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ANALYSIS OF FLEXIBLE PILES SUBJECTED TO STATIC LATERAL LOADS (FREE HEADED CASE)
UNDER THE GUIDNACE OF: N. VASUDEVANAIDU
(M.Tech)
PROJECT MEMBERS: S. SUDHA (09F61A0136) E. BHARGAVI ( 09F61A0106) P. LAKSHMAIAH (09F61A0117) M. BALAJI (09F61A0103)
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1. ABSTRACT2. SCOPE OF THE WORK3. TYPES OF NUMERICAL METHODS4. DESIGN PARAMETERS5. DEFLECTION VALUES OF THE PILE6. MOMENT VALUES OF THE PILE7. SHEAR VALUES OF THE PILE8. SOIL REACTION VALUES OF THE PILE9. GRAPHS10. REFERENCES
CONTENTS
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The abstract of the project includes analysis of flexible piles subjected to static lateral loads using numerical methods.
Deep foundations are used when the soil is very weak below the ground surface.
A pile subjected to lateral loading is one of the class of problems that involve interaction of soil and structures.
The main purpose of implementing pile is to carry vertical loads when the soil is weak.
ABSTRACT
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When the pile is subjected to lateral loading a solution cannot be obtained without accounting for the deformation of both pile and soil.
The deflection of the pile and the lateral resistance of soil are interdependent.
Therefore iterative techniques are almost necessary to achieve a solution for particular case of loading on the pile.
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The present scope of the work is to calculate the structural parameters like slope, deflection, moment, shear and soil reaction.
In this project we are using a numerical method called finite difference method.
This method is used to calculate stresses and strains, deflections and moments at each and every point.
SCOPE OF THE WORK
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Numerical methods are classified into five categories.
1. Finite element method2. Finite difference method3. Boundary element method4. Discrete element method5. Fast lagrangian analysis of continum
TYPES OF NUMERICAL METHODS
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FINITE ELEMENT METHOD
Finite element analysis was developed as a numerical method of stress analysis.
This method is coined by clough in 1960. FEM is used to determine structural
parameters in irregular shapes. This method is also used in stress
analysis, fluid flow and heat transfer.
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FINITE DIFFERENCE METHOD
Finite difference method is a method which is used to calculate stresses and strains, deflections and moments at each and every point.
This is used for regular shapes. In the finite difference method at each of the
pivotal points at the intervals an equations expressing the differential equations by the finite difference can be established
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Deflection= y Slope= dy/dx Moment= EI d2y/dx2
Shear = EI d3y/dx3
Soil reaction = EI d4y/dx4
After calculating the design parameters the values are compared with Cprogram using matrix inversion method and also manually by using MS excel.
DESIGN PARAMETERS
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The derivatives can be expressed in terms of deflection
dy/dx= yi-1-yi+1/2h EI d2y/dx2= yi-1-2yi+yi+1/h2
EI d3y/dx3= yi-2-2yi-1+2yi+1-yi+2/2h3
EI d4y/dx4= yi-2-4yi-1+6yi-4yi+1+yi+2/h4
Where h= pile interval = total length/number
of parts i= nodal points
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The table shows the flexural rigidity, soil modulus and relative stiffness of pile material
