Iss25 Art3 - Simulation of Nail Structures.pdf - Plaxis

exactly known, D can be taken as two to threetimes the vertical depth of excavation H .Further, for known values of D and H , width ofexcavation W e can be taken equal to three to fourtimes D and the horizontal distance from wall faceto the end of mesh boundary B e can be chosenequal to three to four times (H + D). Figure 1shows the mesh boundaries and fixity conditions.Material modelsMost commonly used material model to simulatein-situ soil for excavation and retaining structuresapplications is the HS-model (Hardening soilmodel). However, if all the input parameters forHS-model are not available, alternatively Mohr-Coulomb material model can be used. Facings andnails can be modeled as elastic materials.Use of interface elementsIt has been reported in the literature that thecoefficient of soil-reinforcement interactionobtained from field pullout tests (e.g. Wang andRichwein 2002) is found to be significantly morethan unity. Therefore, use of interface elementsbetween nail and soil can be eliminated anddefault setting of “Rigid Interface” in material setsmenu for soil and interfaces can be used in thesimulation process.Equivalent nail parametersSoil nail structures are modeled as plane strainproblem in PLAXIS 2D. As stated earlier, plate (orgeogrid) structural elements can used to simulatenails. The most important input materialparameters for plate elements are the flexuralrigidity (bending stiffness) EI and the axialstiffness EA (for geogrid structural element onlythe axial stiffness EA is required). Both plate andgeogrid structural elements are rectangular inshape with width equal to 1 m in out-of-planedirection.Since, the soil nails are circular in cross-sectionand placed at designed horizontal spacing, itis necessary to determine equivalent axial andbending stiffnesses for the correct simulation ofcircular soil nails as rectangular plate or geogridelements. A detailed discussion on the suitabilityof plate or geogrid structural elements to modelsoil nails is presented later, given below is thegeneral procedure to determine equivalentmaterial parameters.Figure 1: Mesh boundaries and fixity conditions (Briaud and Lim 1997)For the grouted nails, equivalent modulus ofelasticity E eq shall be determined accounting forthe contribution of elastic stiffnesses of both groutcover as well as reinforcement bar. From thefundamentals of strength of materials, E eq can bedetermines as:E EAnAgeq = n`E(1)Aj + g`Ajwhere: E g is the modulus of elasticity of groutmaterial; E n is the modulus of elasticity of nail;E eq is the equivalent modulus of elasticity of2grouted soil nail; A = 0.25rD DHis the total cross-sectional area of grouted soil nail;Ag= A - Anis the cross-sectional area of grout2cover; An= 0.25rdis the cross-sectional area ofreinforcement bar and D DH is the diameter of drillhole. If, S h is horizontal spacing of soil nails,knowing the equivalent modulus of elasticityE eq (equation 1) for the grouted soil nail, the axialand bending stiffnesses can be determined usingequations (2) and (3) respectively.2EeqAxial stiffness EA kN/mD DH6 @ = crm (2)S h 442 EeqBending stiffness EI kNm / mrD DH6 @ = c m (3)S h 64www.plaxis.nl l Spring issue 2009 l Plaxis Bulletin 17

Plaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2DSubstituting, EA and EI values in the materialproperties menu for Plate elements, PLAXISautomatically determines the equivalent platethickness in meter d eq using equation (4).deq= 12c EAEI mProcedure for numerical simulationsPLAXIS (2006) and the information available inleterature (e.g. Shiu et al. 2006; Fan and Luo2008) may be referred for the understandingof simulations of soil nail walls with complexgeometry and loading conditions.Staged construction option shall be used tosimulate the infuence of construction sequence ofsoil nail walls (indicated as E 1, E 2, …E n, in Figure1). In each excavation stage, soil clusterrepresenting excavation lift (defined in inputprogram) is deactivated and nails (modeled asp(4)plate or geogrid elements) and facing (modeled asplate element) shall be activated. This procedurecan be followed till finish livel of the soil nail wall isreached.Updated mesh analysisIn order to take into account the effects of largedeformations, PLAXIS 2D provides an optional‘Updated Mesh’ analysis to perform