Static Response of Reinforced Soil Retaining Walls with Modular Block Facing Morteza Sabet 1, Amir M. Halabian 2, Kazem Barkhordari 3 1 Graduate Student, Department of Civil Engineering, Yazd University 2 Assistant Professor, Department of Civil Engineering, Isfahan University of Technology 3 Assistant Professor, Department of Civil Engineering, Yazd University Morteza.sabet@gmail.com Mahdi@iut.ac.ir Kbarkhordari@yazduni.ac.ir Abstract Effect of backfill compaction, reinforcement connection type, geogrid-soil interface properties, and facing inclination on static response of Geosynthetic Reinforced Soil Walls (GRSW), was investigated using finite difference method. The numerical simulation of wall was included sequential construction of the wall. Backfill soil was modeled with Elastic-plastic Mohr Coulomb model and modular block was modeled with elastic model. Results include the facing displacement, maximum load reinforcement and lateral earth pressure. Numerical results show the magnitude of lateral displacement decrease with increasing facing inclination and compaction load, the maximum reinforcement load increased significantly with an increase in compaction load. It was found that finite difference procedure was able to simulate the static response of GRS wall very well. Keywords: Reinforced soil walls, Numerical models, Reinforcement, FLAC 3D 1. INTRODUCTION GRS structures are cost effective alternatives for the most applications where the reinforced concrete or gravity type walls have traditionally been used to retain soil. The performance, economics and expediency of construction of these reinforced walls made them popular. In the USA they have been demonstrated to be 50 percent of the cost of traditional concrete gravity structures [1]. So the reinforced soil walls have been the subject of some researches, and many researchers have examined the effect of different parameters on the design of reinforced walls. Current practice consists of determining the geometric and reinforcement requirements to prevent internal and external failure using limit equilibrium methods of analysis. Many conducted researches have shown that the current limit equilibrium-based analysis methods over-estimate reinforcement forces under operational conditions [2]. In the limit equilibrium methods reinforcement load is calculated from classic active earth pressure theories such as Rankine or Coulomb earth pressure theory [3]. The Federal Highway Administration provides design guidelines for a variety of mechanically stabilized earth (MSE) walls. It introduces the same computational scheme for all wall systems, including metallic and polymeric reinforcement, using empirical parameters to adjust for the specific properties of each system. It means that the geogrid-soil interface properties, reinforcement connection type, reinforcement stiffness and other factors have not been considered. Researches have shown using reinforcement with high stiffness layer will attract more load. Therefore, the possibility of exceeding the tensile strength for stiffer reinforcement layers should be examined. In the field of retaining walls, previous studies focused on effect of wall and reinforcement geometry, mechanical properties of reinforcement and backfill soil. Effect of parameters such as backfill compaction, reinforcement connection type, geogrid-soil interface properties have often been ignored [4]. The objectives of this study were, at first, to verify numerical simulation conducted by other researchers, Then it was persuaded to identify static behavior of these walls and to investigating the effect of missing parameters on static response. 2. CALIBRATION The finite difference model developed in this study was verified with the results of the model that employed by Huang et al. [5]. Huang et al. through a numerical study examined the effect of different constitutive soil models. The model geometry dimensions were shown in Fig 1. Properties of material and reinforcement were described in Table 1.
Figure1. FLAC 2D Numerical grid, Huang et al. (2009) Table1. Properties of materials elastic-plastic Parameters Index Backfill soil material E Bulk modulus (MPa) 40 (Possion ratio) 0.3 Friction angle ( ) 44 Dilation angle ( ) 11 Density(KN/m 3 ) 16.8 Modular Block Elastic Model K Bulk modulus (MPa) 11430 G Shear modulus (MPa) 10430 The wall facing was built as a modular block, while the soil was assumed as a purely frictional, behaving elastic-plastic material with a Mohr-Coulomb failure criterion and non associated flow rule. The reinforcement layers were modeled using cable elements with a cross-sectional area of 0.002 m 2. The stiffness of the reinforcement and tensile yield strength were assumed to be J = 3,100 kn/m, Ty = 7 kn/m. A graphical comparison of results stem from this study and huang et al. [5] illustrated in Fig 2. As it can be seen, a good agreement is observed. Figure2. Compare between obtain results by author and Huang (2009) 2
