Numerical Analysis of a Novel Piling Framed Retaining Wall System

Transcription

1 The 12 th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 2008 Goa, India Numerical Analysis of a Novel Piling Framed Retaining Wall System Eli L. Branch Mueser Rutledge Consulting Engineers, New York, NY Eric C. Drumm, Richard M. Bennett Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN Saieb Haddad Tennessee Department of Transportation, Knoxville, Tennessee Keywords: Retaining Structures, Excavations, Numerical Analysis ABSTRACT: This paper summarizes the results of a practical application of a 2D non-linear finite element (FE) analysis for a novel retaining wall developed by the Tennessee Department of Transportation (TDOT). The wall design eliminates the need for a construction right of way behind the wall, thus it is ideal for urban areas. The design concept consists of vertical and battered H pile sections as the structural frame, and wood lagging that is installed as the soil is excavated during top-down construction. Vertical tie-down anchors and a concrete cap and facing are used to counteract overturning moments. A 2-D FE analysis of the wall system was conducted to understand how the earth pressures are applied to the sloped wall, and how the loads are distributed throughout the piling frame. An increased understanding of the performance of this new system will lead to more economic pile sections, anchors, and spacing under service loads. In addition, the construction sequence was modeled to investigate the non-linear response of the wall system. Parametric studies were conducted to investigate wall performance for different soil moduli, boundary conditions, and tie-down forces. The results show that active earth pressures are adequate for design and that TDOT s original design was conservative. 1 Introduction The construction of conventional retaining walls in urban settings is often difficult due to right-of-way restraints and/or cost restrictions. Conventional retaining walls include concrete cantilever walls, soldier pile with lagging, pile secant drilled cantilever walls, and walls using tie-back anchors for lateral support. Property adjacent to proposed walls is often unavailable or too expensive, prohibiting the construction of cantilever or mechanically stabilized earth retaining walls which require ample space behind the wall for construction. Walls utilizing tiebacks anchors have the same restrictions but instead of above ground, they require underground easements behind the wall to avoid buried utilities or adjacent building foundations. To overcome the challenges of retaining walls in urban environments, the Tennessee Department of Transportation (TDOT) has developed a new concept for a retaining wall. Their new wall is constructed from the top down thus greatly reducing the easement required behind the wall as well as the total costs. The concept consists of battered and vertical piles as the structural frame of the wall, and vertical anchors to provide additional stability against overturning (Pate and Haddad, 2007). After the piles are driven to refusal on rock, two vertical tie-down anchors per frame are anchored to rock to hold down the wall against overturning. Frames are spaced 3.04m on center, and the anchors are spaced 0.76m on either side of a frame. To transmit the soil forces to the frame, a concrete facing is poured spanning the frames. Pate and Haddad (2007) outline the details of the wall design as well as a description of the construction of the first pile-framed wall that was built in Knoxville, Tennessee in Figure 1 shows a cross-section view of the pile framed wall system (Pate and Haddad, 2007) along with a 3D schematic framing system and anchors. 4033

2 Figure 1. a) Cross Section of Wall (Pate and Haddad, 2007) b) 3D Schematic The pile-framed retaining wall designed by TDOT is a novel design that is unlike conventional retaining walls. As a result there are no previous studies of such a wall system. For conventional walls the earth pressure formulations of Rankine and Coulomb are still in wide use today. The earth pressures behind conventional walls are well recognized (e.g. Lambe and Whitman, 1969, Coduto, 2001) and have been investigated by the FEM (Goh, 1993). However, in conventional retaining walls it is typically assumed that the wall is free to translate at the top, producing active earth pressures. In the pile framed wall the anchor causes some lateral movement of the system into the soil, which could create passive conditions. Currently there is no previous research that provides a rational approach or justification of the assumption of active or passive conditions for the design of a pile-framed retaining wall. One the main objectives of this paper are to provide numerical results of the earth pressures that may develop in such a wall. The pile-framed wall consists of a battered pile inclined towards the soil, connected to a vertically driven pile, and a whaler pile that spans the frames. There is extensive data on the behavior and capacity of individual driven piles and piles in groups, and the response battered piles have been investigated (Amde et. al., 1997; and Rajashree, and Sitharam 2001). Previous studies have examined individual piles under combined loads and also tensile loads, but not piles framed together. In addition, studies of driven piles are for deep foundation applications, not retaining walls where the piles will extend to heights above final grade and soil is excavated on one side of the piles. Thus, it is questionable to simply extend conclusions obtained from studies of driven piles to the behavior of driven piles for retaining wall applications. Therefore this paper attempts to examine the behaviour of driven piles that are framed together for use as earth retention systems. 2 Numerical Model Development 2.1 Finite Element Program This study presents results from 2D FE analyses of pile framed retaining behavior with a representative soil with low cohesion. For validation, results are compared with earth pressures calculated by Rankine and Coulomb classical methods. The numerical analysis was performed with the 900-node version of the Automatic Dynamic Incremental Non-linear Analysis (ADINA) 8.4 computer program (ADINA, 2006). The Full Newton Iteration Scheme with a sparse equation solver was used for nonlinear analysis. The default convergence criterion was set to Energy, and the chosen energy tolerance was or 0.1%. Units of kilonewtons and meters were used in analysis for all geometry and input parameters. 4034

