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)

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

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

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.

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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)

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)

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

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

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)

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)

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)

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)

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

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

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

THANK YOU