Figure3. Geometry and mesh configuration of Reinforced Soil Retaining Walls with Modular Block Facing 3. NUMERICAL MODELLING A main model was built to perform parametric analysis. The parameters were changed according to the practical values. The height and width of wall were assumed to be 4.2 m, 8m; the wall front batter is 8 degrees. To take into account the construction sequences, the supporting soil with 3 m height and concrete leveling pad also were simulated. In this study the wall was constructed step by step in which each lift soil has 0.2m thick. After each step a transient uniform pressure 4 KPa was applied to each soil lift to take into account the compaction process. [6]. Modular facing was selected in which each block has 200 mm height, 300 mm width and 250 mm length. High density geogrid was selected as reinforcement layers. In the main model a simple connection between geogrid and block was assumed (a non-rigid geogrid-facing connection). All analyses were carried out in the large strain mode accounting for the event of wall large deformations. Numerical model developed in this study was shown in Fig 3. 3.1. PROPERTIES OF MATERIALS The properties of block, backfill soil and foundation soil were summarized in Table 2. The backfill and foundation soils were assumed to have same materials and time independent. Facing is behaving the elastic zone. The weight of the modular block was selected to correspond to the solid concrete block. According to Huang s report [5], a simple soil constitutive model is suitable for modeling behavior backfill soil. So a linear elastic-perfectly plastic material with Mohr-Coulomb failure criterion and dilation angle was adopted to model the behavior of backfill sand. Parameters Index Table2. Property of soil and blocks Backfill and foundation soil elastic-plastic material E Bulk modulus (MPa) 40 (Possion ratio) 0.3 Friction angle ( ) 35 Dilation angle ( ) 5 Density(KN/m 3 ) 17 Modular Block Elastic Model E Bulk modulus (MPa) 2000 Shear modulus (MPa) 0.14 Density(KN/m 3 ) 24 3
All interfaces between different materials include block-block, block-soil were simulated with the interface element that incorporated in FLAC 3D [7]. FLAC 3D provides interfaces that are characterized by Coulomb sliding and/or tensile and shear bonding. Properties of interfaces were shown in Table 3. Table3. Interfaces properties Parameter friction angle dilation angle normal stiffness shear stiffness cohesion Block-Block 55 11 100 MN/m/m 1 MN/m/m ---------- Block-Soil 30 ------------------ 1000 MN/m/m 40 MN/m/m 46 KPa 3.2. REINFORCEMENT The reason that analysis was performed in 3 dimensions is due to that the geogrid structural element was used to model reinforcement. Because the behavior at the geogrid-soil interface is set automatically, no interface element was used for considering interactions between geogrid and backfill. GRS walls were reinforced with a high-density polyethylene HDPE unaxial geogrid. Creep analysis (time-dependent behavior) for long time duration in geosynthetic is necessary; However for the sake of simplification in the current study this phenomenon was not taken into account. The number of reinforcement layers are 7 (vertical spacing of layers is 60 cm) and the reinforcement length to wall height ratio, L/H, was selected 0.6. Table4. Parameters of Linear, Elastic and Isotropic Model of Geogrid Parameter value Coupling spring cohesion 1 MPa Coupling spring friction angle 35 Coupling spring stiffness per unit area 2 MPa tensile strength 54 KN/m Thickness 2 mm Young s modulus 250 MPa Possion ratio 0.2 4. RESULTS Results including the displacement, maximum load reinforcement and lateral earth pressure have been presented in Fig 4. As it can be seen the maximum horizontal displacement occurs close to the mid of the wall. Therefore it can also be concluded that the deformation mode is pretty much like bulging deformation. Also the maximum reinforcement force is observed at the mid of the wall. The reinforcement forces at the top of the wall are lesser than the other layers. It is seen that distribution of lateral pressure behind reinforced soil is triangular shape between at-rest condition and active condition (K 0 : at-rest lateral earth pressure coefficient; K a : active lateral earth pressure coefficient that calculate from classic 2 relation, 1 sin, tan (45 ) ). 2 5. PARAMETRIC ANALYSIS Four parameters including geogrid-facing connection type, compaction load, the inclination of wall and friction angle between geogrid-backfill on static response were investigated. At the beginning, the connection between wall and facing was assumed to be simple or rigid. Three compaction loads (CL), 4 KPa, 6 KPa and 8 KPa were selected while the front wall inclination was changed 0, 4, 8, 12 degree. Four friction angles 27, 31, 35, 38 degree were also selected. Other parameters such as length and spacing of geogrid, height of wall etc. were assumed fixed. 4
5.1. EFFECT OF CONNECTION TYPE Effect of geogrid-facing connection type was shown in Fig 5. It can be seen that the fixed connection induces less displacement and reinforcement forces as well, compared to the simple connection case. Moreover lateral earth pressure is similar in both cases approximately. It indicates that at the at-rest state condition at bottom of the wall height and approach an active condition toward the top of the backfill. Figure4. Main analysis results a) facing horizontal displacement b) maximum reinforcement force c) lateral earth pressure reinforced zone. Figure5. Effect of type geogrid-facing connection a) facing horizontal displacement b) maximum reinforcement force c) lateral earth pressure reinforced zone 5.2. EFFECT OF COMPACTION LOAD The selected values of load compaction were at the range that adequates for walls construction with geosynthetics. (Higher loading use for metallic reinforcements). Fig 6 shows the value of wall displacement and lateral earth pressure increase with increasing the load compaction up to 6 KPa. Also distribution manner 5