S.NO PILE MATERIAL
FLEXTURAL RIGIDITY (EPIP) N-MM2
SOIL MODULUS (K) MPA
RELATIVE STIFFNESS (KR)
1 PVC 3.990*107 0.34 1.789*10-4
2 ALUMINUM 1.136*109 0.34 5.093*10-3
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The table shows the values of deflection for particular depth for aluminum
DEFLECTION VALUES
S.NO
DEPTH (M)
DEFLECTION (Y)M
FOR LOAD
57.01 N
FOR LOAD
129.3 N
FOR LOAD
191.08 N
FOR LOAD
269.75 N
FOR LOAD
401.27 N
1 0 -0.0046053 -0.0101169 -0.0149503 -0.0218474 -0.0314021
2 0.25 0.00125686 0.002734701 0.004041202 0.005849943 0.008487878
3 0.5 0.003590421 0.008143352 0.01203415 0.01750139 0.02527634
4 0.75 0.000711947 0.001614798 0.00238627 0.003465682 0.005012049
5 1 -0.00531426 -0.0118260 -0.0174768 -0.0254393 -0.0367082
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The table shows the values of deflection for particular depth for pvc
S.NO
DEPTH (M)
DEFLECTION (Y)M
FOR LOAD
57.01 N
FOR LOAD
129.3 N
FOR LOAD
191.08 N
FOR LOAD
269.75 N
FOR LOAD
401.27 N
1 0 0.00122795 0.002782756 0.00411567 0.005810109 0.008642962
2 0.25 0.000017364 0.000039569 0.000058083 0.000081995 0.000121948
3 0.5 0.000043164 0.000097785 0.000145291 0.000205531 0.000305747
4 0.75 -0.00000534 -0.0000121 -0.00001937 -0.00002734 -0.00004067
5 1 -0.00000208 -0.0000047 0.000011783 0.000016635 0.000024746
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The table shows the values of moment for particular depth for aluminum
MOMENT VALUES
S.NO
DEPTH (M)
MOMENT (M) N-M
FOR LOAD
57.01 N
FOR LOAD
129.3 N
FOR LOAD
191.08 N
FOR LOAD
269.75 N
FOR LOAD
401.27 N
1 0 -1.99535 -4.5255 -6.6878 -9.44125 -14.04445
2 0.25 -59.6442 -135.279 -199.909 -290.650 -419.893
3 0.5 -95.6640 -216.978 -320.639 -466.889 -673.471
4 0.75 -55.3955 -125.633 -185.671 -270.364 -389.983
5 1 0 0 0 0 0
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The table shows the values of moment for particular depth for pvc
S.NO
DEPTH (M)
MOMENT (M) N-M
FOR LOAD 57.01 N
FOR LOAD 129.3 N
FOR LOAD 191.08
N
FOR LOAD 269.75
N
FOR LOAD 401.27
N
1 0 1.99535 4.5255 6.6878 9.44125 14.044
2 0.25 0.78929 1.78841 2.64623 3.73569 5.5571526
3 0.5 -0.0474356 -0.107315 -0.161176 -0.22753 -0.338489
4 0.75 0.0330461 0.074875 0.125199 0.176738 0.262914
5 1 0 0 0 0 0
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SHEAR VALUES The table shows the values of shear for
particular depth for aluminumS.NO
DEPTH (M)
SHEAR (V) N
FOR LOAD
57.01 N
FOR LOAD
129.3 N
FOR LOAD
191.08 N
FOR LOAD
269.75 N
FOR LOAD
401.27 N
1 0 57.01 129.3 191.08 269.75 401.27
2 0.25 219.828 443.006 654.653 949.552 1375.005
3 0.5 -8.4972 -19.292 -28.4768 -42.772 -59.8193
4 0.75 -191.328 -433.9558 -641.279 -933.779 -1346.9416
5 1 0 0 0 0 0
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The table shows the values of shear for particular depth for pvc
S.NO
DEPTH (M)
SHEAR (V) N
FOR LOAD
57.01 N
FOR LOAD
129.3 N
FOR LOAD
191.08 N
FOR LOAD
269.75 N
FOR LOAD
401.27 N
1 0 57.01 129.3 191.08 269.75 401.27
2 0.25 4.0848 9.2645 13.698 19.33765 28.765
3 0.5 1.51252 3.42708 5.0420 7.117909 10.58848
4 0.75 -0.09487 -0.21463 -0.32235 -0.45506 -0.67679
5 1 0 0 0 0 0
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The table shows the values of soil reaction for particular depth for aluminum
SOIL REACTION VALUES
S.NO
DEPTH (M)
SOIL REACTION (V) N/M
FOR LOAD 57.01 N
FOR LOAD 129.3 N
FOR LOAD
191.08 N
FOR LOAD
269.75 N
FOR LOAD
401.27 N
1 0 -1516.4 -3439.38 -5082.56 -7427.32 -10675.57
2 0.25 -409.89 929.702 1373.86 1988.756 2885.56
3 0.5 1220.61 768.689 4091.173 5949.845 8593.04
4 0.75 242.033 548.62 811.246 1178.2099 1703.938
