CANTILEVER SHEET PILE ANALYSIS FOR STRATIFIEDCOHESIVE SOIL DEPOSITS (COMPUTER PROGRAM, SPILE)

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Authors Ibarra, German A., 1959-

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Cantilever sheet pile analysis for stratified cohesive soil deposits

Ibarra Encinas, German Alberto, M.S.

The University of Arizona, 1987

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CUfTHEVER SHEET PILE ANALYSIS FOR STRATIFIED

COHESIVE son. DEPOSITS

by

Germap. A. Ibarra

A Thesis Submitted to the Faculty of the

EEPAKUENT CF CIVIL ENGINEERING AND ENGINEERING MECHANICS

In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE WITH A MAJOR IN CIVIL ENGINEERING

In the Graduate College

THE UNIVERSITY CF ARIZONA

Copyright 1987 Gexsan A. Ibarra

19 8 7

S32UQ9CNT EY AD3B0R

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate ackncwledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder.

SIGNEDT

JHTOWL BY THESIS DIRECTOR

This thesis has been approved on the date shown below: # « •

0̂ 1 S- l̂$7 Jay S. DeNatale Date

Professor of Civil Engineering and Engineering Mechanics

ACXHDWIHXMNIS

This thesis has been ccmpleted under the direct supervision

of Professor Jay S. DeNatale. I am indebted to him for his constructive

criticism and encouragement during the preparation of this manuscript.

I am also deeply grateful to him for his continuous assistance and

guidance throughout the course of this investigation.

Grateful appreciation is also extended to Professors Edward

A. Nowatzki and Fanos D. Kiousis, both members of my thesis committee,

for their review of this manuscript, and for their many useful

suggestions.

iii

DEDICATION

A mis Queridos Padres

Par su gran ejenplo de dedicacicn a la vida

y apcryo haria ccrx sus hijos

A mi Querida Esposa Reyna e Hi jo

Que han sido mis grandes inspiracicnes

iv

TABX£ OF OUWiMBS

Page

LIST OF FIGURES vii

LIST OF TABLES ix

ABSTRACT X

1.- INTRODUCTION 1

2.- LITERATURE REVIEW 3

2.1 Wall Entirely in Cohesive Soil 6 2.2 Wall in Cohesive Soil Belcw Dredge Line

with Granular Backfill Above Dredge Line 10 2.3 Wall in Cohesive Soil Belcw Dredge Line

with Any Number of Soil Strata Above Dredge Line ... 10

3.- MATERIALS AND METHODS 14

3.1 Two Strata Below Dredge Line 14 3.2 N Strata Below Dredge Line 17 3.3 Special Case of Stability for z > Do 19 3.4 Finding the Maximum Mcment 21 3.5 The Sheet Pile Program SPILE 23 3.6 The Testing Program 25

4.- PRESENTATION AND DISCUSSION OF RESULTS 26

4.1 Set 1: Homogeneous Cohesive Soil Below Dredge Line with Granular Backfill 26

4.2 Set 2: Homogeneous Cohesive Soil Below Dredge Line with Cohesive Backfill 29

4.3 Set 3: Homogeneous Cohesive Soil Below Dredge Line with Multiple Layers Above Dredge Line 29

4.4 Set 4: Two Soil Strata Below Dredge Line with Multiple Soil Strata Above Dredge Line 34

4.5 Set 5: Multiple Cohesive Soil Strata Below Dredge Line with Multiple Soil Strata Above Dredge Line 34

4.6 Role of Engineering Judgment 39

v

vi

TABLE OF OCfflENTS—Continued

Page

5.- SUMMARY AND CONCLUSIONS 40

5.1 Summary 40 5.2 Conclusions 40 5.3 Recommendations for Future Research 41

APPENDIX A: Mathematical Derivations 42

APPENDIX B: User's Manual 50

APPENDIX C: Listing of Computer Program SPILE 64

REFERENCES 107

LIST GF FEGQRBS

Figure Page

1.- Earth Pressure Distribution for Cantilever Sheet Piling in Cohesionless Soil 5

2.- Earth Pressure Distribution for Cantilever Sheet Piling Entirely in Cohesive Soil 8

3.- Earth Pressure Distribution for Cantilever Sheet Piling in Cohesive Soil Backfilled with Granular Soil (after Teng, 1962) 11

4.- Stress Distribution for Multiple Soil Strata Above Dredge Line 12

5.- Earth Pressure Distribution for Cantilever Sheet Piling in Two Cohesive Layers Below Dredge Line 15

6.- Net Earth Pressure Distribution for Cantilever Sheet Piling in Multiple Cohesive Layers Below Dredge Line 18

7.- Net Earth Pressure for Design of Cantilever Sheet Piling in Multiple Cohesive Layers Below Dredge Line (Special Case of z > Do) 20

8.- Calculation of Maximum Bending Moment 22

9.- Flow Chart for the Sheet Pile Computer Program SPILE ....... 24

10.- Cantilever Steel Sheet Pile Wall in Cohesive Soil with Granular Backfill (After US Steel, 1969) 27

11.- Cantilever Sheet Pile Wall in Homogeneous Cohesive Soil with Granular Backfill 28

12.- Cantilever Sheet Pile Wall in Homogeneous Cohesive Soil Below Dredge Line with Cohesive Backfill 30

13.- Cantilever Sheet Pile Wall in Homogeneous Cohesive Soil Below Dredge Line with Multiple Layers Above Dredge Line 31

vii

viii

LIST CF gIGDRES—Continued

Figure Page

14.- Stress Distribution for Multiple Soil Strata Above Dredge Line and GWT at 4 Feet Below the Ground Surface 33

15.- Cantilever Sheet Pile Wall in Ttoo Cohesive Soil Strata Belcw Dredge Line with Multiple Soil Strata Above Dredge Line 35

16.- Cantilever Sheet Pile Wall in Multiple Cohesive Soil Strata Below Dredge Line with Multiple Soil Strata Above Dredge Line 37

LIST OF TABLES

Table Page

1.- Comparison of Computer Solutions with Solutions by US Steel Design Charts 28

2.- Cantilever Sheet Pile Wall in Homogeneous Cohesive Soil Below Dredge Line with Cohesive Backfill for Different Values of q 30

3.- Cantilever Sheet Pile Wall in Homogeneous Cohesive Soil Below Dredge Line with Multiple Layers Above Dredge Line for Different Water Levels ... 32