for all cases is similar. Maximum load reinforcement increases with increasing the load compaction except for the top reinforcement layers which have no change. 5.3. EFFECT OF GEOGRID-BACKFILL INTERFACE As it can be seen from Fig 7, the friction angle of soil-geogrid interface at selected ranges has no affect on static response. It may be due to existence of compaction load that causes the stresses transferred between soil and reinforcement by passive resistance. Other reason can be referred to the small loading which produces in geogrids in all cases. It should be mentioned that the value of adhesive strength is 1 MPa that cause system to reach to the equilibrium. To find the net effect of friction angle, value of adhesive strength is set to 0 and four friction angles 10, 20, 30 and 35 degree have been chosen. For all friction expect 35 degree the shear resistance of the geogrid was not mobilized enough, and model was not reached to the equilibrium. For the case in which the friction angle is 35 degree at only one of the top geogrids, failure was occurred. In Fig 8, x-displacement of top wall is shown indicating the wall was collapsed Figure6. Effect of load compaction a) facing horizontal displacement b) maximum reinforcement force c) lateral earth pressure reinforced zone Figure7. Effect of Interface friction angle a) facing horizontal displacement b) maximum reinforcement force c) lateral earth pressure reinforced zone 6
5.4. EFFECT OF FACING INCLINATION Since many GRS walls are constructed with the facing inclination, therefore understanding the effect of facing inclination on the static behavior is essential [8]. Fig 9 shows with increasing the facing inclination from vertical to 12 degree, facing displacement and maximum load geogrids decrease considerably. It can be concluded that batter front wall has a fundamental influence on the wall behavior. As it can be seen Fig 9, the lateral earth pressure decreases with increasing facing inclination. Figure 8. X-displacement of top wall (geogrid-soil interface friction angle of 20 degrees and adhesive strength of 0) Figure9. Effect of batter front wall a) facing horizontal displacement b) maximum reinforcement force c) lateral earth pressure reinforced zone 7
6. CONCLUSIONS A validation procedure was performed in this paper leading to a good agreement between the research results and reported results. The construction processes and numerical modelling issues have been the main features of this validation. The verified numerical approach was then used to investigate the influence of affecting parameters including geogrid-facing connection type, compaction load, facing inclination, friction angle between geogrid-backfill. Main features are summarized as following: 1- Using a simple elastic-plastic Mohr-Coulomb soil model led to sufficiently accurate results. 2- Lateral earth pressure distribution in static condition present that GRS walls work between at-rest and active conditions. Of course this conclusion is correct to for GRS walls and for metallic reinforcement it should be investigated. 3- The nature of the facing blocks is disjointed but bodkin joint or shear key can be used to fix geogrid to facing. In this paper both connection simulated. Numerical method shows the rigid geogrid-facing connection led to less facing displacement and maximum load geogrid. 4- Our results showed the compaction load is an important factor that with increasing it facing displacement, maximum load geogrid and lateral earth pressure are increase. It can be conclude that simulation sequential construction and compaction loading is very important the numerical model. 5- Using friction angle between geogrid-backfil in the numerical simulation alone, led to unstable condition in model. 6- Based on this paper s results it can be said that GRS walls whit inclination behave more proper than the vertical GRS walls. 7. REFERENCES 1. John, W.B, (2009), Numerical Linear and Non-linear Numerical Analysis of Foundations, Taylor & Francis. 2. Bathurst, R. J. and Huang, B., (2008), Numerical Modelling of Geosynthetic Reinforced Retaining Walls, International Association for Computer Methods and Advances in Geomechanics (IACMAG), Goa, pp 4071-4080. 3. Hatami, K. and Bathurst, R. J., and Pietro, P. Di., (2001), Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement, The International Journal of Geomechanics, Volume 1, Number 4, PP 477 506. 4. Bathurst, R. J. and Hatami, K., (2006), Parametric analysis of reinforced soil walls with different height and reinforcement stiffness, Proceedings of the 8th International Conference on Geosynthetics Yokohama, Japan, September 2006, pp. 1343-1346. 5. Huang, B., Bathurst, R. J. and Hatami, K., (2009), Numerical Study of Reinforced Soil Segmental Walls Using Three Different Constitutive Soil Models, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 135, No. 10, pp 1486 1498. 6. Hatami, K. and Bathurst, R. J., (2006), Numerical Model for Reinforced Soil Segmental Walls under Surcharge Loading, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 132, No. 6, pp 673-684. 7. Itasca Consulting Group Inc. (1996), FLAC3D (Fast Lagrangian Analysis of Continua in 3 dimenstions), user Manual, Version 2.10, Minneapolis, Minnesota, USA 8. FHWA, (2001), Mechanicaliiy Stabilized Earth Walls and Reinforced Soil Slopes Design & Construction Guidelines, Publication No.FHWA - NHI -00-043, National Highway Institute. 8