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Assessment of Soil Nailing Performance by Using Finite Element and Finite
Difference Methods Ahmad Safuan A Rashid
Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 UTM, Skudai, Johor, Malaysia
e-mail: [email protected]
Koohyar Faizi Researcher, Department of Geotechnics and Transportation, Universiti
Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia.
e-mail: [email protected]
Roohollah Kalatehjari Post-Doctoral Fellow, Department of Geotechnics and Transportation,
Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia.
e-mail: [email protected]
Ramli Nazir Associate Professor, Department of Geotechnics and Transportation,
Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia. e-mail: [email protected]
ABSTRACT The field performance of a geotechnical structures including its failure mechanism should be evaluated in detail before construction in order to minimize the possibility of potential failure. In this paper, the application of soil nailing system is documented in a detailed based on case study in the north of Tehran, Iran. The total excavation depth for a 15 storey residual building wall brought the cut face close to 12 m. The diameter of nails was 28 mm and their lengths were varied between 8 to 10 m with inclination of 7 degree to the horizontal plane. A series of numerical modelling was conducted to evaluate the deformation during the excavation process using finite difference method (FDM - FLAC 2D) and finite element method (FEM - PLAXIS 2D). In the modelling process, the pattern of wall deflection was simulated with shotcrete facing. A good agreement has been observed between the results of both methods when the pattern of deformation in the first and the last steps of excavation were simulated. Based on the maximum vertical displacement of shotcrete facing, calculated by two methods, the results obtained by FEM were closer to the field measurement. However, a good agreement has been observed between the values of factor of safety which were calculated by FLAC 2D and PLAXIS 2D, for different stages of excavation. KEYWORDS: Soil, Nailing, Excavation, FEM, FDM, FLAC 2D, PLAXIS 2D.
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INTRODUCTION Soil nailing has become a widely accepted method of providing temporary and permanent
earth support, underpinning, and slope stabilization on many civil projects in the world since early of 1970s. In the early years, soil nailing was typically performed only in projects that expertise geotechnical contractors offered as an alternative to other conventional systems. More recently, soil nailing has been specified as the system of choice due to its overall acceptance and effectiveness. Soil nailing consists of the passive reinforcement (i.e. no post-tensioning) of existing ground by installing closely spaced steel bars (i.e. nails), which are subsequently encased in grout. As construction proceeds from the top to bottom, shotcrete or concrete is also applied on the excavation face to provide continuity (Lazarte, et al., 2003). Soil nailing is typically used to stabilize existing slopes or excavations where top-to-bottom construction is advantageous compared to other retaining wall systems. For certain conditions, soil nailing offers a viable alternative from the viewpoint of technical feasibility, construction costs, and construction duration when compared to ground anchor walls, which is another popular top-to bottom retaining system (Zamiran and Saba, 2012). Although the theoretical engineering aspects of soil nailing may be well understood, there is a far lesser degree of understanding, even within the geotechnical community, due to the site conditions and construction problems (Thomas, 2013).
Among researchers who have studied in this field are Liu and Dugan (1972), Hanna and Kurdi (1974), Anderson and Hanna (1977), Matlock, et al. (1981), Lim and Briaud (1997), Briaud & Lim (1997), Dawkins (2001), Krabbenhoft, et al. (2008) and Tan and Paikowsky (2008). One important issue in the design of excavation wall stabilization is to decrease the lateral displacement of the constructed wall. This is because high lateral displacement indicates lack of stability and is followed by collapse of soil into the wall which may damages to the surrounding area. In that sense, the wall displacements should be carefully controlled to prevent any damage (Bara and Qing, 2010). The purpose of this paper is to investigate the soil deformation during soil nailing installation at site in the north of Tehran, Iran. Soil nail properties, procedures and monitoring for case study are presented as a tool to aid in making good decisions and prediction of failure zones. The application of a deep soil nailing system for a project of residual building is presented in this study with the total excavation height reaches 12 m. The deformation of excavation face was measured by surveyor at the last step of excavation and after nailing and shotcrete. Finite element difference software (FLAC2D) and finite element software (PLAXIS2D) have been employed to model the excavation and soil nailing system and predict the horizontal displacements. Both of the software can determine the horizontal and vertical displacements as well as the behaviour of retaining structure based on the plane strain theory (Gareh, 2011; Gareh and Saidi, 2011). For the sake of accuracy, the results of numerical modelling have been compared with the monitoring results and actual behaviour of the wall.
