankment and the foundation. (e) Mechanical adjustment of stresses was allowed by performing mechanical calculations with flow calculations turned off, and forcing the model to equilibrium. During the process of layered construction, pore pressures within the embankment were monitored and when needed, embankment construction was halted and the model was run under coupled conditions for a six month period in order to allow for consolidation and dissipation of excess pore pressures. Once initial stresses for the steady state condition were achieved, the following steps were taken to prepare the model for dynamic analysis: (a) Apply dynamic boundary conditions: In order to enforce free field conditions in the numerical boundaries of the discretized half space foundation, free field boundary conditions available in the code were adopted for the lateral boundaries. As for the horizontal boundary, the simulation of outward propagating waves in the foundation was achieved by employing the absorbing boundary conditions also available in the finite difference code. Absorbing boundaries have been shown to be effective in absorbing outward propagating waves, and hence simulating half space conditions [29]. The viscous boundaries developed by Lysmer and Kuhlemeyer [30] are adopted in the finite difference code, and were employed in the analyses herein. One restriction in applying absorbing boundaries to numerical boundaries in a dynamic analysis is that such boundary conditions cannot be simultaneously applied to a boundary where acceleration or velocity input is applied, as prescribing acceleration or velocities to a boundary would nullify the effect of the absorbing boundary. In such situations it is necessary to convert acceleration or velocity inputs into stress waves, as described below. (b) Prepare input motion and apply seismic loading to the numerical model. Horizontal component of the acceleration record from Tabas earthquake was applied to the base of
Fig. 2. Acceleration time history of Tabas earthquake—horizontal component.
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Fig. 3. Displacement history at center of crest for 25 m dam with 1.5 m reinforcement spacing.
the model. Since quiet boundaries were already attributed to the horizontal boundary, the acceleration time history of the input motion was converted to shear stress waves, as described above. The process of converting an acceleration time history into a shear wave time history has been described elsewhere (Itasca [14]), and was verified by monitoring the acceleration time history of the horizontal boundary where the seismic input was applied. A nearly perfect match between the input acceleration time history and the time history recorded after applying the shear wave time history confirmed the validation of the process employed. There is a limit to the rate at which waves can be accurately transmitted through a grid. Kuhlemeyer and Lysmer [20] have suggested that for accurate wave transmission, the spatial element size should be less than eight to ten times the wavelength associated with the highest frequency content of the input motion (after Itasca [14]). Therefore, since the finite difference grid was chosen to have a grid spacing of 0.5 m, by the aforementioned suggestion, the input motion would have to be filtered by a low pass filter to remove frequency components exceeding 5 Hz. The horizontal acceleration component of Tabas earthquake after applying the aforementioned low pass filter is shown in Fig. 2. It can be seen that the filtered acceleration time history has a peak ground acceleration (PGA) of 6.8 m/s2. After preparing the input motion by filtering the acceleration time history and converting it to a shear stress time history, the resulting shear stress time history was prescribed to each of the grid points at the horizontal boundary where absorbent boundary conditions were previously prescribed. (c) Rayleigh damping was assigned to each element of the model in the mid-range between the natural frequency of the model and the predominant frequency of the input motion. The value of Rayleigh damping was chosen based on shear strains recorded from undamped analysis, by taking 65% of the peak recorded strain. The damping ratios obtained by this procedure ranged from 4% to 15%. (d) Dynamic analysis was performed for the duration of the earthquake, and results were extracted for interpretation and further assessment. It should be mentioned that for simplification purposes, the hydrodynamic interaction effects of the dam reservoir were neglected. Furthermore, the vertical component of the seismic input was not considered in the seismic loading, since the present study aims to provide qualitative results of the behavior of a reinforced dam under seismic loading conditions. In a real case, however, the horizontal and vertical components of the seismic motion would have to be applied to the dam simultaneously. Several studies have been performed to evaluate the effect of
30 1.5 1 0.5 Nonreinforced 25
20
15 0.00
0.05
0.10
0.15
0.25
0.20
0.30
0.35
30
25
20 1.5 1 0.5
15 0
0.1
0.2
0.3
0.4
0.5
0.6
Fig. 4. Distribution of displacement along height of 15 m high dam: (a) relative horizontal displacements and (b) relative vertical displacements.
vertical acceleration on reinforced earth structures including Ling and Leshchinsky [31] and Wolfe et al. [32]. It can be interpreted from these studies that the effect of vertical acceleration on the seismic response of reinforced earth structures depends on the magnitude of the horizontal and vertical peak acceleration.