basic typesof calculations (Plastic calculation, Consolidationanalysis, Phi-c reduction). Results of the finiteelement simulation of the 10 m high soil nail wallusing ‘Updated Mesh Analysis’ are indicated inTable 1. Material properties and other soil nail wallparameters adopted are given in Table 2.It may be observed from Table 1 that the use of‘Updated Mesh’ results in marginal influence onthe soil nail wall simulation results. Additionally,updated mesh analysis increases the calculationtime significantly. Similar observations are madefor the 18 m high soil nail wall.Study on the use of “plate” or “geogrid”elements for simulating soil nailsAs brought out earlier, in practice, both plateand geogrid structural elements are being usedto simulate soil nails in modelling of soil nailstructures using PLAXIS 2D. In the light of fact thatconsideration of bending and shear resistance ofsoil nails is conservatively ignored in the analysisand design of soil nail structures, suitability ofusing plate or geogrid structural element inmodelling soil nails has been examined.Two soil nail walls of 10 m and 18 m vertical heightdesigned conventionally with reference to FHWA(2003) are considered for the study. Two differentheights of soil nail walls are selected for theanalysis so that a comparison can be made basedon the trends observed. Prime objective beingto highlight the implications of the use of plateor geogrid elements to simulate soil nails, similargeometry and same in-situ soil conditions havebeen used throughout the analysis.Parameters Using plate elements Using geogrid elementsGlobal factor ofsafetyMax. lateraldiscplacement(mm)Max. axial force(kN/m)NormalanalysisUpdated meshanalysisNormalanalysisUpdated meshanalysis1.59 1.60 1.57 1.5922.82 22.28 23.86 21.3174.82 73.29 85.44 83.80Table 1: ‘Update Mesh Analysis’ of soil nail wall simulation (H = 10 m)ParameterValueVertical height of walls H [m] 10.0 and 18.0Nailing typeSimulation modelElement typegroutedplane strain15- nodeIn-situ soilMaterial modelMohr-CoulombCohesion c [kPa] 4.0Internal friction angle z[deg] 31.5Unit weight c [kN/m 3 ] 17.0Elasticity modulus E s [MPa] 20.0Poison’s ratio of soil y s 0.3Grouted nails and facingMaterial modelelasticYield strength of reinforcement f y [MPa] 415.0Elasticity modulus of reinforcement E n [GPa] 200.0Elasticity modulus of grout (concrete) E g [GPa] 22.0Diameter of reinforcement d [mm] 20.0 (25.0)Drill hole diameter D DH [mm] 100.0Length of nail L [m] 7.0 (13.0)Declination wrt horizontal i [deg] 15.0Spacing S h x S v [m] 1.0 x 1.0Facing thickness t [mm] 200.0Table 2: Parameters adopted for numerical simulations using PLAXIS 2DNote: Figures in bracket correspond tot he 18 m high soil nail wall; all other parameteres are samefor both 10 m ad 18 m soil nail walls.Both the walls are simulated using PLAXIS2D following the procedure and preliminarysuggestions stated earlier. Two series ofsimulations are performed, one with the useof plate structural elements to simulate soilnails and the other with the use of geogridstructural elements to simulate soil nails. At eachconstruction stage of both the walls, observationsare made with regard to the global factors ofsafety, maximum lateral (horizontal) displacementof walls, maximum axial tensile developed anddevelopment of bending moment and shear forcein nails (for plate elements only).Figure 2 shows the PLAXIS 2D models for both 10m and 18 m high soil nail walls. Various materialproperties and other parameters used forsimulation are as indicated in Table 2. “P” and“G” in the plots of the analysis correspond to theobservations made for simulations using plate andgeogrid structural elements respectively.Figure 3 shows the trend of variation of globalfactor of safety of the soil nail walls withconstruction stage. It is evident from Figure 3that for fully constructed soil nail walls (i.e. 100%construction), consideration of bending stiffnessof nails in the analysis have negligible influence onthe global stability. In other words, both plate andgeogrid structural elements are able to capturesimilar response and hence, either of the two canbe used. However, it is worth noting from Figure3 that consideration of bending stiffness of nailsin the analysis has significant influence duringthe construction stage. Geogrid elements resultsin significantly less factors of safety