Modeling Embankment Induced Lateral Loads on Deep Foundations By Dr. Siva Kesavan URS Corporation And Professor Rajah Anandarajah Johns Hopkins University

z x B y x B Fig. A. Introduction The problem analyzed in this presentation is inspired by a real-world problem where the construction of a landfill at a rate too fast caused damage to an adjacent bridge. Without presenting actual names, the problem is described and analyzed using an elasto-plastic finite element computer code (HOPDYNE) to illustrate how an advanced numerical procedure can help develop an understanding of the failure mechanism, and reveal the true cause of the failure in a complex problem like this, where loading and consolidation take place simultaneously. The problem involves soil-structure interaction. The geometry is too complex, raising questions concerning the validity of one-dimensional assumptions used in Terzaghi’s one-dimensional consolidation theory. The clayey soil in the foundation is too soft and is certain to behave highly plastically, raising questions about the validity of using elastic theories to calculate the stresses in the foundation caused by the weight of the landfill. In other words, the problem is too complex, pointing to the need for a method like the finite element method for not only verifying the validity of the conventional methods normally used in analyses, but also to explain the true cause of failure. Problem Definition A landfill construction took place near a pile-supported bridge as shown in the figure. The foundation soil consisted of a very soft clay sandwiched between a dense sand and stiff clay layers. When the height of the landfill reached 80 feet, some of the piles had cracked at the pile head level and separated from the pile head laterally by about a foot (i.e., in the direction of X-axis shown in the figure). Objectives of the Presentation We first discuss conventional methods of analyses that would normally be used (Part I). The problem is then idealized into a two-dimensional problem and analyzed by FEM using two different further assumptions as follows: Place a rigid vertical wall on section B-B, and calculate the changes in horizontal normally stresses on that wall during the construction of the landfill (Part II), and Include the some of the piles in the model as shown in red in the figure above and repeat the analysis (Part III). The validity of the use of 2D model is then discussed. z x B y x B Fig. A.

Part I: Classical Approach:Elastic Analysis Elastic Change in Horizontal Normal Stress Near the First Pile Due to Embankment Loading: Using elastic equations, the change in horizontal stress near the first pile was calculated at different depths. As seen in the figure, the variation of the stress with depth is approximately linear, with about 1350psf at a depth of 70 feet. Assuming that the pile is fixed at both ends (anchored into the stiff clay at the bottom, and held by the bridge at the top), the end bending moments and shear forces are computed as Elevation (ft) Change in Horizontal Stress (psf) Assuming a compressive strength of about 3000 psi and a shear strength of about 1500 psi, the piles must have cracked in compression, supporting the observation. However, the validity of this analysis is highly questionable.

Part I: Classical Approach: Plastic Flow Analysis Assumption: The soft clay flows like a liquid around the pile, and as it does, it applies a drag force on the pile in the form of shear stress equaling to the undrained cohesion of the soil, which is estimated to be about 434 psf. Introducing this drag force as a uniformly distributed force on the pile, fixed at both ends, one calculates the bending and shear stresses as follows: The maximum calculated bending stress and the shear stress exceeds the limits (3000 psi for bending stress and 1500 psi for shear stress), suggesting that the pile must have experienced cracking. Again, the validity of the assumption on which the calculations are based on needs verification.

Part II: Finite Element Analysis Using HOPDYNE with a Rigid Wall Placed at the Location of the First Pile 100’ Industrial Waste 80’ Sand WT 70’ See Table Sand seams (p=0) Soft Clay Stiff Clay Fig. B Loading: As the failure of the landfill embankment is not of concern here, instead of using staged construction, the loading is applied as followed: A single finite element mesh, including the 80’ tall landfill is used in the analysis. The weight of the landfill is applied as gravity loading with the full loading applied over a period of one year. The analysis is carried out as a fully-coupled analysis. Followed by the load application, the analysis is continued for another year, during which time, excess pore water pressure further dissipates and the soil consolidates.

What Constitutive Models to Choose? Fig. C

Constitutive Models Used for Various Layers DP: Drucker-Prager (1955) ABS: Anisotropic Bounding Surface Clay Model (Anandarajah and Dafalias, 1986) CC: Modified Cam-Clay (Roscoe & Burland, Schofield and Wroth, 1968) EE: Linear Elastic 100’ DP Industrial Waste 80’ Silty Sand DP WT 70’ See Table Sand seams (p=0) Soft Clay CC or ABS with OCR=10 Stiff Clay Analysis Types 1 2 3 4 All elastic CC with M=0.6 ABS with M=0.6 CC with M=1.2 OCR=1 OCR=1, A=1.3 OCR=10 Fully-Coupled Analysis with k = 1.0E-12 ft/s for clays and k=1.0E+02 ft/s for sands

