Numerical investigation of soil nail wall during construction

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2 practice. This paper presents a 2-D FEM analysis of a well-known soil nail wall in Germany and verifies the reliability of 2-D FEM for this 3-D problem. 2 IDEALIZING A SOIL NAIL WALL SYSTEM 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. These methods may be categorized into three methods described below: A. Using composite material to combine the soil and reinforcement into one material; B. Plane strain assumption by simulating discrete reinforcements with a continuous plate; and C. Simulation of nail as an external connection to continues soil as a connector. The Method B 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 p, using area ratio factors such as the axial stiffness (EA). This method is adopted in this study. The interface elements also were used in this study to accurately model the interaction between soil nail and surrounding soil. It is clear that when the nail is idealized as a plate, the surface area in contact with the soil is significantly increased. It would also mean that the transfer of stresses from the soil mass to reinforcement by friction across the increased area would be magnified if no reduction was taken on the interface friction. A factor of equivalent surface area is considered in the interface friction and nail stiffness in this study, a similar method was also used by Al-Hussaini and Johnson (1978) for numerical analysis of a reinforced earth wall. The idealized 2-D plate for a 3-D nail is schematically shown in Figure 1. thorough field measurement over an extensive period of time. The case used in this study is reported by Stocker and Riedinger (1990). This nearly 15 m deep excavation was designed in a sloping terrain in Stuttgart, Germany in One side of excavation is bordered directly upon a city street, another side upon private houses. No anchor was allowed to be driven under the neighbouring buildings. The excavation was carried out in steps of 1 or 1.1 m cover the whole length of the wall. The nails consisted of deformed steel bars with diameters of 25 mm and 28 mm, yield strength of 420 MPA, and failure strength of 500 MPA. Figure 2: Site and layout of walls (Stocker and Riedinger, 1990) Figure 3: Typical layout of nailed walls (Stocker and Riedinger, 1990) Figure 1: Smearing nail into continues plate (Al-Hussaini and Johnson, 1978) 3 A SOIL NAILING CASE IN GERMANY 3.1 Engineering Background A large number of soil nailed walls have been constructed during the last two decades, both for permanent and temporary structures. However, only a few of them have 3.2 Site Soil Conditions The soils at the site consisted of 0.8 to 1.8 m thick upper layer of fill material, underlain by layers of stiff to medium consistency sandy silt. Bellow these layers are a layer of claystone. The soil strata are schematically shown in Figure 3. The soil parameters obtained in the laboratory (Stocker and Riedinger, 1990) are shown in Table 1. Table1 Typical geotechnical parameters of soil layers Density Friction Cohesion E

3 (KN/m2) (KN/m2) (KN/m2) Fill Sandy silt Claystone The 2-D plane strain continueous plate method is used in this analysis. The most important factor in this method is to idealize the 3-D soil nail into a 2-D plain strain shell element with equivalent axial capacity and stiffness. To do so, two equations should be met: measurement for long-term performance and temperature influence can be found in Stocker and Riedinger (1990). (EA) plate= (EA) Nails (1) (EI) plate= (EI) Nails (2) Where E is the modulus of elasticity, A is the correction sectional area of plate or nail, I is the moment of inertia of plate or nail. Based on these equations the thickness of the plate can be calculated from this equation: EI Tplate 12( ) Nail (3) EA E eq=(a nail/a) Enail+(A grout/a) E grout (4) Figure 4: 2-D FEM model of soil nail wall Where A is total gross section of nail and grout. According to the assumptions above, the input parameters for 2-D FEM are shown in Table 2.. Table 2. Input parameters of the nail plate in 2-D FEM 2 E nail (Kn/m ) 200e 6 2 E eq (kn/m ) 37e 6 2 E grout (Kn/m ) 6 30e EI eq (kn.m2/m) 181 D nail (cm) 2 EA eq (kn/m) 2.89e 5 D grout (cm) 10 T plate (cm) 8.7 The Mohr Coulomb failure criterion is used in soil modeling. The soil properties are shown in Table 3. Figure 5: Distribution and change of the nail force with proceeding excavation (Stocker and Riedinger 1990) Table 3: Soil properties for 2-D FEM Soil Type Density (kn/m 3 ) Friction (Degree) Cohesion (kn/m 2 ) Module of elasticity (MN/m 2 ) Fill Sandy Silt claystone Based on the geometry of excavation and soil stratum conditions, a 2-D FEM model is built, as shown in Figure 4, where nails are modelled as 2-D shell elements with the same lengths as the case in the field. 4 FEM RESULT ANALYSES A total of four nails were equipped with strain gages applied to the steel at the intervals of 0.5 to 1.5 meter (Stocker and Riedinger 1990). Thus, stresses could be measured along the axial of the nail during excavation. The distribution of nail force and its increase with the depth of excavation is shown in Figure 5. The nail force increases significantly as excavation goes deeper. The distribution of other force nails at the final excavation level is shown in Figure 6. More detailed about the Figure 6: Distribution of nail force at final excavation level (Stocker and Riedinger 1990) The horizontal movement of soil during construction was also monitored through slope indicators. The movement of soil during excavation is shown in Figure 7. The displacement results are almost the same as measurements in the field and the maximum displacement occurs at the top of the wall, 60 mm. The horizontal displacement field from 2-D FEM is shown in Figure 8. The comparison of the horizontal displacement from 2-D FEM with those of field measurement at the final

