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Modeling of the compaction-induced stress on reinforced soil walls
Geotextiles and Geomembranes 43 (2015) 82e88
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Technical note
Modeling of the compaction-induced stress on reinforced soil walls S.H. Mirmoradi*, M. Ehrlich Dept. of Civil Engineering, COPPE, Federal University of Rio de Janeiro, UFRJ, RJ 21945-970, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 March 2014 Received in revised form 26 October 2014 Accepted 17 November 2014 Available online 3 December 2014
A new simple analytical procedure (AASHTO modified) that includes the effect of the induced stress due to backfill compaction for use with conventional design methods of geosynthetic reinforced soil (GRS) walls is proposed. The proposed analytical procedure may be used with any conventional design methods that do not take into consideration the effect of the compaction-induced stress in their calculations. This approach is based on an equation suggested by Wu and Pham (2010) to calculate the increase in lateral stress in a reinforced soil mass due to compaction. Additionally, two numerical procedures for modeling of compaction are described. Analyses using these procedures were performed to evaluate the capability of the proposed analytical procedure. The results were compared with values predicted using the Ehrlich and Mitchell (1994) method, the modified version of the K-stiffness method (Bathurst et al., 2008) and the AASHTO simplified method. The results show that the AASHTO modified method and the numerical analyses, in which the compaction-induced stress was modeled using two distributed loads at the top and bottom of each soil layer, resulted in values of the maximum reinforcement tension, Tmax, that agree with those from the full-scale test and those calculated by Ehrlich and Mitchell (1994). On the other hand, the K-stiffness method under-predicts the measured Tmax values. Moreover, numerical modeling of compaction using a distribution load only at the top of each soil layer overestimated the measurements. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics GRS walls Analytical procedure Numerical modeling Compaction-induced stresses
1. Introduction The importance of backfill soil compaction on the behavior of geosynthetic reinforced soil (GRS) walls has been demonstrated by a number of laboratory and case studies (Ehrlich and Mitchell, 1994; Bathurst et al., 2009; Ehrlich et al., 2012). Compaction promotes displacement during the construction period and reduces both settlement and horizontal displacement due to surcharge load application after construction. In other words, compaction may lead the reinforced soil mass to exhibit a kind of over-consolidation that promotes a stiffer behavior after construction. Additionally, compaction may be the major contributor to reinforcement tension at shallow depths (Ehrlich and Mitchell, 1994, 1995; Ehrlich et al., 2012; Mirmoradi and Ehrlich, 2014b). However, in most of the current design methods for GRS walls, the effect of the compaction-induced stress is not explicitly taken into consideration (e.g., the AASHTO, 2012 simplified method).
* Corresponding author. E-mail addresses: [email protected] (S.H. Mirmoradi), [email protected] (M. Ehrlich). http://dx.doi.org/10.1016/j.geotexmem.2014.11.001 0266-1144/© 2014 Elsevier Ltd. All rights reserved.
Ehrlich and Mitchell (1994) presented an analytical procedure for the internal design of reinforced soil walls that was based on working stress conditions. This method explicitly takes into account the effect of compaction-induced stress, reinforcement, and soil stiffness properties. Comparison of the predicted results using this method showed good agreement with measured reinforcement tension data for several full-scale walls containing a range of reinforcement types. In recent decades, several numerical analyses using the finite element method (FEM) or finite difference method (FDM) codes have been undertaken to consider the different geometries and parameters in GRS walls. Examples are reported by Hermann and Al-Yassin (1978), Naylor (1978), Ho and Rowe (1997), Rowe and Ho (1998), Helwany et al. (1999), Ling and Leshchinsky (2003), Hatami and Bathurst (2005), Guler et al. (2007), and Mirmoradi and Ehrlich (2013), among others. However, the effect of backfill soil compaction has rarely been considered. Hatami and Bathurst (2005) and Guler et al. (2007) numerically considered the effect of the induced stress due to backfill compaction using FDM (finite difference-based fast Lagrangian analysis of continua program; Itasca Consulting Group, 2001) and FEM (PLAXIS). In both studies, the compaction-induced stresses were modeled using a uniform
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vertical stress applied only to the top of each backfill soil layer as the wall was modeled from the bottom up. Ehrlich and Mirmoradi (2013), Mirmoradi and Ehrlich (2014a,b) and Riccio et al. (2014) simulated the compaction-induced stress by applying an equal distribution load at the top and bottom of each soil layer. This approach is based on the procedure used by Dantas (2004) and Morrison et al. (2006) for the consideration of the induced stress due to backfill soil compaction. The objective of the present study is to propose a simple analytical method (AASHTO modified) for the determination of Tmax that includes the effect of backfill soil compaction. The proposed procedure is based on that suggested by Wu and Pham (2010). The results using the proposed procedure are compared with the results of the numerical modeling using the two compaction procedures as discussed above, the AASHTO (2012) simplified method, the Ehrlich and Mitchell (1994) method and the modified version of K-stiffness method (Bathurst et al., 2008).
where Ds0h;c and Sv are the increases in effective lateral stress due to backfill compaction and the vertical reinforcement spacing, respectively. A procedure was suggested by Wu and Pham (2010) for calculating the increase in lateral stress in a reinforced soil mass due to compaction:
Ds0h;c ¼ Ds0v;c max Ki;c F 1 þ
Ehrlich and Mitchell (1994) suggested a procedure for the internal design of reinforced soil walls that explicitly takes into account the effect of the induced stress due to backfill compaction. Nevertheless, conventional designs of reinforced soil walls usually do not take into consideration the effect of the compaction-induced stress in their calculations. A new simple procedure that includes the effect of the induced stress due to backfill compaction for use with any conventional design methods is described, as follows. For the compacted backfill soil, the value of the maximum tension in the reinforcement may be determined by:
Tmax ¼ Tmax;g þ Tmax;c
(1)
where Tmax,g and Tmax,c represent the values of the maximum mobilized tension in the reinforcement due to geostatic stress and compaction-induced stress, respectively. Tmax,g corresponds to the tension of reinforcement due to geostatic stress, and it may be calculated using any conventional design method that does not take into consideration the effect of the compaction-induced stress on determination. Based on the AASHTO (2012) simplified method, for example, the value of the maximum tensile stress in the reinforcement is determined by using the following equations:
Tmax;g ¼ KSv gz þ q
(2)
wherez is the depth of the reinforcement layer under the crest of the wall, g is the soil unit weight, Sv is the vertical reinforcement spacing, q is the surcharge pressure, and K is the active earth pressure coefficient, as determined by:
K¼
cos2 ∅ þ u cos2 uð1 þ ðsin∅=cos uÞÞ2
(3)
where ∅ and u are the peak friction angle of the soil and the facing inclination from vertical, respectively. Note that the use of the AASHTO (2012) simplified method for Tmax,g determination may be reasonable for situations where there is enough lateral strain mobilization in the reinforced soil mass to reach soil plastic condition (Ka condition); that hypothesis may be considered for typical polymeric reinforcements. The increase of the value of the maximum mobilized tension in the reinforcement due to the induced stresses due to backfill compaction, Tmax,c, is determined by:
Tmax;c ¼ Ds0h;c Sv
(4)
0:7Er Es Sv 0:7Er
(5)
where Ds0v;c max , Ki,c, Es, Er, and Sv are the maximum increases in effective vertical stress due to backfill compaction, lateral earth pressure coefficient, soil stiffness, reinforcement stiffness, and reinforcement spacing, respectively. The value of F can be calculated based on Seed (1983) and Ehrlich and Mitchell (1994) according to
OCR OCRsin4 OCR 1
F ¼1 2. Analytical compaction modeling
83
(6)
where OCR and 4 are the over-consolidation ratio and internal friction angle, respectively.