Analysis Types: For reference, one analysis is performed with a linear elastic material model (EE) for the materials in the entire embankment. In all of the remaining analyses, the landfill material and the top 10-foot thick foundation sandy layer were modeled by the Drucker-Prager model (DP) with a friction angle of 45 degrees, zero cohesion and a dilation parameter of 0.8 The middle and bottom layers of the foundation soil were either modeled with the modified cam-clay model (CC) or the anisotropic bounding surface model (ABS) (Anandarajah and Dafalias, 1986). To make the middle layer very weak and soft as in the real-world problem, very low value was used for the slope of critical state line (M=0.6) with an OCR of 1 To make the bottom layer very stiff, the following parameters were Used: M=1.2, and OCR=10. The stress distributions presented in the following pages are those at the end of five years (i.e., almost at the end of consolidation)

Horizontal Stresses in the Soil Near the Pile Elastic Elevation (ft) Initial Horizontal Effective Stress (psf) Fig. 1. Comparison of initial stresses before embankment construction and elastic stresses after embankment construction

Horizontal Stresses in Soil Near the Pile CC Elastic Elevation (ft) Initial Horizontal Effective Stress (psf) Fig. 2. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

Horizontal Stresses in Soil Near the Pile ABS CC All Stiff Depth Elastic Initial Horizontal Effective Stress Fig. 3. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

M003-1: z = 10 to 60’ ABS with M=0.6 and OCR=1: Deformation (click on the picture)

M003-1: z = 10 to 60’ ABS with M=0.6 and OCR=1: Pore Pressure (click on the picture)

M003-1: z = 10 to 60’ ABS with M=0.6 and OCR=1: Shear Strain (click on the picture)

Soil Failure: Remove Sand Seams and Double the Construction Rate DP: Drucker-Prager ABS: Anisotropic Bounding Surface Clay Model (Anandarajah and Dafalias, 1986) CC: Modified Cam-Clay EE: Linear Elastic 100’ DP Industrial Waste 80’ Silty Sand DP WT 70’ See Table Sand seams (p=0) Soft Clay CC or ABS with OCR=10 Stiff Clay Analysis Types 1 2 3 4 All elastic CC with M=0.6 ABS with M=0.6 CC with M=1.2 OCR=1 OCR=1, A=1.3 OCR=10

M003-1: z = 10 to 60’ ABS with M=0.6 and OCR=1: Deformation (click on the picture)

M003-1: z = 10 to 60’ ABS with M=0.6 and OCR=1: Pore Pressure (click on the picture)

M003-1: z = 10 to 60’ ABS with M=0.6 and OCR=1: Shear Strain (click on the picture)

Horizontal Stresses in Soil Near the Pile Slow Loading with Sand Seams (ABS) No Sand Seams Fast Loading (ABS) Depth Initial Horizontal Effective Stress Fig. 4. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

Comparison of Deformation Slow Loading with Two Sand Seams (ABS Model) 0.9’ 0.65’ Fast Loading with no Sand Seams Fast (10 times) Loading with No Sand Seams (ABS Model) 3.85’ 4.0’ Fig. D

Horizontal Stresses in Soil Near the Pile What happens to forces on piles when DP is used for the middle soft layer as well? Horizontal Stresses in Soil Near the Pile Initial DP with M=0.6 ABS with M=0.6 Depth (ft) Horizontal Effective Stress (psf) Fig. 5. Comparison of initial stresses before embankment construction, and elastic and elasto-plastic stresses after embankment construction

Part III: 2D Finite Element Analysis Using HOPDYNE with Some of the Piles Fig. E

Fig. F

Elastic (without piles) CC (with piles) Horizontal Stresses in Soil Near the First Pile at the End of Consolidation Elastic (without piles) CC (with piles) CC (without piles) Depth (ft) Initial Horizontal Effective Stress (psf) Fig. 6. Results from 2D FEA with Piles

Stresses in the First Pile at the End of Consolidation (Analysis with piles using CC for the middle soft layer) Elevation (ft) Elevation (ft) Fig. 7 Bending (normal) stresses in the First Pile (psi) Shear Stress in the First Pile (psi) Key Observations: Shear stress in the pile reaches about 900 psi near the pile head, which is adequate to cause shear failure (assuming a shear strength of about 1/3 of the compressive strength of about 3000 psi) The bending stress exceeds 3000 psi at many locations, including near the pile head, as well as at locations in the middle soft clay layer. The pile, thus, could have failed in compression as well. The values calculated for the stresses here are much smaller than those calculated by the plastic flow analysis (e.g., about 6000 psi here for the bending stresses versus 12500 psi calculated by the flow analysis). Further conclusions are differed until the correspondence between 2D and 3D analyses are established, because the real problem is 3D. This is done in the next few slides.

Correspondence Between the Results of 2- and 3-Dimensional Analyses. From the literature on buried structures, it can be deduced that when horizontal stresses are increased near a pile, the pile experiences passive arching. That is, the stress in front of the pile increases to a value larger than the value of the increase in stress in the soil (i.e., free-field stresses) and that in the back of the soil decreases to a value smaller than the value of the increase in stress in the soil. The net result is that the pile carries a load larger than that implied by the stress increase in the soil. To illustrate this, we placed a square pile in a plane strain container and increased the stress in the soil by 800 psf. The stress increase in the front and back of the soil are shown in the figure on the following page.