4.- Cantilever Sheet Pile Wall in TWo Cohesive Soil Strata Below Dredge Line with Multiple Soil Strata Above Dredge Line 36

5.- Cantilever Sheet Pile Wall in Multiple Cohesive Soil Strata Below Dredge Line with Multiple Soil Strata Above Dredge Line 38

ix

jffisnucT

Existing methods for analyzing cantilever sheet pile walls in

homogeneous cohesive soil deposits are summarized. The complex nature

of real soil deposits indicates the need for a more general analytical

procedure. A method for designing cantilever sheet pile walls in

stratified cohesive soil deposits is offered, based cm classical earth

pressure theories. A computer program SPILE is written to perform the

necessary calculations. Results of a parametric study are presented

which are consistent with the expected behavior of the pile. Some

practical applications of the method are presented, and suggestions are

made for future research in this general area.

x

CHKFTER 1

WTKDUCTi.CN

Sheet pile walls are flexible lateral support systems used for a

variety of construction projects. They are used in waterfront

construction, and are ideal for difficult subsoil conditions, or when

excavations are conducted near existing structures. The sheet pile is

normally constructed of timber or steel, but steel sheet piling is most

commonly used.

There are two basic types of steel sheet pile walls: cantilever

walls and anchored walls. A cantilever sheet-pile wall is constructed

by driving the sheet piling to a depth sufficient to develop a

cantilever beam-type reaction to resist the active pressures imposed by

the backfill soil. That is, the embedment length must be adequate to

resist both the lateral forces as wall as the bending moment. This type

of support system is suitable for walls of moderate height (typically,

less than 15 feet). An anchored sheet pile-pile wall, on the other

hand, derives its support against lateral pressures by a ccmbination of

embedment (as with cantilever sheet piling) and anchor rods placed near

the top of the piling. This type of support system is suitable for

moderate to high walls (typically, less than 35 feet). Up to 75 96 of

the retaining walls being constructed at the present time are of the

cantilever type (Head and Wynne, 1985).

1

2

Currently available theories of cantilever sheet pile design are

restricted to hcmogeneous or presupposed hcntogeneous soils (below the

dredge line). No method is currently able to handle stratified soils.

Since the structure of natural soil deposits is usually quite complex, a

method must be developed which takes into account the effects of the

stratigraphy of the soil. The purpose of the present research is to

develop a computer program which can be used to aid in the design of

cantilever sheet pile mils in stratified cohesive soil deposits. The

analytical formulation is based on earth pressure theories for

homogeneous layers of soil and the assumption of a linear pressure

distribution within each stratum. The depth of embedment calculations

are based on the laws of static equilibrium. The maximum bending moment

is also calculated so that the material properties and section modulus

of the piling can be selected.

CHAPTER 2

LUERATORE REVIEW

In order to design a sheet-pile retaining wall, the following

successive operations must be performed: (a) evaluate the forces and

lateral pressures that act an the wall, (b) determine the required depth

of piling penetration, (c) compute the maximum bending moment in the

piling, (d) select an appropriate piling section, and (e) design the

waling and anchorage systems (for anchored walls only). A knowledge of

the surface topography and subsurface geology is essential. In order to

initiate the design calculations, certain preliminary controlling

dimensions must be identified. These include the elevation of the top

of the wall, the elevation of the ground surface in front of the wall

(the dredge line level), the maximum cfroundwater level, the normal pool

elevation, and the low water level. Subsoil investigations and

laboratory testing should be carried out in order to determine the

dimensions and engineering properties of the different soil strata.

A sheetpile wall may be subjected to some or all of the

following types of lateral pressure: active and passive earth pressure,

lateral pressure due to surcharge loads, unbalanced water pressure and

seepage pressure, earthquake forces, wave pressure, etc.(Teng, 1962).

Classical theories (Rankine, Coulomb, Log-spiral, and/or Wedge theories)

are generally used to determine the active and passive earth pressures

3

4

acting against the sheetpiling. These are all based on the assumption

that the wall deforms laterally, by a combination of translation and

rotation, to such an extent that the active and/or passive states are

fully developed. This condition is generally satisfied for ordinary

retaining walls.

In practice, several empirical and semiempirical design

procedures have been developed based on classical earth pressure

theories. Walls designed as cantilevers are restricted to a maximum

unsupported height of approximately 15 feet, because they usually permit

large lateral deflections and excessive stresses which must be resisted

by passive pressures exerted on the embedded portion. Therefore a

cantilever wall in cohesionless soil may be designed in accordance with

the principles and assumptions shewn in Figure 1.

When the lateral active pressure Ro is applied to the upper

portion of the wall, the piling rotates about the pivot point b,

mobilizing passive pressure in front of the wall above the pivot point

and in back of the wall belcw the pivot point. The term (Pp - Pa) is

the net passive pressure. At point b the piling does not move and would

be subjected to equal and opposite at-rest earth pressures, with a net

pressure equal to zero. The resulting earth pressure distribution is

represented by curve oabc. For the purpose of design, curve abc is

replaced by a straight line dc. The point d is located so as to ensure

that the sheet piling is in a state of static equilibrium. Although the

assumed pressure distribution is not exact, it is sufficient for design

purposes (US Steel, 1969). For convenience of terminology point d1 will

5

Fig. 1 - Earth Pressare Distribution far Cantilever Sheet Piling in Oofaesionless Soil.

6

hereafter be referred to as the pivot point, even though the true point

of zero lateral deflection is somewhere below this point.

The earth pressure distribution for sheet piling in cohesive

soils is different from that for granular soils, since the active earth

pressure coefficient Ka is equal to the passive earth pressure

coefficient Kp when 0 = 0 (An earth pressure coefficient K relates the

horizontal and vertical effective stresses at a point, for a given state

of earth pressure — active, at rest, or passive). Because of this,

the design procedure for steel sheet piling in cohesive (tf = 0) soils is

somewhat different from than that for cdhesionless soils. For cantilever

sheet piling in cohesive soils, two cases are of particular interest:

(1) sheet pile walls entirely in clay, and (2) walls driven in clay and

backfilled with sand. The lateral earth pressure distribution above the

dredge line is different for each case.