(
. 0 0 OCR ¼ szc;i sz ;
0
0
szc;i > sz 0
OCR ¼ 1;
0
szc;i sz
(7)
0
where sz is the effective vertical stress on each layer at the end of construction. The compacted soil layers are relatively thin, thus it may be assumed that all points in the backfill soil layers are driven 0 to the same vertical induced stress, szc;i , due to compaction. Therefore, the value of the maximum increase in the vertical stress due to compaction in each depth may be calculated as follows:
(
0
0
sv;c max ¼ szc;i g0 z; 0
sv;c max ¼ 0;
0
szc;i > g0 z 0
szc;i g0 z
(8)
Wu and Pham (2010) suggested the Westergaard solution (1938) for calculating the maximum increase in the vertical stress due to backfill compaction. Fig. 1 shows a comparison of the increase in the lateral stress due to backfill soil compaction in a reinforced soil mass presented by Pham (2009) and Wu and Pham (2010) and results based on the mentioned approach (Eq. (8)), assuming that Ki,c is equal to the active Rankine condition, Ka. As previously discussed, the use of the active condition (Ka) may be considered reasonable for soils reinforced with conventional polymeric reinforcements. The results are related to a 6 m high GRS mass for five different values of the vertical maximum pressures due to compaction (44, 100, 200, 300, and 500 kPa). Fig. 1 shows that the results determined by the two procedures differ significantly. It is also notable that the increase in lateral stress determined using Eq. (8) would approach zero at compaction influence depth, Zc, that is a larger depth compared with the results of Pham (2009) and Wu and Pham (2010) and this discrepancy would be 0 greater for the higher value of szc;i . The compaction influence depth Zc, is defined as follows (Ehrlich and Mitchell, 1994): 0
Zc ¼
szc;i
(9)
g 0
where szc;i and g are the vertical stresses induced during compaction and the soil unit weight, respectively. Note that zero increase of lateral stress (for Z > Zc) means that the geostatic stress overcomes the induced stress due to compaction and the effect of compaction is no longer felt by the soil.
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0
Kp-1
1
Depth of Wall, m
2
3
4 44 kPa
100 kPa
5
Fig. 2. Vertical stress increase during a roller operation in the backfill soil (strip load e Boussinesq elastic solution).
200 kPa 300 kPa 500 kPa
6 0
50 100 Lateral stress increase, kPa
Fig. 1. Depth of wall versus lateral stress increase. The solid line represents values from Pham (2009) and the dotted line indicates the suggested procedure.
3. Numerical compaction modeling The effect of the induced stresses due to backfill soil compaction on the behavior of GRS walls has rarely been numerically modeled. Hatami and Bathurst (2005) using FDM (finite difference-based fast Lagrangian analysis of continua program; Itasca Consulting Group, 2001) and Guler et al. (2007) using FEM (PLAXIS) simulated the compaction-induced stresses using a uniform vertical stress applied only to the top of each backfill soil layer as the wall was modeled from the bottom up. Ehrlich and Mirmoradi (2013), Riccio et al. (2014) and Mirmoradi and Ehrlich (2014b) simulated the compaction-induced stress by applying an equal distribution load at the top and bottom of each soil layer. The difference between the two approaches on representation of the actual field behavior are presented and discussed in Mirmoradi and Ehrlich (2014a), and are summarized as follows: Fig. 2 shows a schematic view of the vertical stress increase during a roller operation in backfill. The vertical stress at the top of each layer during the compaction roller operation may be represented by a strip load and an elastic solution can be used to represent its evolution with depth. As shown in Fig. 2 for each soil layer, the maximum stress increase during the roller operation occurs at soil-roller contact and decreases with depth. Ehrlich and Mitchell (1994) stated that “In multilayer construction, the compacted layers are relatively thin, typically 0.15e0.3 m thick, and all points in each soil layer may be assumed to have been driven to the same maximum soil stress state during compaction”. Therefore, it may be assumed that all points in the soil layers are driven to the 0 same vertical induced stress, szc;i , due to compaction. Fig. 3 shows two different approaches for the simulation of the induced stress due to compaction. Fig. 3a and b show a schematic view of the numerical modeling of compaction-induced stress using a distributed load, qc, at the top of each soil layer (hereafter
referred to as procedure type 1) and distribution loads, qc, at the top and bottom of each soil layer (hereafter referred to as procedure type 2), respectively. Stage construction is used in both procedures and compaction modeling is represented by only one cycle of loading and unloading for each soil layer. In Fig. 3, four steps for backfill soil construction in a specific soil layer “n” were considered: (I) soil layer placement, (II) compaction equipment operation, (III) end of compaction, and (IV) next soil layer placement (layer “n þ 1”). Fig. 3a, step (II) shows that when procedure type 1 is used for numerical modeling of the induced stresses due to compaction in soil layer “n”, it leads to the constant increase of the vertical stress due to compaction, qc, in all the layers placed bellow. The dashed line in this figure shows the expected vertical stress increase during the roller operation for soil layer “n” based on the strip load elastic solution, where its maximum value takes place at soil-roller contact and decreases significantly with depth. This figure clearly shows that using the distribution load only at the top of each soil layer for modeling of compaction may not correspond to the actual field condition represented by the elastic solution. Fig. 3b shows a schematic view of the procedure type 2 as suggested by Ehrlich and Mirmoradi (2013) and Mirmoradi and Ehrlich (2014a,b) for the numerical simulation of the induced stress due to compaction. Fig. 3b, step (II) shows that when procedure type 2 is used for the soil layer “n”, all points in this soil layer would be driven to the same vertical stress increase. In addition, for the soil layers placed under this layer, only geostatic stresses occur. A comparison between the curves related to the compaction modeling using procedure type 2 and the dashed line represented by the elastic solution indicates that this procedure may be more representative of the actual induced vertical stress during the roller operation. 4. Numerical model The numerical modeling was carried out using the twodimensional finite-element program PLAXIS (Brinkgreve and Vermeer, 2002). Full-scale reinforced soil wall modeling performed at the Geotechnical Laboratory of COPPE/UFRJ was used for the validation of the numerical analyses (Ehrlich and Mirmoradi, 2013). The physical model was 1.4 m high and surcharge load was applied up to 100 kPa at the end of construction. That physical model may be assumed representing a portion of a 6.8 m high prototype (Fig. 4). The numerical modeling of the prototype was
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85
Fig. 3. Modeling of the vertical stress load-unload cycles verified during the compaction of the backfill soil layer “n”: a: procedure type 1, b: procedure type 2, (I) soil layer placement, (II) compaction, (III) end of compaction, and (IV) next soil layer placement (layer “n þ 1”).