Fig. 8 800 psf Horizontal Stress (psf) Pile (1’x1’) Distance X (ft) Initial Horizontal Stress = 2000 psf Note that the stress in the soil far from the pile increases from 2000 to 2800 psf, whereas it increases to over 4500psf in front on the pile and decreases to almost zero in the back of the pile x 41’

800 psf Vertical Stress (psf) Pile (1’x1’) Horizontal Distance X (ft) Initial Vertical Stress = 2000 psf The results here shows the influence of the boundary conditions on the stresses on the pile x

Determination of Modified Pile Parameters by Elastic Method Fig. 9 From , it follows that if you match the deflection line, the bending stresses must be equal to each other. Referring to the figure above, . But we want: Hence: Let be the load vector corresponding to and be the modified stiffness matrix which will render where is a modifier to be determined.

By least square minimization Steps: Carry out an elastic 3D analysis and determine Carry out an elastic 2D analysis and determine Carry out an elastic 2D analysis with imposed along pile locations and determine 4. Determine by conducting a pile analysis

Determination of Modified Pile Parameters by an Approximate Method Fig. 10

2D Mesh

3D Mesh Fig. 11

3D Mesh: Plan View of a Portion of the Mesh Around the Piles Fig. 12

Deformation of a Sectional Elevation of the 3D Mesh Fig. 13

Comparison of Pile Stresses from Various Types of Elastic Analyses Green: Optimization Method (F=.0327) Red: 45 deg Approx. Method (F=0.0196) 3D F=1 Elevation (ft) Elevation (ft) 2D F=1 Bending Stress (psi) Horizontal Deflection (ft) Elevation (ft) Elevation (ft) Axial Stress (psi) Shear Stress (psi) Fig. 14 Observation: With modified pile properties, stresses from 2D analyses are closer to those from 3D Analyses

Use of Combined 1D/3D Meshes for Modeling the 3D Problem Fig. 15

Comparison Between Results from Full 3D and Combined 1D/3D Meshes Full 3D & 1D/3D Elevation (ft) Horizontal Displacement (ft) Fig. 16

Validity of the Use of Modifier from Elastic Analysis in Elasto-Plastic Analysis Simplified 3D Mesh

3D Mesh: Plan View of a Portion of the Mesh Around the Piles Fig. 17

2D Mesh

Analysis of a Horizontal Slab to Find F Pile Pile Pile Pile Pile (a) Slab with Single Pile Element (b) Slab with 4 pile Elements Observation: F varies with loading 4 Piles F Single Pile Time (c) Variation of F with Time Fig. 13. Comparison of Values of F Calculated with Single and 4 Piles

3D 2D 2D (F=0.162) Observation: Stresses in the piles calculated by the 2D analysis with modified pile properties are close to those calculated by the 3D analysis

Recall: Stresses in the First Pile at the End of Consolidation (Analysis with piles using CC for the middle soft layer) Elevation (ft) Elevation (ft) Bending (normal) stresses in the First Pile (psi) Shear Stress in the First Pile (psi) Key Observations: Shear stress in the pile reaches about 900 psi near the pile head, which is adequate to cause shear failure (assuming a shear strength of about 1/3 of the compressive strength of about 3000 psi) The bending stress exceeds 3000 psi at many locations, including near the pile head, as well as at locations in the middle soft clay layer. The pile, thus, could have failed in compression as well. The values calculated for the stresses here are much smaller than those calculated by the plastic flow analysis (e.g., about 6000 psi here for the bending stresses versus 12500 psi calculated by the flow analysis). Further conclusions are differed until the correspondence between 2D and 3D analyses are established, because the real problem is 3D. This is done in the next few slides.

Deformed Configuration with Modified Pile Width

Two-Dimensional Elasto-Plastic Analysis with Modified Pile Width (F=0 Elevation (ft) F=0.0327 Elevation (ft) F=1 Bending (normal) stresses in the First Pile (psi) Shear Stress in the First Pile (psi) Fig. 20 Observation: The bending and shear stresses in the pile increases many fold. The new values are well over the limiting values and hence the theory supports the observation that the piles cracked and separated from the bridge that they were supporting.

Concluding Remarks The elasto-plastic finite element analyses presented here supports the observation that due to the construction of the landfill near the bridge at a rate too fast caused cracking of piles. The finite element results are very helpful in understanding the failure and deformation mechanisms. The 2D-to-3D FEA connection is nontrivial and must be considered in interpreting the results of 2D analyses. While the conventional simplified techniques that are currently used also lead to the same conclusions, the details of these analysis methods are not exactly supported by the finite element results, suggesting the need for a more refined method.