3 Since properties in the longitudinal direction of the wall are relatively constant, deformations in that direction were assumed zero; the problem was approximated as plane strain. The effective cross section of the wall consists of the pile frame and the tributary width of the concrete facing, therefore the analysis was based on a 3.04m width, which was the spacing of the frames. Seven-node triangular elements using free-form Delaunay meshing was used to model the soil elements and 2-node Hermitian beam elements were used to model the pile elements. The force from the tie down anchor was applied to the frame as a concentrated force instead of meshing the anchor with truss elements since the behaviour of the anchor is not important compared to that of the frame system. The behavior of a retaining wall is a problem of soil-structure interaction and the interface between the soil and the structural members is important to the predicted response. To model this interface, contact elements were employed to represent contact between the soil and the concrete facing of the wall. The default algorithm for solution with contact is the Constraint Function method and the analysis in ADINA becomes nonlinear when contact elements are used even if no nonlinear material models are used (ADINA, 2006). Although, frictionless or contact with Coulomb friction can be modeled, frictionless contact was used for analysis because it is difficult to accurately quantify frictional coefficients, the use of contact requires more computation effort, and a solution without contact should be obtained first before conducting analysis with contact (ADINA, 2006). 2.2 Input Parameters The linear elastic model was used for the pile elements, including the concrete steel composite batter pile. It was assumed the batter section would remain uncracked for service loads so the nonlinearity of the concrete was neglected. The Mohr-Coulomb (MC) model was used to characterize the soil, and a non-associated flow rule was assumed. For this initial study, drained conditions were assumed and the soil stratum was assumed uniform to simplify analysis. Table 1 shows selected values for the input parameters based on site data and typical values found in the literature (Bowles, 1996, Lambe and Whitman, 1968). Soil properties such as cohesion and friction angle were based on representative soil that is nearly cohesionless (full studies with a representative cohesive soil are not presented in this study). Table 1. Model Input Parameters Property Symbol Value Soil Steel Elastic Modulus, kpa E 72, ,000,000 Poisson's Ratio ν Total Unit Weight, kn/m 3 γ Internal Friction Angle, Degrees Φ 32 - Cohesion, kpa C Tension Cut-off, kpa T c Dilatation Angle, Degrees. Ψ 1 - The Poisson s ratio of the soil, ν, controls the lateral deformations of the soil material in ADINA, whereas it is typically represented by the coefficient of lateral earth pressure, Κ o, in soil mechanics. In the MC model in ADINA, K o, is not defined explicitly. In order to do so, the Poisson s ratio was back-calculated from Κ o using the following equation: K o (1) = ν 1 ν The coefficient of lateral earth pressure for the soil was determined by the friction angle, Φ, with the Jaky equation as follows: K o = 1 sinφ (2) 4035

4 Four separate cross sections comprised the pile frame. The vertical pile was a HP 12x53 section and the batter pile was a HP 10x42. The other two sections are concrete facing and HP10x42 composite section, and the concrete cap at the top of the wall encasing the HP12x53 pile. The section properties for the rolled section were taken directly from the AISC Steel Manual (AISC, 2006) and the composite section properties were calculated according to the Steel Manual. ADINA required that the bending moment of inertia, gross section area and the effective shear area be defined. Table 3 shows the section properties as well as the properties per unit width, the latter being input in ADINA. Table 2. Section Properties of Beam Elements Cross Section Moment of Inertia, I g Gross Area, A g Shear Area, A v m 4 m 4 /m m 2 m 2 /m m 2 m 2 /m Batter Pile HP 10x E E E E E E-04 Vertical Pile HP 12x E E E E E E-03 Batter Pile Composite 1.43E E E E E E-04 Vertical Pile Top Encased 2.97E E E E E E Model Geometry and Boundary Conditions For the soil mass, the vertical side boundaries are fixed against lateral translation and rotation, but allow vertical translation. The horizontal bottom boundary is a pinned boundary, restricting translation in each direction but not rotation. Since the underlying bedrock is significantly stiffer than the soil, it does not deform relative to the soil, so the base is pinned, and rock was not meshed. The boundaries distances were sufficiently remote to not significantly influence the solutions. An investigation of the boundary distance impact on results can be found in Branch (2008). The piles are driven to refusal in rock, as a result the fixity condition may not be completely fixed or pinned in reality, they are assumed fixed and compared to other conditions in the following section. The dimensions of the cross section analyzed were based on the typical section used for design by TDOT (Haddad and Pate, 2007). The height from the finished grade to the frame connection point was 7.62m, with the vertical pile extending up another 1.83m. The batter pile was at a slope of 3:1 (vertical: horizontal). Figure 2 illustrates a typical mesh dimensions as well as boundary conditions. Figure 2. Typical 2D Mesh Geometry and Boundary Conditions 2.4 Construction Sequence The construction of the pile frame consists of excavating an initial amount of soil to set up pile driving. The piles are driven and welded together creating the frame. The tie-down anchors are installed, and the soil is then excavated in lifts, with wood lagging being installed as the soil is excavated. Forms are set and the concrete face 4036