for globalstability in comparison to the plate elements.Alternatively, it can be interpreted that bendingstiffness plays important role in the stability ofsoil nail walls during the construction stage. Thisaspect is overlooked if geogrid elements are usedto simulate soil nail in the finite element analysis ofsoil nail walls.Figure 4 shows the trend of maximum lateraldisplacements of the soil nail walls withconstruction stage. It is evident from Figure 4 thatdisplacement response captured by both geogridelements and plate elements closely resemblesand hence, results in negligible influence on theanalysis of soil nail walls.18 Plaxis Bulletin l Spring issue 2009 l www.plaxis.nl

Plaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2DFigure 5 shows the development of maximum axialforce in nails with construction stage. From Figure5, it can be observed that on an average themaximum axial force developed in nails simulatedusing geogrid elements is found to be 15% morein comparison to that developed in nails usingplate elements. In other words, lesser axial forcedeveloped in nails simulated using plate elementsis credited to the contribution of bending stiffnessof the nails.This observation is in good agreement with theliterature. Figure 6 shows the variation of axialforce along the nail length for nails at differentlevels in 10 m high soil nail wall. Very closeresemblance among the axial forces variationalong nail length is evident from Figure 6 for thenails simulated using geogrid and plate elements.Similar observations were made for 18 m high soilnail wall.Development of maximum bending moment andmaximum shear force in nails with constructionstages are shown in Figures 7 and 8 respectively.It is evident from Figures 7 and 8 that bending andshear capacities of soil nail start mobilising withincreasing construction stages. For soil nail wallsof greater heights such as 18 m, the magnitude ofmaximum bending moment and maximum shearforce developed in soil nails with constructionstages are considerable.Figure 9 shows the variation of bending momentsand shear forces along the nail length for nailsat different levels in 10 m high soil nail wall.Similar observations were made for 18 m highsoil nail wall. It is interesting to note that bendingmoments and shear forces are concentrated nearthe face of the wall. This provides an insight intothe facing failure modes of the soil nail walls. Asmentioned previously, in practice, soil nail arerigidly connected with the facing (FHWA 2003;Joshi 2003) and therefore, it may be desirableto appraise the facing design. Improper designmay lead to the bending and/or shear failuresof soil nails at or near the facing. Use of geogridelements for simulating soil nails may lead to thecomplete negligence of this aspect of the soil nailwall analysis.Thus, from the above discussions it is apparentthat the use of plate elements provides betterinsight into the analysis of soil nail walls usingfinite element simulations. Hence, when PLAXIS2D is used to investigate the cause of failure orto assess the performance of soil nail structure, itis advisable that use of plate structural elementsshall be preferred over geogrid structural elementfor simulating soil nails.Influence of mesh density on the soil nailstructures simulationsAnother important aspect of the numericalsimulation of any structure is the density of finiteelement mesh adopted for the analysis. PLAXIS2D provides option to the users to select meshdensity in the range from very coarse to very fine.Influence of mesh density on the analysis of thesoil nail wall and the results corresponding to theanalysis of 10m high soil nail wall are presentedin Table 3. From Table 3, it can be observedthat global factor of safety varies significantlyfrom 1.61 for very coarse mesh to 1.52 for veryfine mesh. Also, maximum lateral displacementvaried from 20.93mm for very coarse mesh to28.35mm for very fine mesh. Similar trends areobserved for the stress parameters in nails suchas development of axial force, bending momentand shear force. Though, denser mesh may resultin more accurate analysis, it is important to notethat increasing the mesh density results in drasticincrease in the overall calculation time (Table 3).Thus, appropriate mesh density shall be useddepending upon the degree of accuracy requiredand the capacity of the