validated using results of the physical model (Ehrlich and Mirmoradi, 2013). Details of the physical model, numerical modeling of the prototype and the relation between them can be found in Ehrlich and Mirmoradi (2013). In this study the numerical model was validated against the configuration of the full-scale laboratory test. The 1.4 m high wall with wrapped facing was modeled with an inclination of 6B to the vertical. The length and the vertical spacing of the reinforcement were 2.1 and 0.4 m, respectively. A hardening soil model was applied. Hyperbolic stressestrain curves were arranged to fit the data measured from laboratory plane-strain tests. Curves were fitted considering lower strain (<1%) in order to better represent the working stress conditions verified in the physical model test
Fig. 4. View of the prototype and physical model.
ref ¼ 3E ref was used, (Ehrlich and Mirmoradi, 2013). The value of Eur 50 which is the default of PLAXIS. The value of m was chosen based on the value suggested by Janbu (1963), who reported values of m of about 0.5 for Norwegian sands. Reinforcement was modeled as a linear elastic material with perfect interface adherence to the adjacent soil. Jewell (1980) and Dyer and Milligan (1984) have shown that perfect adherence is a reasonable assumption for soil-reinforcement interface under working stress conditions. 15-node triangular element was used to model soil layers and a fine mesh was used to discretize the system. Note that the types of structural elements are automatically taken to be compatible with the soil element type. A fixed boundary condition in the horizontal direction was employed on the right-lateral border. At the bottom of the model, a fixed boundary condition in both the horizontal and vertical directions was applied. Table 1 lists the input parameters used in this study. The backfill soil stiffness and shear strength parameters were determined from plane-strain tests. In simulating wall construction in the numerical analyses, soil layers were placed every 0.2 m and compacted until the final wall height was achieved. Compaction was simulated using procedure type 2 by applying a single loadunload stress cycle with a 63 kPa distributed load at the top and bottom of each backfill soil layer. Fig. 5 shows a comparison of the measured values of the maximum tension mobilized in the 2nd, 3rd, and 4th reinforcement layers, Tmax, in the physical model with those determined by PLAXIS for the prototype and for the model at the end of construction (dotted lines) and under a surcharge value of 100 kPa (solid lines). Note that the Tmax values of the reinforcement layers “a,” “b,” and “c” in the prototype were representative of the 2nd, 3rd, and 4th reinforcement layers in the physical model (see Fig. 4). Fig. 5 shows a reasonable agreement between the measured and calculated values of Tmax in individual reinforcement layers at the end of construction. However, under the condition of surcharge
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32
Table 1 Input parameters for numerical analysis. Value
Soil Model Peak plane-strain friction angle, 4 ( ) Cohesion, c (kPa) Dilation angle, J ( ) Unit weight, g (kN/m3) ref (kPa) E50 ref (kPa) Eoed ref (kPa) Eur Stress dependence exponent, m Failure ratio, Rf Poisson's ratio, y Reinforcement Elastic axial stiffness (kN/m) Wrapped face Elastic axial stiffness (kN/m) Elastic bending stiffness (kNm2/m)
HS 50 1 0 21 42,500 31,800 127,500 0.5 0.7 0.25
2
4
16 12 8 4
0
6
1
2
3 4 Equivalent depth, m
5
6
Fig. 6. Comparison of measured and determined summations of the maximum tension along the 2nd, 3rd, and 4th reinforcement layers. The vertical dashed line indicates the compaction influence depth, Zc.
8
10
Measured PLAXIS, Model
Depth of Wall, m
20
0 60 1
0
0.2
24
Zc
600
Tmax, kN/m 0
Summation of Tmax, kN/m
Property
Measured AASHTO AASHTO Modified E&M, NC E&M, 63 kPa K-stiffness PLAXIS, NC PLAXIS, Type 2 PLAXIS, Type 1
28
PLAXIS, Prototype
0.4
0.6
0.8
1
1.2 Fig. 5. Comparison of measured value of the maximum tension along the 2nd, 3rd, and 4th reinforcement layers with those determined by PLAXIS for the prototype and for the model at the end of construction (dotted lines) and under a surcharge value of 100 kPa (solid lines).
loading there is relatively large discrepancy between the results. This behavior may be associated to a local redistribution of load between reinforcements. Note that good agreement was observed between measured and numerically determined value of summation of the maximum tension mobilized in the reinforcement, P Tmax, even under the condition of surcharge loading (see Fig. 6). Additionally, comparison of the two different numerical studies (prototype and model) also presents a good agreement at the end of construction and under 100 kPa surcharge value. These results support the correspondence between the physical model and the prototype, as discussed by Ehrlich and Mirmoradi (2013). 5. Results and discussion In order to verify the analytical and numerical modeling of compaction induced stress in GRS walls using the procedures
described above, the measured values of the summation of the P Tmax, was maximum tension mobilized in the reinforcement, compared with those determined by PLAXIS for compaction procedures type 1 and 2, the AASHTO methods and the values predicted by the Ehrlich and Mitchell (1994) and the K-stiffness methods in Fig. 6. Note that the geometry of the prototype was used for the analyses. The vertical dotted line in Fig. 6 represents the compaction influence depth, Zc (see Eq. (9)). The equivalent depth of the soil layer (Zeq) is defined by:
Zeq ¼ Z þ
q g
(10)
where Z and q are the real depth of a specific layer and the surcharge load value of the physical model, respectively. As shown in Fig. 6, the values measured from the physical model were properly captured by the AASHTO modified method, the Ehrlich and Mitchell 1994 method, and the numerical (PLAXIS) method using compaction procedure type 2. However, regardless of the value of Zeq, the curve corresponding to the numerical simulation using compaction procedure type 1 overestimates the values P of Tmax and this discrepancy increases with equivalent depth. Note that for the curve corresponding to the AASHTO modified method, the values of Tmax determined by the AASHTO simplified method were modified using the simple analytical procedure described earlier to take into consideration the effect of the compaction-induced stress in calculations. On the other hand, the K-stiffness method underpredicts the measured values of the tension in the reinforcements. Calculation using the modified version of K-stiffness method (Bathurst et al., 2008) was performed for the value of the elastic modulus of the facing column equal to 35,000 kPa as suggested by Allen et al. (2003) and assuming the width of the facing wrap was 1 m. Note that K-stiffness method is an empirically based method and as all empirical models, its predictions may be valid for structures with similar features, such as soil type, compaction equipment and reinforcement strength/ deformability. Additional discussion about the prediction capability of this method and other common used procedures could be found in Mirmoradi and Ehrlich (2014b) who numerically evaluated the behavior of GRS walls with segmental block facing under working stress conditions. Comparison of the results corresponding to the conditions with and without induced stresses due to compaction illustrates that for
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Tmax, kN/m 0
5
Tmax, kN/m
10
0
15
0
0
Depth of Wall, m
2
3
PLAXIS, NC PLAXIS, Type 2 PLAXIS, Type 1 E&M, NC E&M, 63 kPa AASHTO AASHTO Modified
Zc
4
1
2 Depth of Wall, m
1
87
5
10
15
20
PLAXIS, NC PLAXIS, Type 2 PLAXIS, Type 1 E&M, NC E&M, 120 kPa AASHTO AASHTO Modified
3
4
5 Zc
5 6
6
7
7 Fig. 8. Depth of wall versus individual values of Tmax at the end of construction; 0 szc;i ¼ 120 kPa.
Fig. 7. Depth of wall versus individual values of Tmax at the end of construction; 0 szc;i ¼ 63 kPa.