2.1 Wall Entirely in Cohesive Soil : The design of sheet piling

in cohesive soils is complicated by the fact that the magnitude and

location of the pressure resultant acting on the wall may change as a

result of consolidation, shrinkage, and the development of tension

cracks, which may occur over a period of time. The depth of penetration

and the size of piling must satisfy the pressure conditions that exist

immediately after installation as well as the long term conditions that

develop after the strength of the clay has changed. Immediately after

installation it is cannon practice to calculate pressures assuming that

the clay derives all its shear strength s from cohesion c and none from

internal friction 0 (i.e., a s = c shear strength characterization).

7

This analysis is sometimes referred to as a total stress analysis or a

"0 = 0" analysis (Cernica, 1982). The analysis may be carried out by

the conventional method in accordance with the principles mentioned

above, or by an approximate method based on further simplifying

assumptions. These methods are illustrated in Figure 2, where the

initial pressure conditions are shown.

Since Ka = Kp = 1 when 0 = 0, the passive earth pressure on the

left side of the piling is given by (Teng, 1962):

Pp = Ye(Z - H) + 2*c

and the active pressure on the right side of the piling is given by:

Pa = ve*Z - 2*c

where:

H = Unsupported wall height above the dredge line, in feet Z = depth below the original ground surface, in feet. Ye = effective unit soil weight (moist unit weight above the

water level and submerged (or bouyant) unit weight below the water level), in pounds per cubic foot.

The negative earth pressure or tension zone (as shown by the dotted line

in Figure 2a) is neglected, because the soil may develop tension cracks

in the upper portion and thereby lose its cohesion. Since the slopes of

the active and passive pressure envelopes are equal (Ka = Kp), the net

passive pressure on the left side of the wall is constant below the

dredge line and has the magnitude:

Pp - Pa = 4*c - Ye*H

Theoretically, there would be no net passive resistance and the wall

would therefore be unstable if Ye*H is greater than 4*c. The height,

He = 4*c / Ye is often called the critical wall height. Below the pivot

8

Orlginot ground

H J ^ l*2c. Dredge

line , Ro

M 4e - Ye H 4o + YtH 4c - YeH 4c+ YeH

Pp«Ye(Z-H)+2c

Fig. 2 - Earth Pressure Distribution focr Cantilever Sheet Filing Entirely in Oofaesive Soil.

g

point, where the piling moves to the right, the net passive pressure is

given by:

Fp - Pa = 4*c + Ye»H

which is illustrated in Figure 2b. The resulting net pressure

distribution on the wall is shown in Figure 2a.

Once the pressure distribution has been established, the point d

and the depth of penetration D are chosen so as to satisfy the

conditions of static equilibrium; i.e., the sum of the horizontal forces

must equal zero and the sum of the moments about any point must equal

zero. From the sum of the forces in the horizontal direction (zFh = 0)

the distance z is given by:

z *= (Ao*D - Ro)/4*c (1)

where:

Ao = 4*c - Ye*H = 4*c - qo

and by summing moments about the bottan of the pile (£Mo - 0):

Ro(D + yo) - AD*D*D/2 + (4*c/3)z2 = 0 (2)

By substituting the value of z into equation (2) the solution equation

becomes:

A*D2 + B*D + C = 0 (3)

where:

A = (Ao2)/(12*c) - (Ao/2) B = Ro - (Ao/6*c) C = Ro*yo + (RO2/12*C)

For stability, 4*c must be greater than qo = Ye*H. If Ro is zero, no

wall is required. A factor of safety can be applied either by

increasing the depth of embedment beyond the point required for

10

equilibrium or by reducing the effective horizontal pressures on the

passive side by applying a factor of safety of 1.5 to 2.00 to the

passive coefficient before the depth of piling is calculated. It is

also possible to use a reduced value of cohesion c. The maximum

allowable earth pressure should be limited to 50 to 70 percent to the

ultimate passive resistance (US Steel,1969).

In the simplified method, the design is made using the pressure

diagram shown in Figure 2c; i.e., by assuming the passive pressure on

the right side of the piling is replaced by the concentrated reaction C.

The depth D should be increased by 20 to 40 percent to obtain the

total design depth of penetration using this method (US Steel, 1969).

2.2 Wall in Cohesive Soil Below Dredge Line with Granular

Backfill Above Dredge Line . The above methods may also be extended to

the case where sheet piling is driven in clay and backfill with granular

soil, as shewn in Figure 3. The simplified method is shewn in Figure

3b. The methods of design are exactly the same as discussed previously.

2.3 Wall in Cohesive Soil Below Dredge Lin*» with any nf

Soil Strata Above Dredge Line . The above method may be extended to the

case where any combination of cohesive and cohesionless soil strata

exist above the dredge line by replacing the actual earth pressure

distribution with an equivalent resultant Ro acting at point yo.

From Figure 4, neglecting the tension zone, the resultant Ro is

the sum of the horizontal pressure resultants due to each individual

stratum. Hence:

Ro = Fj + F2 + . •. + Pfj

11

Wattr Itvtl

Pa

Drtdgt lint

Y«H = V«rtlcol effective prttturt at drtdgt Itvtl dut to

backfill v

(b)

Conventional Method Simplified Method

Fig. 3 - Earth Pressure Distribution for Cantilever Sbeet Piling in Cohesive Soil Backfilled with Granular Soil (after Teng, 1962).

12

F2

Fs

Dradgt lint

Fig. 4 - Stress Distribaticn far Maltiple Soil Strata Above Dredge Line.

13

where:

=*1^2 Fn are the pressure resultants for each stratum.

The point of application yo of resultant Ro is determined by

considering moment equivalence about point o. Thus

Ro*yo = F1*y1 + F2*Y2 + ..• + Fn*yn

yo = {F^yj + F2*y2 + ... + Fn*yn) / Ro

where:

yi'Y2',,*'Yn are monient arms corresponding to pressure resultants Fi,F2, ... »®n*

The effective vertical stress at the dredge line level is given by:

qo = Yi*hj[ + y2*^2 + ••• + Yn*hn

where:

Yi, Y2< ... , Yn are the effective unit weights (dry,moist or bouyant) of each stratum.

h]_, h2, ... , are the thicknesses of each stratum.

This generalization is independent of the number of strata below the

dredge line. Therefore the methods of design discussed above can still

be employed.

No methods are currently able to deal with walls in stratified

soils belcw the dredge line. Therefore, the purpose of the present

research is to develop a mathematical formulation which takes into

account the effect of each individual strata where multiple clay strata

exist below the dredge line.