5 1 -1772.65 -4020.26 -5941.48 -8648.44 -12479.47
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The table shows the values of soil reaction for particular depth for pvc
S.NO
DEPTH (M)
SOIL REACTION (V) N/M
FOR LOAD
57.01 N
FOR LOAD
129.3 N
FOR LOAD
191.08 N
FOR LOAD
269.75 N
FOR LOAD
401.27 N
1 0 417.311 945.72 1398.7106 1974.5660 2937.3111
2 0.25 5.9006 13.445 19.739 27.8660 41.4440
3 0.5 14.669 33.232 49.479 69.8497 103.90796
4 0.75 -1.81566 -4.11127 -6.58235 -9.292111 -13.8231
5 1 1.05702 2.39496 4.00465 4.973822 8.40963
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The graph is drawn between depth vs deflection for aluminum
GRAPHS
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.030
0.2
0.4
0.6
0.8
1
1.2
DEFLECTION VS DEPTH
57.01N129.3N191.08N269.75N401.27N
DEFLCTION (M)
DEP
TH (
M)
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The graph is drawn between depth vs deflection for pvc material
-0.002 0 0.002 0.004 0.006 0.008 0.010
0.2
0.4
0.6
0.8
1
1.2
DEFLECTION VS DEPTH
57.01N129.3N191.08N269.75N401.27N
DEFLECTION (M)
DEP
TH (
M)
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The graph is drawn between depth and moment for aluminum
0 100 200 300 400 500 600 700 800
0
0.2
0.4
0.6
0.8
1
1.2
MOMENT VS DEPTH
57.01N129.3 N191.08 N269.75 N401.27 N
MOMENT N-M
DEP
TH M
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The graph is drawn between depth and moment for pvc material
-2 0 2 4 6 8 10 12 14 16
0
0.2
0.4
0.6
0.8
1
1.2
MOMENT VS DEPTH
57.01 N129.3 N191.08 N269.75 N401.27 N
MOMENT N-M
DEP
TH M
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The graph is drawn between depth vs shear for aluminum
-1500 -1000 -500 0 500 1000 1500 20000
0.2
0.4
0.6
0.8
1
1.2
DEPTH VS SHEAR
57.01N129.3N191.08N269.75N401.27N
SHEAR (N)
DEP
TH (
M)
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The graph is drawn between depth vs shear for pvc
-50 0 50 100 150 200 250 300 350 400 4500
0.2
0.4
0.6
0.8
1
1.2
DEPTH VS SHEAR
57.01N129.3N191.08N269.75N401.27N
SHEAR (N)
DEP
TH (
M)
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The graph is drawn between depth vs soil reaction for aluminum
-15 -10 -5 0 5 100
0.2
0.4
0.6
0.8
1
1.2
DEPTH VS SOIL REACTION
57.01N129.3N191.08N269.75N401.27N
SOIL REACTION (KN/M)
DEP
TH (
M)
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The graph is drawn between depth vs soil reaction for pvc
-0.5 0 0.5 1 1.5 2 2.5 3 3.50
0.2
0.4
0.6
0.8
1
1.2
DEPTH VS SOIL REACTION
57.01N129.3N191.08N269.75N401.27N
SOIL REACTION (KN/M)
DEP
TH (
M)
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For a pile under lateral loading, a solution cannot be obtained without accounting deformation of both pile and soil.
The deflection of the pile and the lateral resistance are interdependent.
In this project a computer code has been developed for the analysis of laterally loaded pile using finite difference method.
CONCLUSION
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Substituting appropriate boundary conditions fictious nodes at top and bottom portion of pile has been eliminated leading to (m+1) unknowns and (m+1).
The program are validated for (m+1) equations and (m+1) unknowns and checked for correctness by solving hypothetical numerical problems
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1. Analysis & design of shallow & deep foundation by lymon c.reese,william M.isenhower,shinetowerwang
2. Numerical methods for engineering problems by N.krishna raju
3. Introductory methods of numerical analysis by s.s.sastry
REFERENCES
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