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The effect of the vertical acceleration has been mentioned to mainly increase the required geotextile length, and to increase the required tensile reinforcement and the permanent displacements in some cases [31]. Although it is important to consider the simultaneous effect of horizontal and vertical components of earthquake motions in seismic design of earth dams as specified by design codes, in the present conceptual study, only the horizontal component has been considered in order to prevent modeling complications, and to reduce analysis time.
4. Results of dynamic analysis The computed deformation time history at crest level for one of the models consisting of a 25 m high dam with 1.5 m geotextile spacing is shown in Fig. 3. Results of the parametric analyses showed that reinforcing the dam decreases both horizontal and vertical crest displacements. Fig. 4 depicts the patterns of the relative displacements along the dam axis for 15 m dam height. Relative displacements were calculated as the difference between the displacements at the crest level and that of the base of the dam. It can be noted that all the reinforced dams show the same
Fig. 5. Displacements recorded at the end of shaking for 1.5 m reinforcement spacing: (a) horizontal displacement and (b) vertical displacement.
qualitative trend of displacements along the dam axis as the reinforced dam. As described by Gazetas [33], the trends observed in the dam models are representative of a second mode response of a shear beam, with the reinforced models showing a stiffer response in the reinforced zone as compared to the nonreinforced dam. Similar patterns were observed in the models with 25 and 40 m heights. Maximum displacements obtained at the end of earthquake loading for reinforced and non-reinforced models are also presented in Fig. 5. Displacements at the crest level were recorded as the difference between displacements of a node on the central axis at crest level and displacements of a node along the same axis at the base of the model. Maximum horizontal crest displacements in the unreinforced models of 15, 25 and 40 m dam height were 0.69, 0.76 and 0.89 m, respectively, while maximum recorded horizontal crest displacements of the reinforced dam with 0.5 m reinforcement spacing were 0.20, 0.21 and 0.44 m, respectively, for the same three heights considered. Moreover, maximum vertical crest displacements in the
Fig. 6. Shear strain reduction due to reinforcement. (a) Distribution along height of 15 m dam. (b) Variation with dam height and reinforcement spacing for three dam heights considered.
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unreinforced dam models with three heights of 15, 25 and 40 m were 0.38, 0.50 and 0.94 m, respectively, whereas in the reinforced dams with 0.5 m reinforcement spacing, these values reduced to 0.17, 0.18 and 0.42 m, respectively. Displacement values from models with geotextile spacing of 1 and 1.5 m showed similar trends. It can be deduced form Fig. 5 and the mentioned values, that maximum reductions of horizontal displacements due to reinforcing for the three dam heights of 15, 25 and 40 m were 3.35%, 2.09% and 1.15% of dam height, respectively, while maximum vertical displacements diminished by 2.18%, 1.55% and 1.30% of dam height, respectively. These values show that beneficial effects of reinforcing the dam decrease as the dam height increases. Fig. 6a compares shear strain distribution along dam height of non-reinforced dam with dams having different reinforcement spacing. In general, peak shear strains decreased as a result of reinforcement. Reduction of peak shear strain for three dam heights and three geotextile spacing considered is summarized in Fig. 6b. Peak shear strain reduction due to reinforcement was generally higher in dams with lower heights and less reinforcement spacing. Maximum reductions of peak shear
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strain due to reinforcement of the shell obtained at the end of shaking were 19.7%, 18.5% and 12.8% for three dam heights of 15, 25 and 40 m, respectively. Shear stress history from one of the models is shown in Fig. 7. Shear stress history consists of higher frequencies and amplitudes in the initial portion of the shaking, both decreasing as shaking continues. This behavior is a result of gradual decrease in soil stiffness and shear strength due to buildup of excess pore pressure, an important mechanism affecting the dynamic response. This recorded response shows that the coupled nonlinear model used in the dynamic analyses was able to appropriately capture the basic response behavior of soil under seismic loading. Acceleration time history obtained at the crest of 15 m high dam height with 1.5 m geotextile spacing is plotted in Fig. 8. There is a clear amplification of the response for low amplitude cycles of the input motion, especially towards the end of shaking. It is known that amplification is a result of elastic response. Higher amplitude cycles cause yield of embankment material which in turn dissipates input energy and prevents amplification of the response. This behavior is evident from the plot of crest
Acceleration (m/sec 2)
Fig. 7. Shear stress history at point A of 15 m high dam with 1.5 m reinforcement spacing.