CHftPTER 3

MKDERIALS AND WIHIW

3.1 TWo Strata Below Dredge Line.- The design of sheet pile

walls in soils where two cohesive layers exist below the dredge line is

conceptually the same as for walls entirely in a single cohesive soil.

The main difference relates to the earth pressure distribution, which

results from different soil properties. A typical earth pressure

distribution is illustrated in Figure 5. An analysis of the horizontal

stresses on both sides of the piling is as follows:

Zone Pressure Left Pressure Right Side Side

(I) (top) 2*ci qo - 2*ci (bottom) qj + 2*ci qo + - 2*o^

(II) (top) qj + 2*C2 qo + qj - 2*C2 (bottom) qj + q2 ~ 2*C2 qp + qj + q2 + 2*C2

Net Pressure in Each Zone

(I) (top) 2*cj - qo + 2*Cj - 4*Ci - qo (bottom) qi + 2*ci - qo - qj + 2*c^ = 4*c^ - qo

(II) (top) qo + 2*C2 - qo - qi + 2*C2 — 4*C2 - qo (bottom) qo + q^ + q2 + 2*C2 - qi - q2 + 2*C2 = 4*C2 + qo

For force equilibrium in the horizontal direction (iFh = 0),

Ro - Aj*^ - A2*DO + 4*c2*z = 0 (4)

where:

qi = Yj^hi *32 = Y2*h2

14

15

~mt prtaaur«

acttvt

I L

Fig. 5 - Earth Pressure Distribution fcxr Cantilever Sheet Piling in TVto Cohesive Layers Below Dredge Line

(ttece cj > cj).

16

A]_ - 4*ci - qo A2 = 4*C2 - qo

Hence:

z = (Ai*hi + A2*Do - Ro) / 4*c2 (5)

Equation (5) for distance z is similar to equation (1), but with the

term A^*hi adding or subtracting depending of the magnitude of 4*ci - qo

which may be smaller or greater than zero.

For moment equilibrium about point o (EMo = 0):

Ro(Do-fyo) - A^hxtDo+hj/a) - (A2*Do2)/2 + (4*c2*z2)/3 = 0 (6)

By subtituing eq. (5) into eq. (6) the solution equation becomes:

A*Do2 + B*Do + C = 0

where:

A = [£A22)/(12*c2)] - A2/2 B = Ro - (A^hi) + [(A1*h1*A2)/(6*c2)] - [<A2*Ro)/(6*c2)] C = Ro*yo - [(Ai^Sj/tZ)] + [(A12«h12)/(12*c2)] - [(A^h^Ro)/^;,)]

+ [(RO2)/(12*C2)]

A Ccmplete mathanatical derivation is included for reference in Appendix

A. As before, the solution equation has a quadratic form. The only

difference resides in the values of the quantities A, B and C,

Previously, 4*c had to be greater than qo for stability.

However, in this particular case, 4*c^ can be less than qo if there

exists a stratum belcw stratum no. 1 for which 4*C2 is greater than qo.

If 4*C2 is less than qo, and the earth passive pressure in front of the

wall within stratum no. 1 is not enough to maintain the equilibrium of

the pile, then the system is unstable, and an alternate support system

must be used.

17

3.2 H Strata Below Dredge T.lne.- The design of a sheet pile

wall which extends into N cohesive layers below the dredge line is an

extension of the previous case. Therefore the same assumptions are

used. The pressure distribution is illustrated in Figure 6. For static

equilibrium, iFh = 0, axv3 therefore.

Ro - Ai*hj - A2*h2 - ... - - A^Do + A*cn*z2 = 0 (7)

where:

Ai = 4*cj - qo A2 = 4*c2 - qo • • • • • •

An = 4*cn - qo

As before, by taking the sum of moments about point o (iMo = 0), and

performing the appropriate substitutions, the solution equation becanes:

A*Do2 + B*D + C • 0

where:

A = C 2̂/(2*Cn)3 - An/2 B = [(T1*An)/(6*pn)] + T2 C = T3*Ro - L^A^h! - L2*A2*h2 - ... - 1^-2*^-2*^-2 ~

" [(An-l*hn-i*hn-i)/2] + T^/12*^

where:

Ti = Ai *hi + Ao*ho + ... + A«_i*hn_i - Ro T2 = Ro - A^hi - A2*h2 -... - An-i*hn-i T3 = hi + h2 + ... + hn_i + yo

= h2 + 113 + ... + hn—1 + hj/2 L2 = h3 + h4 + ... + hn_i + h2/2 • • • • • * * * * •

• • * » •

Ln_2 = hn-l + hn-2/2

As before, for stability, 4*c^ must be greater than qo, where Cj is the

cohesion of stratum i, the last stratum into which the pile is embedded.

18

H

4ci - qo

•w IX

W

Ro

T yo

J i qo

hi ^*4c2- <lo

I c, > c2

h2 4c,-3"^ 2 c2<c3

h3

1 ,1 4cn-r qo

Do patilv* aetlv*

4cn - q0 4cn+ -I

n+ qo

» c3 < ®n-

n-i

cn < cn-i

aetlvt

passive

Fig. 6 - Net Earth Pressure Distribution far Cantilever Sfaeeft Piling In Multiple Gobesive Layers

Below Dredge Lira.

19

3.3 Special Case of Stability far z > Do. The solution equation

for N strata belcw the dredge line was derived from the earth pressure

distribution illustrated in Figure 6. Frcm the pressure distribution

for stratum n, the distance Do was expected to be greater than z. When

this occurs, the conditions for stability will be as described in the

previous section.

A special case of stability must be considered if the solution

equation gives a value of Do less than z. The pressure distribution for

this particular case is illustrated in Figure 7. This situation can

occur if the pressure given by the stratum n-1 is not enough to reach

equilibrium, and the next stratum n contributes only a small amount of

net passive resistance to the right side of the wall. Equilibrium is

possible regardless of the value of 4*^ with respect to qo if and only

if Do is less than or equal to z. Since the solution equation was

derived for a different state of stress, a new equation was derived in

order to obtain Do.

