Iss25 Art3 - Simulation of Nail Structures.pdf - Plaxis

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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
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