SITE INFORMATION The city of Tehran is located at the foothill of the southern slopes of the Alborz Mountain. It
sits on an alluvial plain formed over time by flood erosion of the mountains. As a result of this process, large and small particles have settled respectively on high and low elevations, resulting in varying geological conditions. The source rocks, slope of the mountains, and climate conditions are important factors in determining the properties of the soils deposited at the foot of mountains. The Alborz Mountains Range is steep and mainly consists of tuff, limestone and dolomite (Fakher, et al., (2007); Uromeihy and Nassiri, 2006). The area experiences heavy rains in some seasons and is seismically active. Therefore, non-uniform soil layers have been formed. Figure 1 presents the site location.
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Figure 1: Site location map pointed as red balloon A (Google map, 2013)
The system of nailing was designed for the construction of a residual building covering an area of approximately 7000 m2 with 15 stories. Figure 2 shows overview of activities in the site. The execution of soil nailing consists of making a 12 m vertical cut extending with a horizontal length to be stabilized and shotcreted on the same day. It is important to note that the shotcrete should be applied prior to installing the nails, if there is a concern over the stand-up time and possibility of sloughing of the soil. Besides, shotcrete facing before drilling can reduce hole drill disturbance, which is appeared in the entrance of hole drill during soil drilling. Due to the high depth of excavation and collapsible soil in the studied project, shotcrete was applied before nailing. In order to reinforce the concrete facing, reinforcing material as welded wire mesh was placed along the face of the excavation prior to apply the shotcrete facing. Similar to most temporary shotcrete walls, this process was accomplished by applying a 180 mm thick layer of concrete. The properties of soil in excavation area are provided in Table 1. These properties were collected from the results of a series of laboratory tests (Atterberg, limits, compaction test, sieve analysis, hydrometer, direct shear test, and free vertical swell) on the soil samples from the excavation area (KACE, 2012). These properties were used to analyse the project in both PLAXIS 2D and FLAC 2D software.
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Figure 2: Overview of activities in the site including (a) preparation and shotcreting, (b) soil drilling (c) hole drill (d) nailing
Table 1: Properties of soil in excavation area (KACE, 2012)
Soil specification
Type of soil
Depth (m)
Unit weight
(ɣ ) (kg/cm3)
Poisson ratio (ν)
Elasticity Modulus
(E) (kg/cm2)
Cohesion (C)
(kg/cm2)
Friction Angle(Φ) (degree)
Values* GW-GM SW-SM SC, CL
0-12 1.85-1.91 0.35 50-250 0.15-0.21 20-32
*Water level= 9m
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FINITE DIFFERENCE METHOD (FDM) AND FINITE ELEMENT METHOD (FEM)
For modelling the steps of soil nailing in the studied excavation, PLAXIS 2D and FLAC 2D software were used based on FEM and FDM methods respectively. FDM discretization is based on the differential form of the Partial Difference Equation to be solved. It utilizes a point-wise approximation to a solution. The domain is discretized into a grid of rectangular cells or nodes. The solution will be obtained at each nodal point. Although FDM is easy to implement and the computing time for each step is fast, the number of steps required for convergence is high. The other disadvantage is that the domain is not accurately represented if it is discontinuous or non-rectangular in shape (Fausett, 2003). Figure 3 (a) illustrates a sample FDM mesh. FEM discretization is based on a piecewise representation of the solution in terms of specified basis functions. In FEM the discretization is not restricted to a grid of hexahedral cells or nodes, instead a solution is approximated using interconnecting sub-regions or elements. These elements are typically simple geometrical shapes as illustrated in Figure 3(b). This flexibility in construction of elements allows FEM to accurately model complex geometries. The downside is that FEM is difficult to implement, however there is no agreement on this between researchers (Kalla, 2010; Zienkiewicz and Cheung, 1965).
Figure 3: Discretization methods in (a) FDM (b) FEM
FINITE ELEMENT MODELLING (FEM) PROCEDURES Numerical modelling allows designers to study the soil behaviour in various conditions without resorting to simplified assumptions. Two dimensional finite elements modelling of the different steps of soil nailing is performed using PLAXIS 2D software. A parametric study was performed to arrive at the critical parameters that define the behaviour of the system. The parametric study comprised of all the elements that influence the behaviour of the system. Moreover, various aspects of soil excavating like steps of excavation and vertical displacement were studied. The geometry was drawn using geometric lines and standard fixities were then used to define the boundary conditions. The model was created, properties of different soil materials were assigned to material model, and finite mesh was generated. The water conditions can be specified in the geometry configuration mode by generating pore pressure in phreatic level. A constant ground water level has been considered in this study. Figure 4 illustrates the analysed section of project
Vol. 18 [2013], Bund. Y 5886 and the soil nail configuration used in this section.
Figure 4: illustrates the analyzed section of project and the soil nail configuration used in this section.