6. Conclusions
P compacted backfill soil walls, when Zeq < Zc, the values of Tmax are greater than the values obtained for the no-compaction conditions. However, for Zeq > Zc, the compaction-induced stress was overcome by the geostatic stress and the values determined are the same irrespective of whether or not the induced stress due to the backfill soil compaction is considered in the analysis. In Fig. 6, the results related to the condition without compaction are also shown. These curves were obtained with the Ehrlich and Mitchell (1994) method, the AASHTO simplified method, and by numerical modeling with PLAXIS. As the K-stiffness method implicitly includes the compaction-induced stresses on calculations, it may not be properly compared with the no-compaction conditions. The results show almost the same values for the nocompaction condition. However, the AASHTO simplified method P leads to lower Tmax values due to the assumption that the value of the lateral earth pressure coefficient is taken to be equal to Ka. Figs. 7 and 8 show a comparison of the maximum mobilized tension in each reinforcement layer, Tmax, versus depth determined with PLAXIS for the described numerical compaction modeling (type 1 and 2) and calculated values using the Ehrlich and Mitchell (1994) method and the AASHTO methods, for the compactioninduced stresses of 63 and 120 kPa, respectively. In Figs. 7 and 8, for the analyses in which the compaction modeling type 2 was used, a consistent representation of the expected behavior is found and discussed as follows. For Z > Zc, the effect of compaction vanishes because the geostatic stress overcomes the induced stress due to backfill soil compaction. Furthermore, Tmax is the same; regardless the induced stress due to backfill soil compaction is included (Z > Zc). However, when Z < Zc, Tmax would be greater than the corresponding values for the nocompaction condition. Nevertheless, for the analyses in which the compaction modeling was performed using procedure type 1, the Tmax values are much larger than the previous values and this overprediction increases with depth. Good correspondence is also observed for the determined results using the AASHTO modified method and the Ehrlich and Mitchell (1994) method.
A new simple analytical procedure (AASHTO modified) was proposed that includes the effect of the induced stress due to backfill compaction for use with conventional design methods of geosynthetic reinforced soil (GRS) walls. Note that the proposed analytical procedure may be used with any conventional design methods that do not take into consideration the effect of the compaction-induced stress in their calculations. The results of the proposed analytical procedure were compared with those measured from a compatible full-scale wrapped face wall experiment conducted at the Geotechnical Laboratory of COPPE/UFRJ and with numerical modeling results using two different procedures for the modeling the induced stress due to backfill soil compaction. The results were also compared with values predicted using the Ehrlich and Mitchell (1994) method, the K-stiffness method, the AASHTO simplified method. Analysis of the results showed that: The AASHTO modified method and the numerical modeling of compaction-induced stress using two distributed loads at the top and bottom of each soil layer (compaction procedure type 2) were shown to have a good predictive capability, as demonstrated by comparing the data from the physical model study and from calculated values using the Ehrlich and Mitchell (1994) analytical procedure. On the other hand, the K-stiffness method underestimated the measured value of tension in the reinforcement. Furthermore, the results show that modeling of compaction using a distribution load only at the top of each soil layer overestimated the measurements and the discrepancy increased with both depth and compaction effort. Comparison of the measured values of the tension in the reinforcement and those calculated with the AASHTO modified method, numerical modeling using compaction procedure type 2 and the Ehrlich and Mitchell (1994) method showed that for Z > Zc, the effect of vertical induced stress due to compaction vanishes because the geostatic stress overcomes the induced stress due to backfill soil compaction. Accordingly, the maximum tension mobilized in the reinforcement, Tmax, remains the same regardless
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if the analysis considers the induced stress due to backfill soil compaction. However, when Z < Zc, Tmax would be greater than that corresponding to no-compaction condition. References AASHTO, 2012. AASHTO LRFD Bridge Design Specifications, sixth ed. American Association of State Highway and Transportation Officials, Washington, D.C., USA. Allen, T.M., Bathurst, R.J., Holtz, R.D., Walters, D., Lee, W.F., 2003. A new working stress method for prediction of reinforcement loads in geosynthetic walls. Can. Geotech. J. 40 (5), 976e994. Bathurst, R.J., Miyata, Y., Nernheim, A., Allen, A.M., 2008. Refinement of K-stiffness method for geosynthetic-reinforced soil walls. Geosynth. Int. 15 (No. 4), 269e295. Bathurst, R.J., Nernheim, A., Walters, D.L., Allen, T.M., Burgess, P., Saunders, D.D., 2009. Influence of reinforcement stiffness and compaction on the performance of four geosynthetic reinforced soil walls. Geosynth. Int. 16 (1), 43e59. Brinkgreve, R.B.J., Vermeer, P.A., 2002. PLAXIS: Finite Element Code for Soil and Rock Analyses. Balkema version 8. Dantas, B.T., 2004. Working Stress Analysis Method for Reinforced Cohesive Soil Slopes. D.Sc. thesis. COPPE/UFRJ, Rio de Janeiro (in Portuguese). Dyer, N.R., Milligan, G.W.E., 1984. A photoelastic investigation of the interaction of a cohesionless soil with reinforcement placed at different orientations. In: Proc., Int. Conf. on in Situ Soil and Rock Reinforcement, pp. 257e262. Ehrlich, M., Mirmoradi, S.H., 2013. Evaluation of the effects of facing stiffness and toe resistance on the behavior of GRS walls. Geotext. Geomembr. 40, 28e36. Ehrlich, M., Mitchell, J.K., 1994. Working stress design method for reinforced soil walls. J. Geot. Eng. ASCE 120 (4), 625e645. Ehrlich, M., Mitchell, J.K., 1995. Working stress design method for reinforced soil walls disclosure. J. Geotech. Eng. ASCE 121 (11), 820e821. Ehrlich, M., Mirmoradi, S.H., Saramago, R.P., 2012. Evaluation of the effect of compaction on the behavior of geosynthetic-reinforced soil walls. Geotext. Geomembr. 34, 108e115. Guler, E., Hamderi, M., Demirkan, M.M., 2007. Numerical analysis of reinforced soilretaining wall structures with cohesive and granular backfills. Geosynth. Int. 14 (No. 6), 330e345. Hatami, K., Bathurst, R.J., 2005. Development and verification of a numerical model for the analysis of geosynthetic reinforced-soil segmental walls. Can. Geotech. J. 42 (4), 1066e1085. Helwany, S.M.B., Reardon, G., Wu, J.T.H., 1999. Effects of backfill on the performance of GRS retaining walls. Geotext. Geomembr. 17 (1), 1e16.