As in the previous case the solution equation has a quadratic

form:

A*Do2 + B*Do + C = 0

where:

A = E(2*(fln-1j2)/(3*T4)] - AN_!/2 B = [(4*T4*AN_1)/(3*T4)] + (T2) C = RO*T3 - LI*AI»hi - L2*A2*h2 - ... - (1*1-2)*An-2**¥I-2 ~

- cW-l*iU'hn-l)/2] + [<2.(T7?2)/(32T4)]

where:

20

H

hi

4c.-

W

<?o\_

mm •w

nu r I H H I *

4c2-q0

4c*-3" <lo*^X

hs

1 T

hn-2 4cn-2- q0 n- 2

hn-i powlvt active

d'

n-i (i)

octUt p'attivt

Do

_L. *

I 4Cn-i ~<Jo

J* 4cn + qo

Fig. 7 — Het Earth Pressure Dlstrlbatica far Design of Cantilever Sheet Piling in Multiple Cohesive Lagers Below

Dredge Line (Special Case of z > Do).

21

t4 _ Afi-l + t1't2,T3,Li...etc., are as previously defined.

The sheet pile size is computed as follows:

Sheet Pile Size = H + hj + h2 + ... + hn-i + Do

3.4 Finding the Maxjaua Mnaent. To obtain the maximum moment

(Mnax) per unit length of the wall, one must determine the point of zero

shear (Gere and Timoshenko, 1984). The net pressure distribution on the

pile is illustrated in Figure 8, and the maximum moment is computed as

follows:

where:

thf = distance from the top of stratum i to the point of zero shear. Rj - Ro - Ai*hi ~ A2*h2 - ... - Aj_i*hi_i R2 = hj + h2 + ... + hj^ + yo lah — + A2*L2 + ... + Aj_^*Lj[_j Lj = h2 + h3 + ... + hj_i + hj/2 L2 = h. 3 + h^ + . . . + + h2/2

Applying the theory of maximum and minimum of one function, the point of

maximum moment or zero shear can be determined by setting the first

derivative of Mnax with respect to thf equal to zero. Hence:

Mnax = thf*Rx + Ro*R2 - lah - (Ai*thf2)/2 ( 8 )

Li-i = (hi-^/2

d(Mnax)/d(thf) = Rj - thf*Ai = 0 (9)

and:

thf = Rj/Aj (10)

Therefore:

Mnax = [(Ri2)/(Ai)] + Ro*R2 - lah - [(Ra2/(2*Ai)] (11)

22

4ct - q0

ILLLL—

^J-4c2- q0

t point of zero thear

4cn-i- qo

activ* pa«»lv«

paitiv«

I L .

4cn - qo ^Cn-* qo

Fig. 8 - Calculation of Hagdw Bending Monent.

23

3-5 The Sheet Pile Proqran A computer program was

developed in order to solve the mathematical formulations described

above. A flew chart illustrating the program's logic is shown in Figure

9. The logic of the program is as follows {see Figures 6 and 9):

First, the system is solved as if it were homogeneous, by using

the soil properties of the first stratum below the dredge line. If the

value of 4*Ci is greater than qo, the solution equation is solved for

Do. If 4*c^ is less than qo, and there is not a stratum i+1 below the

stratum i = 1, the system is unstable and the program stops. If the

value of Do is less than hj, the final length of the pile (H + Do) as

well as the maximum moment (Mnax) are computed, and the program stops.

However, if Do is greater than h^, the earth pressure due to stratum i+1

must be taken into account to compute the new value of Do. If 4*ci+i is

less than qo and there is not a stratum i+2 below stratum i+1, the

system is unstable and the program ends with an appropriate message. If

4*Ci+i is greater than qo then the solution equation is solved for Do.

As previously, if Do is less than hi+j, the final pile length {H + Xhj_i

+ Do) as well as the maximum moment are computed, and the program stops.

Finally, if Do is greater than , the third and fourth steps are

repeated until system equilibrium is satisfied. If the pile needs be

driven into stratum N, and 4*cn is less than qo, the system is unstable.

The special case of stability for z > Do described in Section 3.3 is

applied where it occurs.

Some limitations of the program are: 1) only purely cohesive

(0 = 0) strata are permitted belcw the dredge line, 2) the ground water

24

STARTI J«first stratum bslo*

drsdgs tins no Ml | STOP

compurt 4c I • go

no yss

no

no Do> hi

no ytt

computt

system Is Unstoblt. STOP.

PI Is length « H + lht+ Do

solve

ADo • BDo+ C = 0 •or Do

Fig. 9 - Flaw Chart for the Sbeet Pile Ocepater Progr* SPH£.

25

elevation must be the same on both sides of the sheet pile, and 3) the

surface surcharge must be uniformly distributed.

The program was written in FORTRAN 77 and compiled with the

Microsoft FORTRAN Compiler. All examples were run on a Sperry - XT

Personal Computer, which is an IBM PC-Compatible machine. A complete

listing of the program is included for reference in Appendix C.

3.6 The Besting Progran.- In order to verify the logic of the

program, a number of test problems were examined. This testing was done

to examine how variations in the soil parameters and deposit geometry

affect the results. The soil parameters which can be varied are: 1)

cohesion, 2) friction angle of the soil strata above the dredge line,

and 3) soil unit weight. The dimensions which can be varied are: 1}

number of strata, 2) thickness of the individual strata, 3) dredge line

level, and 4) ground water level. Also, an external parameter which can

be varied is the applied surcharge.

The testing was done in two phases. The program was first

tested for homogeneous cohesive soils below the dredge line with

granular backfill. The results were compared with the solutions

obtained using the US Steel Design Curves (US Steel, 1969). The program

was then tested for stratified cohesive soil deposits. Multiple tests

were made for each basic soil configuration by varying a different

parameter while holding rest constant. Cases of instability were

purposely provoked by varying the cohesion, strata thicknesses, applied

surcharge, or ground water level.

CHAPTER 4

PRESENTATION AND DISCUSSION GF RESULTS

Several series of tests were carried out in order to examine the

effect of variations in soil parameters and deposit geometry on the

required depth of piling penetration Do and maximum moment Mnax. The

results for each set of tests are discussed individually.

4.1 Set 1: Hoaogenoos Cohesive Soil Below Dredge Line with

Granular Backfill. The purpose of this set of trials was to compare the

computer solutions with solutions obtained using the US Steel Design

Chart shewn in Figure 10. The basic problem is illustrated in Figure

11. Both the unsupported height H and water table elevation *H were

varied in a parametric study. Table 1 shows a comparison of the

results. Both methods give practically the same values for the embedded

depth Do and the maximum moment Mnax, which suggests that the computer

solutions are correct. Lowering the ground water table (GWT) from the

top of the pile (a = o) to the dredge line level (a = l) increases the

embedded depth and maximum moment (Trials l,2,and 3). Changing the GWT

below the dredge line does not have any effect on either Do or Mnax

(Trials 3, 4, and 5), since the variation in the effective horizontal

pressure is the same on both side of the pile. Therefore the critical

c o n d i t i o n c o r r e s p o n d s t o a G W T a t t h e d r e d g e l i n e l e v e l ( a = l ) .