The following is the detail of modelling process including the choice of material models, finite element mesh, and boundary condition to simulate field conditions and obtain settlements of the excavation. There are many modelling methods developed to simulate 3-D soil nailing problem using 2-D FEM. Each method poses advantages and limitations in approximating the true behaviour of soil nails (Olia and Liu, 2011). The method was proposed by Al-Hussaini and Johnson (1978) where the discrete reinforcement was smeared into continues plate across the spacing. This is achieved by factoring the Young’s modules of the plate (E) using area ratio factors such as the axial stiffness (EA). Thus, this method is adopted in this study.
Two types of triangular elements are used in the PLAXIS as 6-node and 15-node triangular elements. Advantages of higher order triangular elements is that they better represent the description of continuous strain and stress variations and also provide good description of a continuous displacement field compare with relatively few elements. The disadvantages of higher order elements is that the failure loads may be dependent on the mesh and makes poor description of discontinuous stress and strain. In PLAXIS, the program automatically creates unstructured mesh as there is no possibility of making a so-called structured mesh (Gómez, 2011). The mesh is generated based on random seeds and its size cannot be set explicitly. The size of mesh may be changed globally by means of global coarseness or locally by means of local coarseness. Figure 5 shows a typical mesh generated for the present study. Where shotcrete wall of 18 cm thickness with reinforced wire mesh is modelled as beam elements with axial stiffness (EA) = 5.4 x 106
Vol. 18 [2013], Bund. Y 5887 kN/m, bending stiffness (EI) = 1.458 x 104 kNm2/m, and Poisson’s ratio (ν) = 0.2; and soil nails are modelled as geotextile elements with EA = 6.87 x 104 kN/m and ν = 0.
Figure 5: A typical mesh generated for the present study by PLAXIS 2
FINITE DIFFERENCE MODELLING (FDM) PROCEDURES FDM is possibly the oldest numerical technique used for the solution of sets of differential equations, given initial values and/or boundary values (Desai and Christian, 1977). For FDM analysis, the computer code FLAC 2D (i.e. Fast Lagrangian Analysis of Continua) was selected because of its flexibility and wide acceptance (FLAC 4.0, 2000). It easily includes key factors and phenomena that affect the behaviour of ground conditions. The FDM code is an explicit two dimensional finite difference program that performs a Lagrangian analysis. Here, explicit means it uses a time stepping procedure to solve the problem without forming the stiffness matrix. The Lagrangian formulation enables the grid to move and deform with the material it represents, since the incremental displacements are added to the coordinates (Fakher, et al., 2007). FLAC 2D is a powerful tool for assessing the effect of different material properties. It is also a robust tool because it can handle any constitutive model with no adjustment to the solution algorithm. In FLAC 2D, grid generation is limited to simple and regular shaped regions. There is a Fish function which can be used to generate user defined grids with varying zones. The advantage of using FISH function is that it can easily adjust grid boundary and zone density using “SET” command. The plane strain model was used in this study. The size of the model was set to 25 m in width and 15 m in height. Here the grid is composed of several zones consist of constant
Vol. 18 [2013], Bund. Y 5888 height. A reasonably medium grid should be selected to ensure that the displacement contours will be well-defined as it develops. Figure 6 shows a typical mesh generated for the present study by FLAC 2D.
Figure 6: A typical mesh generated for the present study by FLAC 2D
The Mohr-Coulomb plasticity is applicable for most general engineering studies (Olia and Liu, 2011). This model is used for materials that yield when subjected to shear loading. In this model, the yield stress depends on the major and minor principal stresses and the intermediate principal stress has no effect on it. Also, Mohr-Coulomb parameters (cohesion and friction angle) are usually more readily available and more easily reachable than other properties for geo-engineering materials. Moreover, Mohr-Coulomb models are the most computationally efficient plasticity models (Gareh and Saidi, 2011).
RESULTS AND DISCUSSIONS Since FLAC 2D models a nonlinear system as it evolves in time, the interpretation of its
results may be more difficult than a conventional finite-element program which produces “a solution” at the end of its calculation phase. The calculation is continued using step command and update interval of plot must be used to estimate the effects of time. The SOLVE command is used to find the equilibrium state (Desai and Christian, 1997).
Failure zone contours at the first step of the numerical simulations using FDM and FEM are presented in Figs. 7. This step represents the excavation with depth of 2 m without shotcreting or nailing. In FLAC 2D, soil is modelled as a viscoelastic material (Mohr-Columb). The shotcrete cover is modelled as elastic beam elements and nails are modelled as cable element.