computing machine. Ingeneral, coarse mesh density globally and finemesh density in the vicinity of the soil nail wall canbe used.Concluding remarksIn this article, an attempt has been made to bringout implications of the use of plate and geogridstructural elements for simulating soil nails onthe analysis of soil nail structures using PLAXIS2D. Based on the observations from the analyses,use of plate structural elements in comparison togeogrid structural element is advised to simulatesoil nails. Further, influence of mesh density onthe analysis of soil nail structures is highlighted.Preliminary suggestions made regardingnumerical simulations of the soil nail structuresthat may be useful for the Plaxis user community ingeneral and soil nailing practitioners in particular.Figure 2: Simulated soil nail walls using PLAXIS 2DAcknowledgementsThe work presented in this article is a part ofthe research project Guidelines for Soil NailingTechnique in Highway Engineering (R-86) financedby the Ministry of Shipping, Road Transport andHighways, India. The authors express thanks tothe Ministry for funding and providing necessarysupport for the project.continue on page 21Figure 3: Trend of global factor of safety with construction stagewww.plaxis.nl l Spring issue 2009 l Plaxis Bulletin 19

Plaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2DFigure 4: Trend of lateral displacements with construction stageFigure 5: Development of maximum axial force with construction stageFigure 6: Variation of axial force along nail length (10 m high soil nail wall)Figure 7: Development of maximum bending moment with construction stageFigure 8: Development of maximum shear force with construction stageFigure 9: Variation of shear force and bending moment along nail length(10 m high soil nail wall)20 Plaxis Bulletin l Spring issue 2009 l www.plaxis.nl

Plaxis Practice: Simulation of Soil Nail Structures using PLAXIS 2DReferences• Babu, G. L. S. and Singh, V. P. (2007). “Plaxispractice - Stabilization of vertical cut using soilnailing.” Plaxis Bulletin, October, No. 22, 6-9.• Briaud, J.-L. and Lim, Y. (1997). “Soil nailed wallunder piled bridge abutment: simulation andguidelines.” J. Geotech. Geoenviron. Eng.,123(11), 1043–1050.• Fan, C. C. and Luo, J. H. (2008). “Numericalstudy on the optimum layout of soil nailedslopes.” Comput. Geotech., 35(4), 585–599.• FHWA. (2003). “Geotechnical engineeringcircular No. 7 - soil nail walls.” Report FHWA0-IF-03-017, U. S. Department of Transportation,Federal Highway Administration, WashingtonD. C.• Jewell, R. A. and Pedley, M. J. (1992). “Analysisfor soil reinforcement with bending stiffness.” J.Geotech. Eng., 118(10), 1505–1528.• Joshi, B. (2003). “Behaviour of calculated nailhead strength in soil-nailed structures.” J. Geotech.Geoenviron. Eng., 129(9), 819–828.• Juran, I., Baudrand, G., Farrag, K. and Elias, V.(1990). “Kinematical limit analysis for design ofsoil-nailed structures.” J. Geotech. Eng., 116(1),54–72.• Liew, S. S. and Khoo, C. M. (2006). “Soil nailstabilisation for a 14.5m Deep excavation atuncontrolled fill ground.” Proc. 10th Int. Conf.On Piling and Deep Foundations, 31 st May – 2 ndJune, Amsterdam, The Netherlands.• Plaxis (2002). “Plaxis practice I.” Plaxis Bulletin,June, No. 12, 14-17.• PLAXIS. (2006). Plaxis user manual, Delft Universityof Technology & Plaxis bv The Netherlands.• Schlosser, F. (1991). “Discussion – The multicriteriatheory in soil nailing.” Groun. Eng.,November, 30-33.• Shiu, Y. K. and Chang, G. W. K. (2006). “Effectsof inclination, length pattern and bendingstiffness of soil nails on behavior of nailedstructures.” GEO Report No.197. GeotchnicalEngineering Office. Hong Kong.• Wang, Z. and Richwien, W. (2002). “A study ofsoil-reinforcement interface friction.” J. Geotech.Geoenviron. Eng., 128(1), 92-94.Mesh densityElements perunit volumeGlobal factorof safetyMax. lateraldisplacement(mm)Total calculation time (min)Very coarse 0.39 1.610 20.93 1.13Coarse 0.60 1.598 22.31 1.51Medium 0.98 1.592 22.86 2.45Fine 2.08 1.553 24.79 5.51Very fine 4.14 1.521 28.35 15.15Table 3: Influence of mesh density on finite element simulationNote: (1.) FS values correspond to the fully constructed wall. (2.) If FS is to be determinedafter each construction stage, calculation time may increase even more drastically.www.plaxis.nl l Spring issue 2009 l Plaxis Bulletin 21