Doubling the backfill height H causes a marked increase in the embedded

26

" 0

- -- -·- - -1 ~ I I I I I I 1-+-+4-+-H MOMENT RATIO'

3.0 0.25

I I

0 m ~ 2.5 0.50 X C ~ 0 ~ ~ ~ m 0 • z . ~

0 ~

; 2.0 0.75 g z ~ n m ~ ~ m ~ ~ . m ~ m --< 1.6 feH • VEft.TICAL "'ESSUAE AT DREDGE LINE 1.00 ~

~ CANTILEVER STEEL SHEET PILE ~ ~ WALL IN COHESIVE SOIL I t W/GRANULAR BACKFILL )C=:t

~ FIGURE 10 (USS, 1969) ~ ~ -0 = ~ 1.0 1.25 w

en :.n

· ·· · ··--· ·- - ·---

0.5 1 1 NOTE: CURVES BASED ON "SIMPLIFIED" METHOD OF ANALYSIS 1.50 WITH l'" 2l'' DEPTH RATIO, Dill INCREASED BY 20,

0 0.2 0.3

TO EQUATE TO "OONVENTtONAL" METHOD.

I I tllllll tJl~ ---- -- ---- . ,_,5 0.4 0.5 0.6 0 .1 0.8 0.9 1.0 2.0 3.0 4.0 5.0 6.0 1.0 8.0 9.010.0

(2qu - l~tllfl' K,H

1\) ......,

28

1 «

1 ]

Granular toll

Y = wet unit wt.

1 i Y'*«ub. unit wt. |

H i l l *

>0

Cohesive soil

Y = 2 Y* 2

Fig. 11 - Cantilever Sfaeet Pile Hall in Oofaesive Soil Kith Granular Backfill.

STRATUM PROPERTIES (in psf,pcf,ft)

Stratum Unit SatU. U, . Friction Cohesion Ka Kp Thickness Weight Weight Angle

Kp Thickness

1 124.90 124.90 30. ,00 0.00 0.31 3.22 10.00(») 2 124.90 124.90 0. .00 600.00 1.00 1.00 500.00

SPILE USS

Trial H a Do Mnax Do Mnax

1 10.00 0.00 3.33 3493.52 3.00 3487.50 2 10.00 0.50 5.18 7037.28 5.00 7071.87 3 10.00 1.00 6.23 8090.47 6.40 8137.50 4 10.00 1.25 6.23 8090.47 6.40 8137.50 5 10.00 45.00 6.23 8090.47 6.40 8137.50 6 20.00 0.50 43.20 92233.07 48.00 93000.00 7 26.00 0.50 IM IM ND ND

ND = not defined, IM = instability message, (*) = variable

Table 1 - Caparison of Counter Solutions Mith Solutions ty (S Steel Design Cbarts.

. 29

depth and maximum moment (Trials 2 and 6). A further increase of the

backfill height provokes instability of the system, meaning that a

stable cantilever wall design is not possible (Trial 7).

4 .2 Set 2; Humaieans Cohesive Soil Below Dredge Line with

Onhpsive Backfill. The purpose of this set of trials was to examine the

effect of the applied surcharge g. The basic problem is illustrated in

Figure 12. Table 2 shows the results for different values of g. For

cohesive soils, there exists a backfill height for which no wall is

required (Trial 8). This height is dependent an the value of the

cohesion of the backfill and of the magnitude of the applied surcharge.

As before, an increase in backfill height causes an increase in Do and

Mnax (Trials 8 and 9). Also, an increase in the applied surcharge

produces an increase in D and Mmax. (Trials 9 and 10). A further

increase in the applied surcharge provokes instability in the system

(Trial 11).

4.3 Set 3: HnfmeTKOUs Cohesive Soil Below Dredcp TVfn*» with

Multiple layers Above Dredge The purpose of this set of trials

was to vary the ground water table (GWT) elevation to make sure there

are no errors in the stress calculations for multiples layers above the

dredge line. The basic problem is illustrated in Figure 13. Table 3

shows the results for different ground water table levels. As before,

lowering the GWT level from the top of the pile to the dredge line

causes an increase Do and Mmax (Trials 12, 13, 14, and 15). Figure 14

illustrates the stress distribution for a GWT located at 4 feet below

the ground surface. The resultant and its application point are

30

Fig. 12 - Cantilever Sheet Pile Mall in Homogeneous Cbhesive Soil Below Dredge Line with

Cohesive Backfill.

STRATUM PROPERTIES (in psf,pcf,ft)

Stratum Unit Satu. U. Friction Cohesion Ka Kp Thickness Weight Weight Angle

1 125 .00 135 .00 .00 600.00 1.00 1.00 9.00(*) 2 125 .00 135 .00 .00 600.00 1.00 1.00 500.00

Trial H a q D Mnax

8 9.00 1.00 0.00 NP MP 9 10.00 1.00 0.00 0.07 1.38 10 10.00 1.00 200.00 11.02 199.56 11 10.00 1.00 1200.00 IM IM

NP = no pile is required, IM = instability message, {») = variable

Uble 2 - Cantilever Sheet Pile Nail in Honogeneoos Cohesive Soil Below Dredge Line Mint Cohesive

Backfill for Different Values of q.

31

oH

Dredge lint

Do

Fig. 13 - Cantilever Sheet Pile Nail in Banogaaeous Cdhesive Soil Below Dredge Line with Multiple layers Above Dredge Line.

32

STRATUM PROPERTIES (in psf,pcf,ft)

Stratum Unit Satu. U. Friction Cohesion Ka Kp 1 thickness Weight Weight Angle

Kp 1

1 120.00 130.00 .00 600.00 1.00 1.00 3.00 2 125.00 135.00 30.00 .00 .31 3.22 2.00 3 115.00 125.00 35.00 .00 .26 3.84 3.00 4 125.00 135.00 .00 600.00 1.00 1.00 4.00 5 110.00 115.00 25.00 .00 .36 2.78 2.00 6 125.00 135.00 .00 500.00 1.00 1.00 500.00

Surcharge q = 100 psf

Trial H a D Hnax

12 14.00 0.000 20.06 7093.10 13 14.00 0.285 22.56 10860.35 14 14.00 0.571 26.05 14496.52 15 14.00 1.000 42.70 2B208.20

Table 3 - Cantilever Sheet File Wall in Homogeneous Cohesive Soil Below Dredge Line with Multiple

Layers Above Dredge Line far Different Hater Levels.