4 excavation is shown in Figure 9, where it can be found that the 2-D FEM can provide very reliable analysis results of soil movement during construction. very similar. This shows that results from 2-D FEM are more conservative in predicting nail load. The development of Nail 3 during excavation is shown in Figure 12, where the nail load increases as excavation goes deeper and deeper. This is similar to the field measurement, though there are discrepancies in the magnitude and the locus of maximum nail load. Figure- 7: Horizontal wall deformation base on different excavation level (Stocker and Riedinger 1990) Figure 9: Comparison on horizontal displacement between FEM and field measurement Figure 10: Load at different levels of nails at the end of excavation Figure 8: Horizontal displacement of soil at the end of construction (color scale in cm) The distribution of nail load along its length is shown in Figure 10, where the maximum nail load occurred at some distance from the facing. This is similar to the field measurement. But the variation of soil nail load is much larger in FEM than field measurement. It seems the friction between nail and soil is more mobilized in the field than the one in FEM. Nails 3,7,9 and 12 are located approximately in the depth of 3,7,9 and 12 meter under earth. The comparison between the maximum nail loads at different levels of nails is shown in Figure 11, where the FEM predicts much larger nail loads than the field measurement. However the trends from both cases are

5 Figure: 11. Comparing nail force based on measurement and FEM Publication FHWA0-IF , Federal Highway Plumelle, C., Schlosser, F., Delage, P., and Knochenmus, G French national research project on soil nailing: Clouterre. Design and Performance of Earth Retaining Structures. ASCE, GSP Stocker, M., Riedinger, G The bearing behaviour of nailed retaining structures. Design and Performance of Earth Retaining Structures, ASCE GSP 25, Zhou, Y. D., Cheuk, C.Y., et al An embedded bond-slip model for finite element modelling of soil-nail interaction. Computers and Geotechnics, 36(6): Figure 12: Development of nail load in Nail 3 with excavation CONCLUSIONS AND DISCUSSIONS A numerical investigation of a soil nail wall is presented in this paper. A well-known case in Germany is used in this study. A 2-D FEM is used to simplify this 3-D problem. The results show that 2-D FEM can provide reliable results, particularly in soil deformation during soil nail construction. For soil nail load, 2-D FEM tends to provide more conservative results. There are also some discrepancies for the locus of the maximum nail load compared with field measurement. With the rapid improvements in computer technology, it is expected that more 3-D FEM analyses will be implemented with greater ease in the future. However, this study shows that a 2-D FEM can provide reliable results and will be still popular in practice due to its simplicity and easy implementation. ACKNOWLEDGEMENT The editorial help from Mr. Yudong Wu of the University of Toronto is greatly appreciated. REFERENCES Al-Hussaini, M.M. and L.D. Johnson Numerical analysis of a reinforced earth wall. ASCE, Symposium on Earth Reinforcement, Briaud, J. L. and Y. Lim Soil-nailed wall under piled bridge abutment: Simulation and guidelines. J. of Geotechnical and Geoenvironmental Engineering, 123(11): Byrne, R.J., Cotton, D., Porterfield, J., Wolschlag, C., and Ueblacker, G Manual for design and construction monitoring of soil nail walls. Report FHWA-DP-96-69R, Federal Highway Elias, V. and Juran, I. (1991). Soil nailing for stabilization of highway slopes and excavations. Publication FHWA-RD , Federal Highway Lazarte, C.A., Elias, V., et al Geotechnical engineering circular No. 7: Soil nail walls.

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