Hermann, L.R., Al-Yassin, Z., 1978. Numerical Analysis of Reinforced Soil Systems. ASCE Symp. Earth Reinf, Pittsburgh, PA, USA, pp. 428e457. Ho, S.K., Rowe, R.K., 1997. Effect of wall geometry on the behavior of reinforced soil walls. Geotext. Geomembr. 14, 521e541. Janbu, J., 1963. Soil compressibility as determined by oedometer and triaxial tests. In: Proceedings of the European Conference on Soil Mechanics and Foundation Engineering, Wiesbaden, vol. 1, pp. 19e25. Jewell, R.A., 1980. Some Effects of Reinforcement on the Mechanical Behavior of Soils. PhD thesis. Univ. of Cambridge, Cambridge, England. Ling, H.I., Leshchinsky, D., 2003. Finite element parametric study of the behavior of segmental block reinforced-soil retaining walls. Geosynthet. Int. 10 (3), 77e94. Mirmoradi, S.H., Ehrlich, M., 2013. Numerical evaluation of the behavior of reinforced soil retaining walls. In: Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering, Paris, pp. 773e776. Mirmoradi, S.H., Ehrlich, M., 2014a. Modeling of the compaction-induced stresses in numerical analyses of GRS walls. Int. J. Comput. Methods (IJCM) Special Issue “Comput. Geomech.” 11 (2), 14. Mirmoradi, S.H., Ehrlich, M., 2014b. Numerical evaluation of the behavior of GRS walls with segmental block facing under working stress conditions. ASCE J. Geotech. Geoenviron. Eng. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001235. Morrison, K.F., Harrison, F.E., Collin, J.G., Dodds, A., Arndt, B., 2006. Shored Mechanically Stabilized Earth (SMSE) Wall Systems Design Guidelines. Report FHWA-CFL/TD-06e001. Federal Highway Administration, Lakewood, Colorado, p. 210. Naylor, D.J., 1978. A Study of Reinforced Earth Walls Allowing Strip Slip. ASCE Symp. Earth Reinf, Pittsburgh, PA, USA, pp. 618e643. Pham, T.Q., 2009. Investigating Composite Behavior of Geosynthetic-reinforced Soil (GRS) Mass. A thesis submitted to the University of Colorado Denver In partial fulfillment of the requirements for the degree of Doctoral of Philosophy Civil Engineering, 358 pp. Riccio, M., Ehrlich, M., Dias, D., 2014. Field monitoring and analyses of the response of a block-faced geogrid wall using fine-grained tropical soils. Geotext. Geomembr. 42 (2), 127e138. Rowe, R.K., Ho, S.K., 1998. Horizontal deformation in reinforced soil walls. Can. Geotech. J. 35 (2), 312e327. Seed, R.M., 1983. Compaction-induced Stresses and Deflections on Earth Structure. PhD. thesis. University of California, Berkeley, CA, 447 pages. Westergaard, C.M., 1938. A Problem of Elasticity Suggested by a Problem in Soil Mechanics: a Soft Material Reinforced by Numerous Strong Horizontal Sheet. Contributions to the Mechanics of Solids, Stephen Timoshenko 60th Anniversary Volume. Macmillan, New York, pp. 268e277. Wu, J.T.H., Pham, T.Q., 2010. An analytical model for evaluation of compactioninduced stresses in a reinforced soil mass. Int. J. Geotech. Eng. 4, 549e556.
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Technical note
Modeling of the compaction-induced stress on reinforced soil walls S.H. Mirmoradi*, M. Ehrlich Dept. of Civil Engineering, COPPE, Federal University of Rio de Janeiro, UFRJ, RJ 21945-970, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 March 2014 Received in revised form 26 October 2014 Accepted 17 November 2014 Available online 3 December 2014
A new simple analytical procedure (AASHTO modified) that includes the effect of the induced stress due to backfill compaction for use with conventional design methods of geosynthetic reinforced soil (GRS) walls is proposed. The proposed analytical procedure may be used with any conventional design methods that do not take into consideration the effect of the compaction-induced stress in their calculations. This approach is based on an equation suggested by Wu and Pham (2010) to calculate the increase in lateral stress in a reinforced soil mass due to compaction. Additionally, two numerical procedures for modeling of compaction are described. Analyses using these procedures were performed to evaluate the capability of the proposed analytical procedure. The results were compared with values predicted using the Ehrlich and Mitchell (1994) method, the modified version of the K-stiffness method (Bathurst et al., 2008) and the AASHTO simplified method. The results show that the AASHTO modified method and the numerical analyses, in which the compaction-induced stress was modeled using two distributed loads at the top and bottom of each soil layer, resulted in values of the maximum reinforcement tension, Tmax, that agree with those from the full-scale test and those calculated by Ehrlich and Mitchell (1994). On the other hand, the K-stiffness method under-predicts the measured Tmax values. Moreover, numerical modeling of compaction using a distribution load only at the top of each soil layer overestimated the measurements. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics GRS walls Analytical procedure Numerical modeling Compaction-induced stresses
1. Introduction The importance of backfill soil compaction on the behavior of geosynthetic reinforced soil (GRS) walls has been demonstrated by a number of laboratory and case studies (Ehrlich and Mitchell, 1994; Bathurst et al., 2009; Ehrlich et al., 2012). Compaction promotes displacement during the construction period and reduces both settlement and horizontal displacement due to surcharge load application after construction. In other words, compaction may lead the reinforced soil mass to exhibit a kind of over-consolidation that promotes a stiffer behavior after construction. Additionally, compaction may be the major contributor to reinforcement tension at shallow depths (Ehrlich and Mitchell, 1994, 1995; Ehrlich et al., 2012; Mirmoradi and Ehrlich, 2014b). However, in most of the current design methods for GRS walls, the effect of the compaction-induced stress is not explicitly taken into consideration (e.g., the AASHTO, 2012 simplified method).
* Corresponding author. E-mail addresses: [email protected] (S.H. Mirmoradi), [email protected] (M. Ehrlich). http://dx.doi.org/10.1016/j.geotexmem.2014.11.001 0266-1144/© 2014 Elsevier Ltd. All rights reserved.
Ehrlich and Mitchell (1994) presented an analytical procedure for the internal design of reinforced soil walls that was based on working stress conditions. This method explicitly takes into account the effect of compaction-induced stress, reinforcement, and soil stiffness properties. Comparison of the predicted results using this method showed good agreement with measured reinforcement tension data for several full-scale walls containing a range of reinforcement types. In recent decades, several numerical analyses using the finite element method (FEM) or finite difference method (FDM) codes have been undertaken to consider the different geometries and parameters in GRS walls. Examples are reported by Hermann and Al-Yassin (1978), Naylor (1978), Ho and Rowe (1997), Rowe and Ho (1998), Helwany et al. (1999), Ling and Leshchinsky (2003), Hatami and Bathurst (2005), Guler et al. (2007), and Mirmoradi and Ehrlich (2013), among others. However, the effect of backfill soil compaction has rarely been considered. Hatami and Bathurst (2005) and Guler et al. (2007) numerically considered the effect of the induced stress due to backfill compaction using FDM (finite difference-based fast Lagrangian analysis of continua program; Itasca Consulting Group, 2001) and FEM (PLAXIS). In both studies, the compaction-induced stresses were modeled using a uniform
S.H. Mirmoradi, M. Ehrlich / Geotextiles and Geomembranes 43 (2015) 82e88
vertical stress applied only to the top of each backfill soil layer as the wall was modeled from the bottom up. Ehrlich and Mirmoradi (2013), Mirmoradi and Ehrlich (2014a,b) and Riccio et al. (2014) simulated the compaction-induced stress by applying an equal distribution load at the top and bottom of each soil layer. This approach is based on the procedure used by Dantas (2004) and Morrison et al. (2006) for the consideration of the induced stress due to backfill soil compaction. The objective of the present study is to propose a simple analytical method (AASHTO modified) for the determination of Tmax that includes the effect of backfill soil compaction. The proposed procedure is based on that suggested by Wu and Pham (2010). The results using the proposed procedure are compared with the results of the numerical modeling using the two compaction procedures as discussed above, the AASHTO (2012) simplified method, the Ehrlich and Mitchell (1994) method and the modified version of K-stiffness method (Bathurst et al., 2008).