5 is poured, followed by the concrete cap. Due to the complexity of the construction details, some simplifications and assumptions were made in the numerical analyses. To induce geostatic stress in the soil gravity was applied to the entire soil mass except for the top 1.83m of soil, which for simplicity was represented with a uniform pressure equivalent to the vertical stress of 1.83m of soil. The pressure load was applied with gravity in 10 steps. The pile elements were present and connected from time zero, using the rolled section properties for the piles so that the properties were consistent along the length of the batter pile and vertical pile respectively. In order for the piles to have the geometry of the soil deformed due to gravity, the steel was given a small modulus. This allowed the piles to deform with the soil, but introduced slightly different results compared with soil deforming with no piles. The differences were neglected since all results due to construction were taken relative to the results after gravity application. With the geostatic stress in the soil, the restart analysis option was used so that model inputs could be updated and a new analysis performed. In the second analysis, time functions are updated to start at the time of the end of the first analysis and include the construction sequence. The modulus of the steel and the cross sections were updated to their actual values. Although the composite section does not reach full rigidity until the concrete hardens, this construction detail was neglected, and the composite properties were present before excavation commenced. The excavation sequence was simulated by removing the soil elements in the excavated zone in four lifts as shown in Table 3. The entire construction sequence is summarized in Table 3. Table 3. Construction Sequence Summary Time Load Construction Process 1.1 Self Weight of Steel Piles Top Soil Removed 1.2 Anchor Force Applied (Design Force: 245 kn per Anchor) Soil Removed in 4 Lifts Prepare for Pour 1.8 Weight on Batter Pile Above grade Weight on Top of Vertical Pile Weight of Backfill Backfill in 2 Lifts 2.5 Verification of Model TDOT designed the first wall based on active earth pressures, so the magnitude of lateral earth pressures acting behind the concrete face were compared to classical earth pressure calculations in Figure 3. The concrete facing begins 1.83m below the pre-construction and final ground surface so the calculated stresses begin there while the theoretical pressures are relative to the original ground surface. The predicted results compare well with Rankine s Active pressures for the top 2/3 of the concrete face, but large earth pressures at the base of the concrete facing were predicted. This large thrust at the base was also predicted by a simpler model of the wall that idealized the soil-pile interface as a beam on an elastic foundation with springs to represent the soil, and is reasonable due to the increased system stiffness at the base where the piles are embedded into the ground. 3 Results 3.1 Mohr-Coulomb Yielding A typical illustration of the yield zones in the soil behind the pile-framed wall system is shown in Figure 4 for the initial model with the 245kN design anchor force specified by TDOT. The use of the Mohr-Coulomb model revealed significant amounts of yielding behind the wall. The yield zone extended the top 2/3 of the wall, and the failure surface is inclined to active failure planes. There is additional yielding near the toe along with tension yielding. This suggests that soil in front of toe heaves up due to the reduction of vertical stress from the excavation and the outward movement of the wall. The presence of plastic yielding proves the importance of a non-linear soil model to more closely evaluate the behavior of the soil and pile-framed wall system. 4037

