Modeling Embankment Induced Lateral Loads on Deep Foundations By Dr. Siva Kesavan URS Corporation...
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Modeling Embankment Induced Lateral Loads on Deep Foundations By Dr. Siva Kesavan URS Corporation And Professor Rajah Anandarajah Johns Hopkins University
Modeling Embankment Induced Lateral Loads on Deep Foundations By Dr. Siva Kesavan URS Corporation And Professor Rajah Anandarajah Johns Hopkins University
Modeling Embankment Induced Lateral Loads on Deep Foundations
By Dr. Siva Kesavan URS Corporation And Professor Rajah Anandarajah
Johns Hopkins University
Slide 2
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 Terzaghis 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: 1.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 2.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. x z x y B B
Slide 3
Elevation (ft) Change in Horizontal Stress (psf) 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 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:Elastic Analysis
Slide 4
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.
Slide 5
See Table WT Sand Soft Clay Stiff Clay 70 80 100 Industrial
Waste Sand seams (p=0) Part II : Finite Element Analysis Using
HOPDYNE with a Rigid Wall Placed at the Location of the First Pile
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. Fig. B
Slide 6
What Constitutive Models to Choose? Fig. C
Slide 7
DP See Table 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 CC or ABS with OCR=10 DP WT Silty Sand Soft Clay
Stiff Clay 70 80 100 Industrial Waste Sand seams (p=0) 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 Constitutive Models Used for
Various Layers Fully-Coupled Analysis with k = 1.0E-12 ft/s for
clays and k=1.0E+02 ft/s for sands
Slide 8
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)
Slide 9
Initial Elastic Horizontal Effective Stress (psf) Elevation
(ft) Horizontal Stresses in the Soil Near the Pile Fig. 1.
Comparison of initial stresses before embankment construction and
elastic stresses after embankment construction
Slide 10
Initial Elastic CC Horizontal Effective Stress (psf) Elevation
(ft) Horizontal Stresses in Soil Near the Pile Fig. 2. Comparison
of initial stresses before embankment construction, and elastic and
elasto-plastic stresses after embankment construction
Slide 11
Initial Elastic All Stiff ABS CC Horizontal Effective Stress
Depth Horizontal Stresses in Soil Near the Pile Fig. 3. Comparison
of initial stresses before embankment construction, and elastic and
elasto-plastic stresses after embankment construction
Slide 12
M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Deformation
(click on the picture)
Slide 13
M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Pore Pressure
(click on the picture)
Slide 14
M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Shear Strain
(click on the picture)
Slide 15
DP See Table DP: Drucker-Prager ABS: Anisotropic Bounding
Surface Clay Model (Anandarajah and Dafalias, 1986) CC: Modified
Cam-Clay EE: Linear Elastic CC or ABS with OCR=10 DP WT Silty Sand
Soft Clay Stiff Clay 70 80 100 Industrial Waste Sand seams (p=0)
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 Soil Failure: Remove Sand
Seams and Double the Construction Rate
Slide 16
M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Deformation
(click on the picture)
Slide 17
M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Pore Pressure
(click on the picture)
Slide 18
M003-1: z = 10 to 60 ABS with M=0.6 and OCR=1: Shear Strain
(click on the picture)
Slide 19
No Sand Seams Fast Loading (ABS) Slow Loading with Sand Seams
(ABS) Initial Horizontal Stresses in Soil Near the Pile Horizontal
Effective Stress Depth Fig. 4. Comparison of initial stresses
before embankment construction, and elastic and elasto-plastic
stresses after embankment construction
Slide 20
Comparison of Deformation Fast Loading with no Sand Seams Fast
(10 times) Loading with No Sand Seams (ABS Model) 0.9 0.65 3.85 4.0
Slow Loading with Two Sand Seams (ABS Model) Fig. D
Slide 21
What happens to forces on piles when DP is used for the middle
soft layer as well? Initial ABS with M=0.6 DP with M=0.6 Horizontal
Stresses in Soil Near the Pile Horizontal Effective Stress (psf)
Depth (ft) Fig. 5. Comparison of initial stresses before embankment
construction, and elastic and elasto-plastic stresses after
embankment construction
Slide 22
Part III: 2D Finite Element Analysis Using HOPDYNE with Some of
the Piles Fig. E
Slide 23
Fig. F
Slide 24
Horizontal Stresses in Soil Near the First Pile at the End of
Consolidation Depth (ft) Horizontal Effective Stress (psf) Initial
Elastic (without piles) CC (without piles) CC (with piles) Fig. 6.