where Ds0h;c and Sv are the increases in effective lateral stress due to backfill compaction and the vertical reinforcement spacing, respectively. A procedure was suggested by Wu and Pham (2010) for calculating the increase in lateral stress in a reinforced soil mass due to compaction:
Ds0h;c ¼ Ds0v;c max Ki;c F 1 þ
Ehrlich and Mitchell (1994) suggested a procedure for the internal design of reinforced soil walls that explicitly takes into account the effect of the induced stress due to backfill compaction. Nevertheless, conventional designs of reinforced soil walls usually do not take into consideration the effect of the compaction-induced stress in their calculations. A new simple procedure that includes the effect of the induced stress due to backfill compaction for use with any conventional design methods is described, as follows. For the compacted backfill soil, the value of the maximum tension in the reinforcement may be determined by:
Tmax ¼ Tmax;g þ Tmax;c
(1)
where Tmax,g and Tmax,c represent the values of the maximum mobilized tension in the reinforcement due to geostatic stress and compaction-induced stress, respectively. Tmax,g corresponds to the tension of reinforcement due to geostatic stress, and it may be calculated using any conventional design method that does not take into consideration the effect of the compaction-induced stress on determination. Based on the AASHTO (2012) simplified method, for example, the value of the maximum tensile stress in the reinforcement is determined by using the following equations:
Tmax;g ¼ KSv gz þ q
(2)
wherez is the depth of the reinforcement layer under the crest of the wall, g is the soil unit weight, Sv is the vertical reinforcement spacing, q is the surcharge pressure, and K is the active earth pressure coefficient, as determined by:
K¼
cos2 ∅ þ u cos2 uð1 þ ðsin∅=cos uÞÞ2
(3)
where ∅ and u are the peak friction angle of the soil and the facing inclination from vertical, respectively. Note that the use of the AASHTO (2012) simplified method for Tmax,g determination may be reasonable for situations where there is enough lateral strain mobilization in the reinforced soil mass to reach soil plastic condition (Ka condition); that hypothesis may be considered for typical polymeric reinforcements. The increase of the value of the maximum mobilized tension in the reinforcement due to the induced stresses due to backfill compaction, Tmax,c, is determined by:
Tmax;c ¼ Ds0h;c Sv
(4)
0:7Er Es Sv 0:7Er
(5)
where Ds0v;c max , Ki,c, Es, Er, and Sv are the maximum increases in effective vertical stress due to backfill compaction, lateral earth pressure coefficient, soil stiffness, reinforcement stiffness, and reinforcement spacing, respectively. The value of F can be calculated based on Seed (1983) and Ehrlich and Mitchell (1994) according to
OCR OCRsin4 OCR 1
F ¼1 2. Analytical compaction modeling
83
(6)
where OCR and 4 are the over-consolidation ratio and internal friction angle, respectively.
(
. 0 0 OCR ¼ szc;i sz ;
0
0
szc;i > sz 0
OCR ¼ 1;
0
szc;i sz
(7)
0
where sz is the effective vertical stress on each layer at the end of construction. The compacted soil layers are relatively thin, thus it may be assumed that all points in the backfill soil layers are driven 0 to the same vertical induced stress, szc;i , due to compaction. Therefore, the value of the maximum increase in the vertical stress due to compaction in each depth may be calculated as follows:
(
0
0
sv;c max ¼ szc;i g0 z; 0
sv;c max ¼ 0;
0
szc;i > g0 z 0
szc;i g0 z
(8)
Wu and Pham (2010) suggested the Westergaard solution (1938) for calculating the maximum increase in the vertical stress due to backfill compaction. Fig. 1 shows a comparison of the increase in the lateral stress due to backfill soil compaction in a reinforced soil mass presented by Pham (2009) and Wu and Pham (2010) and results based on the mentioned approach (Eq. (8)), assuming that Ki,c is equal to the active Rankine condition, Ka. As previously discussed, the use of the active condition (Ka) may be considered reasonable for soils reinforced with conventional polymeric reinforcements. The results are related to a 6 m high GRS mass for five different values of the vertical maximum pressures due to compaction (44, 100, 200, 300, and 500 kPa). Fig. 1 shows that the results determined by the two procedures differ significantly. It is also notable that the increase in lateral stress determined using Eq. (8) would approach zero at compaction influence depth, Zc, that is a larger depth compared with the results of Pham (2009) and Wu and Pham (2010) and this discrepancy would be 0 greater for the higher value of szc;i . The compaction influence depth Zc, is defined as follows (Ehrlich and Mitchell, 1994): 0
Zc ¼
szc;i
(9)
g 0
where szc;i and g are the vertical stresses induced during compaction and the soil unit weight, respectively. Note that zero increase of lateral stress (for Z > Zc) means that the geostatic stress overcomes the induced stress due to compaction and the effect of compaction is no longer felt by the soil.
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0
Kp-1
1
Depth of Wall, m
2
3
4 44 kPa
100 kPa
5
Fig. 2. Vertical stress increase during a roller operation in the backfill soil (strip load e Boussinesq elastic solution).
200 kPa 300 kPa 500 kPa
6 0
50 100 Lateral stress increase, kPa
Fig. 1. Depth of wall versus lateral stress increase. The solid line represents values from Pham (2009) and the dotted line indicates the suggested procedure.