6 1.83 Depth Below Ground Surface, m Jaky At Rest Rankine Active, Cohesive Coulomb Active, Cohesionless ADINA Horizontal Stress Horizontal Earth Pressure, kpa Figure 3. Calculated Earth Pressures vs. Classical Theories Figure 4. Mohr Coulomb Yield Zones 3.2 Effect of Boundary Condition As stated previously, piles driven into rock are not completely fixed or pinned so the model was analyzed for both conditions. TDOT s design of the wall assumed the pile actually developed fixity about 3.6 m below grade in front of the wall. This was investigated by restraining all degrees of freedom for a node along the pile near this depth as well as fixing the node at the grade for further comparisons. The effect of pile fixity on the moment in the batter pile is shown in Figure 5. The boundary condition at the base makes no difference, whereas the vertical location of fixity decreases the positive moment in the span but increases the negative moment. 3.3 Effect of Soil Stiffness Since the elastic modulus of soil can be highly variable and difficult to predict, the response at the top of the wall due to different soil moduli was compared over the construction sequence, after the anchor was applied, Figure 6. The displacement when the anchor was applied was taken as zero and subsequent displacements measured relative to that stage, since the anchor is applied before any soil is removed and displacements in the field at that stage should be practically zero. The deflections for all moduli show deflections away from the retained soil during excavation, and tipping back to the soil when the massive concrete cap is poured. The displacements increase with decreasing stiffness, but differences are less significant when the modulus increases past 72,000 kpa. 4038

7 3.4 Effect of Tie-Down Anchor Force The installation of the tie-downs is one of the most difficult and costly aspects of the process, so understanding the effects of the anchors is essential. TDOT s original design included a force per anchor of 245 kn, which was based on engineering judgement. In a later wall, designers increased the force to 445 kn. The displacements of the batter pile with 3 levels of anchor load are shown in Figure 7. Increasing the anchor load decreases the outward deflection of the pile, but even with no anchor the predicted deflection is less than 2.5cm. In addition, the slope of the displaced pile at the top of the wall decreases with anchor force, suggesting that the anchor limits rotations as well. The maximum anchor force that can be applied is limited by the bending capacity of the horizontal whaler and the battered pile. Thus the deflection of the wall can be controlled by selection of member sizes which will allow greater anchor forces. 15 Positive Moment: Compression on Exposed Side of Wall Negative Moment: Compression on Interior Side Frame Connection Height, Top of Facing 12 Distance Along Pile, m 9 6 Finished Road Grade, Bottom of Facing Base Fixed 3 Base Pinned TDOT Design Fixity, 3.65m Below Grade Fixed at Grade 0 Bedrock Bending Moment, kn-m Figure 5. Effect of Pile Boundary Conditions -2.5E-02 E =25 MPa -2.0E-02 E=72 MPa E=125 MPa Lateral Displacement, m -1.5E E E E E Anchor Applied to Frame 1st Lift of Soil Removed 2nd Lift Removed 3rd Lift Removed 4th Lift Removed Time Prepare for Pour Batter Face Parapet Poured Half of Backfill Complete Backfill Figure 6. Top of Wall Response as a Result of Soil Stiffness 4039

8 15 Frame Connection Height, Top of Facing 12 Distance along Pile, m 9 6 ` Finished Road Grade, Bottom of Facing 3 No Anchor 245 kn per Anchor 445 kn per Anchor Bedrock E E E E E E+00 Displacement, m Figure 7. Tie-Down Anchor Force Effects on Deflected Shape of Batter Pile 4 Conclusions The results of this study suggest that the design assumption for active earth pressures may be appropriate; however the location of the earth pressure resultant may be less than the third or quarter point, decreasing the overturning moments on the wall. Based on the wall displacements and bending moments, the design tie down force of 245 kn is conservative for most conditions. For concrete facing heights less that 7.62m, the tie-down anchor could be left out for moderately stiff soils because the deflections would be small and members would not approach yielding. The deflected shape of the batter pile exhibits relative movement into the soil near the grade suggesting a shift from active toward passive conditions in that portion of the wall. 5 Acknowledgements The authors are grateful for the support provided to the first author by Graduate School at The University of Tennessee. 6 References ADINA R&D, Inc, Theory and Modeling guide, Report ARD 06-7, vol. I; AISC Steel Construction Manual, American Institute of Steel Construction; 13th edition Amde, A.M., Chini, S.A., Mafi, M. (1997). Model study of H-piles subjected to combined loading, Geotechnical and Geological Engineering,,15(4), Bowles, J.E Foundation Analysis and Design, McGraw-Hill Science, New York (USA). Branch, E. L Numerical Analysis of Pile-Framed Retaining Wall, Master s Degree Thesis, University of Tennessee (USA) Coduto, D.P Foundation Design: Principles and Practices, Prentice Hall, New Jersey (USA) Goh, A. T Behavior of cantilever retaining walls, Journal of Geotechnical Engineering, 119(11), Lambe, W. W., Whitman, R Soil Mechanics, Wiley, New York (USA). Pate, H., Haddad, S Piling framed tie-down concrete retaining wall, The Magazine of The Deep Foundations Institute (Spring 2007), Rajashree, S. S., Sitharam, T. G. (2001). Nonlinear finite-element modeling of batter piles under lateral load, Journal of Geotechnical and Geoenvironmental Engineering, 127(7),