Results from 2D FEA with Piles
Slide 25
Shear Stress in the First Pile (psi) Bending (normal) stresses
in the First Pile (psi) Elevation (ft) Elevation (ft) Stresses in
the First Pile at the End of Consolidation (Analysis with piles
using CC for the middle soft layer) Key Observations: 1.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) 2.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.
3.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. Fig.
7
Slide 26
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.
Slide 27
Distance X (ft) Horizontal Stress (psf) Pile (1x1) 800 psf x 41
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 Fig. 8
Slide 28
Horizontal Distance X (ft) Vertical Stress (psf) Pile (1x1) 800
psf x Initial Vertical Stress = 2000 psf The results here shows the
influence of the boundary conditions on the stresses on the
pile
Slide 29
Determination of Modified Pile Parameters by Elastic Method
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. Fig. 9
Slide 30
By least square minimization Steps: 1.Carry out an elastic 3D
analysis and determine 2.Carry out an elastic 2D analysis and
determine 3.Carry out an elastic 2D analysis with imposed along
pile locations and determine 4. Determine by conducting a pile
analysis
Slide 31
Determination of Modified Pile Parameters by an Approximate
Method Fig. 10
Slide 32
2D Mesh
Slide 33
3D Mesh Fig. 11
Slide 34
3D Mesh: Plan View of a Portion of the Mesh Around the Piles
Fig. 12 Pile
Slide 35
Deformation of a Sectional Elevation of the 3D Mesh Fig.
13
Slide 36
Elevation (ft) Elevation (ft) Horizontal Deflection (ft)
Bending Stress (psi) Green: Optimization Method (F=.0327) Red: 45
deg Approx. Method (F=0.0196) 2D F=1 3D F=1 Elevation (ft) Shear
Stress (psi) Elevation (ft) Axial Stress (psi) Comparison of Pile
Stresses from Various Types of Elastic Analyses Fig. 14
Observation: With modified pile properties, stresses from 2D
analyses are closer to those from 3D Analyses
Slide 37
Use of Combined 1D/3D Meshes for Modeling the 3D Problem Fig.
15
Slide 38
Elevation (ft) Horizontal Displacement (ft) Full 3D & 1D/3D
Comparison Between Results from Full 3D and Combined 1D/3D Meshes
Fig. 16
Slide 39
Validity of the Use of Modifier from Elastic Analysis in
Elasto-Plastic Analysis Simplified 3D Mesh
Slide 40
3D Mesh: Plan View of a Portion of the Mesh Around the Piles
Fig. 17
Slide 41
2D Mesh
Slide 42
Pile F Time Single Pile 4 Piles (a) Slab with Single Pile
Element (b) Slab with 4 pile Elements (c) Variation of F with Time
Fig. 13. Comparison of Values of F Calculated with Single and 4
Piles Analysis of a Horizontal Slab to Find F Observation: F varies
with loading
Slide 43
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
Slide 44
Shear Stress in the First Pile (psi) Bending (normal) stresses
in the First Pile (psi) Elevation (ft) Elevation (ft) Recall:
Stresses in the First Pile at the End of Consolidation (Analysis
with piles using CC for the middle soft layer) Key Observations:
1.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) 2.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. 3.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.
Slide 45
Deformed Configuration with Modified Pile Width Fig. 19
Slide 46
Two-Dimensional Elasto-Plastic Analysis with Modified Pile
Width (F=0.0397) Elevation (ft) Elevation (ft) Shear Stress in the
First Pile (psi) Bending (normal) stresses in the First Pile (psi)
F=0.0327 F=1 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.
Fig. 20
Slide 47
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.