3. Numerical compaction modeling The effect of the induced stresses due to backfill soil compaction on the behavior of GRS walls has rarely been numerically modeled. Hatami and Bathurst (2005) using FDM (finite difference-based fast Lagrangian analysis of continua program; Itasca Consulting Group, 2001) and Guler et al. (2007) using FEM (PLAXIS) simulated the compaction-induced stresses using a uniform vertical stress applied only to the top of each backfill soil layer as the wall was modeled from the bottom up. Ehrlich and Mirmoradi (2013), Riccio et al. (2014) and Mirmoradi and Ehrlich (2014b) simulated the compaction-induced stress by applying an equal distribution load at the top and bottom of each soil layer. The difference between the two approaches on representation of the actual field behavior are presented and discussed in Mirmoradi and Ehrlich (2014a), and are summarized as follows: Fig. 2 shows a schematic view of the vertical stress increase during a roller operation in backfill. The vertical stress at the top of each layer during the compaction roller operation may be represented by a strip load and an elastic solution can be used to represent its evolution with depth. As shown in Fig. 2 for each soil layer, the maximum stress increase during the roller operation occurs at soil-roller contact and decreases with depth. Ehrlich and Mitchell (1994) stated that “In multilayer construction, the compacted layers are relatively thin, typically 0.15e0.3 m thick, and all points in each soil layer may be assumed to have been driven to the same maximum soil stress state during compaction”. Therefore, it may be assumed that all points in the soil layers are driven to the 0 same vertical induced stress, szc;i , due to compaction. Fig. 3 shows two different approaches for the simulation of the induced stress due to compaction. Fig. 3a and b show a schematic view of the numerical modeling of compaction-induced stress using a distributed load, qc, at the top of each soil layer (hereafter
referred to as procedure type 1) and distribution loads, qc, at the top and bottom of each soil layer (hereafter referred to as procedure type 2), respectively. Stage construction is used in both procedures and compaction modeling is represented by only one cycle of loading and unloading for each soil layer. In Fig. 3, four steps for backfill soil construction in a specific soil layer “n” were considered: (I) soil layer placement, (II) compaction equipment operation, (III) end of compaction, and (IV) next soil layer placement (layer “n þ 1”). Fig. 3a, step (II) shows that when procedure type 1 is used for numerical modeling of the induced stresses due to compaction in soil layer “n”, it leads to the constant increase of the vertical stress due to compaction, qc, in all the layers placed bellow. The dashed line in this figure shows the expected vertical stress increase during the roller operation for soil layer “n” based on the strip load elastic solution, where its maximum value takes place at soil-roller contact and decreases significantly with depth. This figure clearly shows that using the distribution load only at the top of each soil layer for modeling of compaction may not correspond to the actual field condition represented by the elastic solution. Fig. 3b shows a schematic view of the procedure type 2 as suggested by Ehrlich and Mirmoradi (2013) and Mirmoradi and Ehrlich (2014a,b) for the numerical simulation of the induced stress due to compaction. Fig. 3b, step (II) shows that when procedure type 2 is used for the soil layer “n”, all points in this soil layer would be driven to the same vertical stress increase. In addition, for the soil layers placed under this layer, only geostatic stresses occur. A comparison between the curves related to the compaction modeling using procedure type 2 and the dashed line represented by the elastic solution indicates that this procedure may be more representative of the actual induced vertical stress during the roller operation. 4. Numerical model The numerical modeling was carried out using the twodimensional finite-element program PLAXIS (Brinkgreve and Vermeer, 2002). Full-scale reinforced soil wall modeling performed at the Geotechnical Laboratory of COPPE/UFRJ was used for the validation of the numerical analyses (Ehrlich and Mirmoradi, 2013). The physical model was 1.4 m high and surcharge load was applied up to 100 kPa at the end of construction. That physical model may be assumed representing a portion of a 6.8 m high prototype (Fig. 4). The numerical modeling of the prototype was
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85
Fig. 3. Modeling of the vertical stress load-unload cycles verified during the compaction of the backfill soil layer “n”: a: procedure type 1, b: procedure type 2, (I) soil layer placement, (II) compaction, (III) end of compaction, and (IV) next soil layer placement (layer “n þ 1”).
validated using results of the physical model (Ehrlich and Mirmoradi, 2013). Details of the physical model, numerical modeling of the prototype and the relation between them can be found in Ehrlich and Mirmoradi (2013). In this study the numerical model was validated against the configuration of the full-scale laboratory test. The 1.4 m high wall with wrapped facing was modeled with an inclination of 6B to the vertical. The length and the vertical spacing of the reinforcement were 2.1 and 0.4 m, respectively. A hardening soil model was applied. Hyperbolic stressestrain curves were arranged to fit the data measured from laboratory plane-strain tests. Curves were fitted considering lower strain (<1%) in order to better represent the working stress conditions verified in the physical model test
Fig. 4. View of the prototype and physical model.
ref ¼ 3E ref was used, (Ehrlich and Mirmoradi, 2013). The value of Eur 50 which is the default of PLAXIS. The value of m was chosen based on the value suggested by Janbu (1963), who reported values of m of about 0.5 for Norwegian sands. Reinforcement was modeled as a linear elastic material with perfect interface adherence to the adjacent soil. Jewell (1980) and Dyer and Milligan (1984) have shown that perfect adherence is a reasonable assumption for soil-reinforcement interface under working stress conditions. 15-node triangular element was used to model soil layers and a fine mesh was used to discretize the system. Note that the types of structural elements are automatically taken to be compatible with the soil element type. A fixed boundary condition in the horizontal direction was employed on the right-lateral border. At the bottom of the model, a fixed boundary condition in both the horizontal and vertical directions was applied. Table 1 lists the input parameters used in this study. The backfill soil stiffness and shear strength parameters were determined from plane-strain tests. In simulating wall construction in the numerical analyses, soil layers were placed every 0.2 m and compacted until the final wall height was achieved. Compaction was simulated using procedure type 2 by applying a single loadunload stress cycle with a 63 kPa distributed load at the top and bottom of each backfill soil layer. Fig. 5 shows a comparison of the measured values of the maximum tension mobilized in the 2nd, 3rd, and 4th reinforcement layers, Tmax, in the physical model with those determined by PLAXIS for the prototype and for the model at the end of construction (dotted lines) and under a surcharge value of 100 kPa (solid lines). Note that the Tmax values of the reinforcement layers “a,” “b,” and “c” in the prototype were representative of the 2nd, 3rd, and 4th reinforcement layers in the physical model (see Fig. 4). Fig. 5 shows a reasonable agreement between the measured and calculated values of Tmax in individual reinforcement layers at the end of construction. However, under the condition of surcharge
86
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32
Table 1 Input parameters for numerical analysis. Value
Soil Model Peak plane-strain friction angle, 4 ( ) Cohesion, c (kPa) Dilation angle, J ( ) Unit weight, g (kN/m3) ref (kPa) E50 ref (kPa) Eoed ref (kPa) Eur Stress dependence exponent, m Failure ratio, Rf Poisson's ratio, y Reinforcement Elastic axial stiffness (kN/m) Wrapped face Elastic axial stiffness (kN/m) Elastic bending stiffness (kNm2/m)
HS 50 1 0 21 42,500 31,800 127,500 0.5 0.7 0.25
2
4
16 12 8 4
0
6
1
2
3 4 Equivalent depth, m
5
6
Fig. 6. Comparison of measured and determined summations of the maximum tension along the 2nd, 3rd, and 4th reinforcement layers. The vertical dashed line indicates the compaction influence depth, Zc.