33

MOO

142.60

181.35

203.86 170.96. 233.38

219.80

-354.60 -105.00 v y

469.40

Ro • 1796.39 Lb.

4.86 435.00

408.89 908.09

759.00 Drtdg* tin* 446.76 1070.76

Do *8.55

Above drtdgt lint Total horizontal «tr«M. (p«f.) EfUcttvi horizontal atr«st. (psf.) Naglecttd zonta.

Fig. 14 - Stress Distribution far Multiple Soil Strata Above Dredge Line and GOT at 4 Feet Below

the Ground Surface.

34

computed as mentioned before. All stress calculations were checked

against hand calculations and were found to be correct.

4.4 Set 4: Be Soil Strata Below Dredge T.lne with Multiple Soil

Strata Above Dredge Line. The purpose of this set of trials was to

examine hew the program deals with weak soils. The basic problem is

illustrated in Figure 15. Table 4 shows the variation of cohesion

values for the two soil strata below the dredge line. If the first

stratum below the dredge line (i.e., stratum 6) is enough strong to

satisfy equilibrium the embedded depth will be within this stratum only

(Trial 16). A decrease in the cohesion of the first strata causes the

depth of embedment to be extended into the next strata. (Trial 17). If

the cohesion of stratum 6 is reduced to a value such that 4*c@ is less

than go, the embedded depth and Mnax will increase, due to the increase

in active pressure on the right side of the pile by an amount equal to

qo - 4*ce (Trial 18). Therefore, if the cohesion of stratum 7 is

reduced in the same manner, an instability condition is provoked (Trial

19). The special case of stability where z > Do can be provoked by

decreasing the cohesion of both strata to an amount such that the

embedded depth into the lower one is no greater than z (Trial 20),

4.5 Set 5: Multiple Cohesive Soil Strata Below Dredge Line with

Multiple Soil Strata Abowe Dredge Line. The purpose of this set of

trials was to examine the variations examined above for stratified soil

deposits. The basic problem is illustrated in Figure 16. Table 5 shows

the results. As one can see, the same commentaries made for two strata

35

t u i n i i '

®2F 0

®jl" 0

0>4 t* o

®g ffcO Dr*da* line

C7JFTO

Fig. 15 - Cantilever Sheet Pile tfell in TMO Cohesive Soil Strata Below Dredge Line with Naltiple

Soil Strata Above Dredge Line.

36

STRATUM PROPERTIES {in psf,pcf,ft)

Stratum Unit Satu. U. Friction Cohesion Ka Kp Thickness Weight Weight Angle

1 120.00 130.00 .00 600.00 1.00 1.00 3.00 2 125.00 135.00 30.00 .00 .31 3.22 2.00 3 115.00 125.00 35.00 .00 .26 3.84 3.00 4 125.00 135.00 .00 600.00 1.00 1.00 4.00 5 110.00 115.00 25.00 .00 .36 2.78 2.00 6 125.00 135.00 .00 700.00( *) 1.00 1.00 10.00 7 120.00 130.00 .00 800.00( *) 1.00 1.00 500.00

Surcharge q = 100 psf

Trial H a C6 C7 D Mnax

16 14.00 1.00 700.00 800.00 22.92 15053.96 17 14.00 1.00 600.00 800.00 26.43 17421.72 18 14.00 1.00 300.00 800.00 43.59 93018.28 19 14.00 1.00 300.00 400.00 IM IM 20 14.00 1.00 650.00 400.00 24.58 15950.84

IM - instability message, (*) = variable

Kble 4 - Cantilever Sheet Pile Wall in IVJO Oobesive Soil Strata Below Dredge Line with Multiple

Soil Strata Above Drtdge Line.

37

l l l l l l l l l o

1 1 hl °H ®,«o 1

h . . ,j * T C2"° ? h

| * ®2 1* 0

t I >3

CjEB. 0 ©3*=° 3

¥

I >4 C4^0 ®4« 0

1 IB Drtdga Una

c5®"° K ©5^0 5

1 *6 Ce 9^0 « © 6 = 0 6

1 >7 c7 * J 7 ©7 «s 0 '

: i '8

CB^° o ©a a o °

t

i

9 ®9 * J 9 Og » 0

Fig. 16 - Cantilever Sheet Pile Hall in Multiple Cohesive Soil Stzata Below Dredge Idne with Miltlple Soil Strata Above Dredge Line.

38

STRATUM PROPERTIES (in psf,pcf,ft)

Stratum Unit Satu. U. Friction Cohesion Ka Kp Thickness Weight Weight Angle

1 120.00 130.00 .00 600.00 1.00 1.00 3.00 2 125.00 135.00 30.00 .00 .31 3.22 2.00 3 115.00 125.00 35.00 - .00 .26 3.84 3.00 4 125.00 135.00 .00 600.00 1.00 1.00 4.00 5 110.00 115.00 25.00 .00 .36 2.78 2.00 6 125.00 135.00 .00 600.00(*) 1.00 1.00 5.00 7 120.00 130.00 .00 400.00(*) 1.00 1.00 2.00 8 125.00 135.00 .00 600.00(*) 1.00 1.00 3.00 9 120.00 130.00 .00 500.00(») 1.00 1.00 500.00

Surcharge q = 100 psf

Trial Ha C6 C7 C8 C9 D Mrax

21 14.00 1.00 600.00 400.00 600.00 500.00 30.12 17421.72 22 14.00 1.00 300.00 400.00 600.00 500.00 72.69 89521.41 23 14.00 1.00 300.00 400.00 300.00 500.00 101.68 187584.60 24 14.00 1.00 300.00 650.00 300.00 300.00 84.52 123993.90 25 14.00 1.00 500.00 650.00 300.00 500.00 49.35 24482.25 26 14.00 1.00 800.00 650.00 400.00 500.00 21.34 14015.47

(*) - variable

Table 5 - Cantilever Sheet Pile fbll in Multiple Cohesive Soil Strata Below Etredge Line with Multiple Soil Strata Above Dredge Line.

39

are also valid for this case (Trials 21 to 26). It is clear that the

program works correctly for all possible cases.