6 4 2 0 -2 -4 -6 0
4
8
12
16
20
24
28
20
24
28
Time (sec)
Acceleration (m/sec 2)
6 4 2 0 -2 -4 -6 -8 0
4
8
12
16
Time (sec) Fig. 8. Acceleration time history recorded at the base and crest of 15 m high dam with 1.5 m reinforcement spacing—(a) base acceleration and (b) crest acceleration.
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Fig. 9. Variation of amplification factor for reinforced and non-reinforced models.
acceleration time history shown in Fig. 8, and can be supported by the plot of displacement time history from Fig. 3, where significant displacements occur as a result of intense shaking. It can be seen that from seconds 8 to 12 of the earthquake loading, where the peak acceleration pulse is observed, less amplification of peak acceleration is observed at crest level, which is due to yielding of the embankment soil. Fig. 9 compares amplification values for the different models considered in the parametric analyses. It can be seen that as the vertical reinforcement spacing decreases in the embankment, amplification of the input motion increases. Once again, this behavior can be attributed to the tendency for elastic response in the reinforced dam as a result of decrease in shaking-induced displacements. The distribution and magnitudes of maximum recoded geotextile load, Tmax, in the upstream and downstream section of each dam at the end of shaking are plotted in Fig. 10. Maximum load value recorded at each level corresponds to the maximum tensile load recorded along the entire reinforcement length at that level. Different patterns were observed in the upstream and downstream reinforcements. The peak reinforcement load along the upstream occurs at nearly one third of the height of the reinforced zone. This pattern becomes more evident as the dam height increases, where the ratio of maximum to minimum reinforcement load exceeds 5. In the downstream reinforcements, however, a more uniform distribution of maximum load with height was observed, especially in the upper half of the reinforced zone. Comparison of the maximum mobilized reinforcement load with the tensile strength of the reinforcements indicates that the rupture of the geotextile layers did not occur during the seismic loading. Since relatively large deformations were recorded after the shaking, it is postulated the weak geotextile–soil interface properties resulted in slippage at the interface, preventing full mobilization of the reinforcement strength.
5. Conclusions The results of parametric seismic analyses of embankment dam with shells of reinforced cohesive soil have been reported. Three dam heights of 15, 25 and 40 m, as well as three vertical reinforcement spacing of 0.5, 1 and 1.5 m were considered in the analyses. Several features of the dynamic response to actual acceleration time history are summarized below:
Fig. 10. Distribution of maximum reinforcement load along height of the embankment. (a) Upstream and (b) downstream.
1- Reinforcement of the dam decreased both crest displacements and displacements along the height of the dam. Amount of decrease in horizontal displacements for three heights of 15, 25 and 40 m were 3.35%, 2.09% and 1.15% of dam height, respectively, while maximum vertical displacements reduced at 2.18%, 1.55% and 1.30% of dam height, respectively. 2- Strain distribution along height of the dam decreased as a result of reinforcement. It was observed that maximum reduction in shear strains due to reinforcement increased when reinforcement arrangements with lower vertical spacing were considered. Moreover, beneficial effects of reinforcement diminished as dam height increased. 3- Input acceleration was amplified at the crest level due to reinforcement. The amplification factor ranged between 1.05 and 1.48. The low amplification factors observed were attributed mainly to the high amount of damping due to yielding of embankment material. Reinforcing the embankment increased the elastic response and resulted in higher amplification as compared to the non-reinforced dam. 4- Different patterns of maximum tensile load distribution were observed along the upstream and downstream reinforcements.
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Maximum tensile load along the upstream occurred at around one third of the reinforced zone height, while relatively uniform distribution was observed along the downstream.
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