8
10
Measured PLAXIS, Model
Depth of Wall, m
20
0 60 1
0
0.2
24
Zc
600
Tmax, kN/m 0
Summation of Tmax, kN/m
Property
Measured AASHTO AASHTO Modified E&M, NC E&M, 63 kPa K-stiffness PLAXIS, NC PLAXIS, Type 2 PLAXIS, Type 1
28
PLAXIS, Prototype
0.4
0.6
0.8
1
1.2 Fig. 5. Comparison of measured value of the maximum tension along the 2nd, 3rd, and 4th reinforcement layers with those determined by PLAXIS for the prototype and for the model at the end of construction (dotted lines) and under a surcharge value of 100 kPa (solid lines).
loading there is relatively large discrepancy between the results. This behavior may be associated to a local redistribution of load between reinforcements. Note that good agreement was observed between measured and numerically determined value of summation of the maximum tension mobilized in the reinforcement, P Tmax, even under the condition of surcharge loading (see Fig. 6). Additionally, comparison of the two different numerical studies (prototype and model) also presents a good agreement at the end of construction and under 100 kPa surcharge value. These results support the correspondence between the physical model and the prototype, as discussed by Ehrlich and Mirmoradi (2013). 5. Results and discussion In order to verify the analytical and numerical modeling of compaction induced stress in GRS walls using the procedures
described above, the measured values of the summation of the P Tmax, was maximum tension mobilized in the reinforcement, compared with those determined by PLAXIS for compaction procedures type 1 and 2, the AASHTO methods and the values predicted by the Ehrlich and Mitchell (1994) and the K-stiffness methods in Fig. 6. Note that the geometry of the prototype was used for the analyses. The vertical dotted line in Fig. 6 represents the compaction influence depth, Zc (see Eq. (9)). The equivalent depth of the soil layer (Zeq) is defined by:
Zeq ¼ Z þ
q g
(10)
where Z and q are the real depth of a specific layer and the surcharge load value of the physical model, respectively. As shown in Fig. 6, the values measured from the physical model were properly captured by the AASHTO modified method, the Ehrlich and Mitchell 1994 method, and the numerical (PLAXIS) method using compaction procedure type 2. However, regardless of the value of Zeq, the curve corresponding to the numerical simulation using compaction procedure type 1 overestimates the values P of Tmax and this discrepancy increases with equivalent depth. Note that for the curve corresponding to the AASHTO modified method, the values of Tmax determined by the AASHTO simplified method were modified using the simple analytical procedure described earlier to take into consideration the effect of the compaction-induced stress in calculations. On the other hand, the K-stiffness method underpredicts the measured values of the tension in the reinforcements. Calculation using the modified version of K-stiffness method (Bathurst et al., 2008) was performed for the value of the elastic modulus of the facing column equal to 35,000 kPa as suggested by Allen et al. (2003) and assuming the width of the facing wrap was 1 m. Note that K-stiffness method is an empirically based method and as all empirical models, its predictions may be valid for structures with similar features, such as soil type, compaction equipment and reinforcement strength/ deformability. Additional discussion about the prediction capability of this method and other common used procedures could be found in Mirmoradi and Ehrlich (2014b) who numerically evaluated the behavior of GRS walls with segmental block facing under working stress conditions. Comparison of the results corresponding to the conditions with and without induced stresses due to compaction illustrates that for
S.H. Mirmoradi, M. Ehrlich / Geotextiles and Geomembranes 43 (2015) 82e88
Tmax, kN/m 0
5
Tmax, kN/m
10
0
15
0
0
Depth of Wall, m
2
3
PLAXIS, NC PLAXIS, Type 2 PLAXIS, Type 1 E&M, NC E&M, 63 kPa AASHTO AASHTO Modified
Zc
4
1
2 Depth of Wall, m
1
87
5
10
15
20
PLAXIS, NC PLAXIS, Type 2 PLAXIS, Type 1 E&M, NC E&M, 120 kPa AASHTO AASHTO Modified
3
4
5 Zc
5 6
6
7
7 Fig. 8. Depth of wall versus individual values of Tmax at the end of construction; 0 szc;i ¼ 120 kPa.
Fig. 7. Depth of wall versus individual values of Tmax at the end of construction; 0 szc;i ¼ 63 kPa.
6. Conclusions
P compacted backfill soil walls, when Zeq < Zc, the values of Tmax are greater than the values obtained for the no-compaction conditions. However, for Zeq > Zc, the compaction-induced stress was overcome by the geostatic stress and the values determined are the same irrespective of whether or not the induced stress due to the backfill soil compaction is considered in the analysis. In Fig. 6, the results related to the condition without compaction are also shown. These curves were obtained with the Ehrlich and Mitchell (1994) method, the AASHTO simplified method, and by numerical modeling with PLAXIS. As the K-stiffness method implicitly includes the compaction-induced stresses on calculations, it may not be properly compared with the no-compaction conditions. The results show almost the same values for the nocompaction condition. However, the AASHTO simplified method P leads to lower Tmax values due to the assumption that the value of the lateral earth pressure coefficient is taken to be equal to Ka. Figs. 7 and 8 show a comparison of the maximum mobilized tension in each reinforcement layer, Tmax, versus depth determined with PLAXIS for the described numerical compaction modeling (type 1 and 2) and calculated values using the Ehrlich and Mitchell (1994) method and the AASHTO methods, for the compactioninduced stresses of 63 and 120 kPa, respectively. In Figs. 7 and 8, for the analyses in which the compaction modeling type 2 was used, a consistent representation of the expected behavior is found and discussed as follows. For Z > Zc, the effect of compaction vanishes because the geostatic stress overcomes the induced stress due to backfill soil compaction. Furthermore, Tmax is the same; regardless the induced stress due to backfill soil compaction is included (Z > Zc). However, when Z < Zc, Tmax would be greater than the corresponding values for the nocompaction condition. Nevertheless, for the analyses in which the compaction modeling was performed using procedure type 1, the Tmax values are much larger than the previous values and this overprediction increases with depth. Good correspondence is also observed for the determined results using the AASHTO modified method and the Ehrlich and Mitchell (1994) method.
A new simple analytical procedure (AASHTO modified) was proposed that includes the effect of the induced stress due to backfill compaction for use with conventional design methods of geosynthetic reinforced soil (GRS) walls. Note that the proposed analytical procedure may be used with any conventional design methods that do not take into consideration the effect of the compaction-induced stress in their calculations. The results of the proposed analytical procedure were compared with those measured from a compatible full-scale wrapped face wall experiment conducted at the Geotechnical Laboratory of COPPE/UFRJ and with numerical modeling results using two different procedures for the modeling the induced stress due to backfill soil compaction. The results were also compared with values predicted using the Ehrlich and Mitchell (1994) method, the K-stiffness method, the AASHTO simplified method. Analysis of the results showed that: The AASHTO modified method and the numerical modeling of compaction-induced stress using two distributed loads at the top and bottom of each soil layer (compaction procedure type 2) were shown to have a good predictive capability, as demonstrated by comparing the data from the physical model study and from calculated values using the Ehrlich and Mitchell (1994) analytical procedure. On the other hand, the K-stiffness method underestimated the measured value of tension in the reinforcement. Furthermore, the results show that modeling of compaction using a distribution load only at the top of each soil layer overestimated the measurements and the discrepancy increased with both depth and compaction effort. Comparison of the measured values of the tension in the reinforcement and those calculated with the AASHTO modified method, numerical modeling using compaction procedure type 2 and the Ehrlich and Mitchell (1994) method showed that for Z > Zc, the effect of vertical induced stress due to compaction vanishes because the geostatic stress overcomes the induced stress due to backfill soil compaction. Accordingly, the maximum tension mobilized in the reinforcement, Tmax, remains the same regardless
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