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(a) (b)
Figure 7: Failure zone in the first step of excavation modelled by (a) FLAC 2D and (b)
PLAXIS 2D Displacement vectors and Horizontal displacement contours were obtained from numerical
simulations by using FDM and FEM in the last step of excavation with depth of 12 m. This step of excavation was reinforced by shotcreting and nailing. The results are presented in Figs. 8 and 9.
(a) (b)
Figure 8: Displacement vectors in the last step of excavation modelled by (a) FLAC 2D and (b) PLAXIS 2D
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(a) (b) Figure 9: Maximum displacement in the last step of excavation modelled by (a) FLAC
2D and (b) PLAXIS 2D
Shear strain zones for both models are shown in Figure 10. Based on these figures, a similar pattern in observed in shear strain zones obtained by FEM and FDM. The shear strains within the reinforced soil mass were developed along the potential slip surface of the active zone as a result of soil nailing. This is fairly close to the formation of an active wedge in the retaining wall design.
(a) (b)
Figure 10: Shear Strain zones in the last step of excavation modelled by (a) FLAC 2D and (b) PLAXIS 2D
Vol. 18 [2013], Bund. Y 5891 The deformation of excavation face was measured by surveyor as 14 mm. Figure 11 shows the maximum vertical displacement of shotcrete facing prepared from field measured and the results of FLAC 2D and PLAXIS 2D.
Figure 11: Horizontal displacement calculated by FLAC 2D and PLAXIS 2D for different steps of excavation
A comparison between the values of factor of safety (FOS) obtained by FLAC 2D and PLAXIS 2D in different steps of excavation is shown in Figure 12. The trends show that the overall value of FOS decreased with increasing of excavation depth. However, the value of FOS for the first step (excavation up to 2 m) is less than the second step (excavation up to 4 m). The execution of soil nailing consisted of making an initial 2 m vertical cut supported by shotcrete without any horizontal stabilizing (e.g. nail). Then, nailing system was applied in the second step (excavation up to 4 m), which played a key role to affectedly recover the value of FOS. From this point onwards, the FOS continuously decreased with increase of the depth of excavation. This reduction in the FOS was due to decrease of lateral earth pressure by increasing the depth of excavation (Wu, et al., 2000). The FOS predicted by numerical modelling in FEM and FDM between excavations depths of 4 m to 10 m was almost the same. However, the difference FOS predicted between two different methods for excavation depth of 12 m was notable. This difference might be related to different methods applied to consider the effect of water table in depth of 9 m. In designing of deep excavations, a major problem is often dominated by water flow around the walls. Water flow, influences the global stability of the wall and the stability of the excavation bottom where bulk heaving or boiling may occur (Fonte, 2010). Water flow patterns obtained by FLAC 2D and PLAXIS 2D are shown in Figure 13.
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Figure 12: FOS calculated by FLAC 2D and PLAXIS 2D for different steps of excavation
(a) (b)
Figure 13: Water flow vectors (a) FLAC 2D and (b) PLAXIS 2D
CONCLUSIONS
In this paper, a real case of soil nailing in an excavation project was studied. Six steps of excavation were studied through numerical modelling by FLAC 2D (FDM) and PLAXIS 2D (FEM) software to better realize the soil nailing displacements occurred during excavation. Numerical modelling were used to determine the maximum displacement, prediction of shear strain zone, and calculate FOS for the 6 steps of excavation. Mohr-coulomb model were used in modelling the excavation material by both software. According to the experimental measurement and numerical analyses the following conclusions are drawn:
1) It was found that finite difference software (FLAC 2D) and finite element software (PLAXIS 2D) are powerful tools for investigating the behaviour of a wall stabilized by soil anchorage and steel pile.
Vol. 18 [2013], Bund. Y 5893 2) FOS decreased with increase in the excavation depth. The decreasing rate compounds with
the progress of the excavation operation. However, using soil nailing system helps to improve factor of safety rather than unreinforced excavating.
3) A good agreement has been observed between the FOS predicted by numerical modelling in FEM and FDM for excavation depths of 6 m to 12 m. However, in the first and second step of excavation respectively with depth of 2 m and 4 meter, the FOS obtained by FDM was higher than the obtained FOS by FEM. These results might be related to different method of initial condition which was allocated by two different software.
4) Finite difference analysis needed appropriate constitutive model for a particular soil type and took considerable time for a complete analysis. In contrast, finite element analysis was more powerful and gave better results that match with interpretations of maximum displacement in X direction using the measured data.
ACKNOWLEDGMENT
The work was financially supported by Universiti Teknologi Malaysia under Research University Grant (Q.J130000.2622.06J95) and the Ministry of Education of Malaysia, MOE. The authors also deeply appreciate the significant contribution of Khesht Azma Consulting Engineering Company and its technical supervision office for providing the required data to make this research possible.
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