4.6 Role of Sgjineerirp Judgement. As mentioned previously, a

factor of safety must be applied to the coraputer solution by adding 20

to 40 percent to the calculated depth of penetration or reducing the

value of the passive earth pressure coefficient. This means that the

engineer must exercise judgment when interpreting the computer

solutions. This engineering judgement is particularly important in two

particular cases. One occurs when the predicted depth of embedment Do

is very small, and the engineer needs to decide if a wall will actually

be required. The other occurs when the predicted depth of embedment Do

is very large, and a cantilever sheet pile wall may not be economically

practical.

CHAPTER 5

StMHHY AMD OCHCUOSICK5

5.1 Siwury. A number of methods are available for the analysis

and design of cantilever sheet pile walls. However, these methods are

restricted to homogeneous or presupposed homogeneous soils, and no

method is currently able to handle stratified soil deposits. A method

which takes in to account the effects of stratigraphy was developed for

the design of cantilever sheet pile walls in stratified coihesive soil

deposits. A computer program SPILE was written to perform the necessary

calculations.

5.2 Oooclusicns. Parametric studies were carried out in order

to examine the logic of the program and the validity of the results.

This study pointed out the similarities between stratified soils and

homogeneous soils with respect to the prediction of embedded depth and

maximum moment. One of the most interesting features of this analysis

is the stability condition for cases vtfiere the portion of the pile below

the rotation point is embedded in weak soils.

It is important to mention that a slope stability analysis

should also be carried out in order to check the overall stability of

the system. Although the effect of other lateral pressures (such as

unbalanced water tables, seepage, earthquake, etc.) were not included in

40

41

the analysis, the method gives a good idea of the sheet pile dimension

required for cases where these pressures are not present.

5.3 ReiATfcn»3aticPB far Future Research. This study provides

the basis for future studies in this area. For instance, the computer

program SPILE could be generalized to handle either cohesionless or

canbined cohesive-cohesionless stratified soil deposits. The effect of

other lateral pressures could be incorporated into the analysis,

especially the effect of seepage pressures. Also, the program could be

extended to anchored wall systems.

APPENDIX A

Mathematical Derivaticos

42

MATHEMATICAL EHtfVATICKS

Cantilever Sheet Pile fell in PIP Cobesive Layers Below Dredge

Line. The active and passive lateral earth pressures at any depth Z

are given by:

oh = Ka*Y'*Z + qo*Ka + - 2*c* Ka (1)

ojj = Kp*Y'*Z + qo*Kp + YW*ZW + 2*c* Kp (2)

where:

Z = depth below the original ground surface Zyq = depth belcw the ground water level Ka = active earth pressure coefficient Kp = passive earth pressure coefficient Y1 = effective unit weight of the soil Yw = unit weight of the water c = cohesion

Since Ka = Kp = 1 when 0 = 0, equations (1) and (2) becomes:

OH = Y'*Z + GO + Yw%, - 2*c

°H = Y'*Z + qo + Yw*z„ + 2*c

A) Above the Dredge Line.

Fran Figure 4, neglecting the tension zone, the resultant Ro is

the sum of the horizontal pressure resultants due to each individual

stratum.

Hence:

Ro — F^ + F2 + ... + Fjj

where:

Fi,F2, ... ,Fn are the pressure resultants for each stratum.

The point of application yo of resultant Ro is determined by

43

44

considering moment equivalence about point o. Thus:

Ro*yo = Fi*yi + F2*Y2 + ... + Fn*yn

yo = (F1*y1 + F2*V2 + ••• + Fn*yn) / Ro

where:

Yl»Y2'• • • »Yn are "t^ ie moment arms corresponding to pressure r e s u l t a n t s F i » F 2 , . . .

The effective vertical stress at the dredge line level is given by:

qo — Y^hj + ^2*^2 •*••••+ Yn*hn

where:

Yj, Y2# ••• , Yn are the effective unit weight (dry,moist or buoyant) of each stratum,

hj, h2/ ... / hm are the thickness of each strata.

B) Below the Dredge Line.

From Figure 5, an analysis of the horizontal stresses on both

sides of the piling is as follows:

Zone Pressure Left Pressure Right Side Side

(I) (top) 2*ci qo - 2*ci (bottom) q^ + 2*cj qo + qj - 2*ci

(II) (top) qj + 2*C2 qo + qj - 2*C2 (bottom) qi + q2 - 2*C2 qo + qi + q2 + 2*C2

Net Pressure in Each Zone

(I) (top) 2*ci - qo + 2*c^ = 4*ci - qo (bottom) qi + 2*cj - qo - q^ + 2*cj = 4*cj - qo

(II) (top) qo + 2*C2 - qo - qj + 2*C2 = 4*C2 - qo (bottom) qo + q^ + q2 + 2*C2 - qj_ - q2 + 2*C2 = 4*C2 + qo

For force equilibrium in the horizontal direction (iFh = 0),

Ro - Area(abco'a) - Area(defocd) + Area(efoge) = 0

or

45

Ro — A^*hj — A2*Do + 4*c2*z — 0 ( 3 )

where:

qi = Yi*hi 92 = Y2*h2 Ai = 4*cj - qo A2 = 4*C2 - qo

Hence:

z = + A2*DO - Ro) / 4*C2 (4)

For monent equilibrium about point o (ZMo = 0):

Ro(Do+yo) ~ AI^fDo+hi^) - (A2*Do2)/2 + (4*C2*Z2)/3 = 0 (5)

By subtituing eq. (4) into eq. (5)

A = [(A22)/(12*C2)] - A2/2 B = Ro - {Aa*h!) + [(A1*h1*A2)/j[6*ca)] - [(A2*Ro)/(6*c2)] C = Ro*yo - £ (A1*h12)/23 + [(A12*h12)/(12*c2)] - [(A1*h1*Ro)/(6*c2)]

+ [(Ro2)/(12*c2)]

Cantilever Sheet Pile Wall in Multiple Cohesive Layers Below

Dredge Line. This case is an extension of the previous case. Thus,

from Figure 6, for static equilibrium (rFh = 0):

Ro*Do + Ro*yo - Aj*h]*Do - - A2*Do2/2 + + (A12*h12)/(12*c2) + (A1»h1*a2»Do)/(6*c2) -- (A1*h1*Ro)/(6*c2) + (A22*Do2*)/(12*c2) -- (A2*DO*RO)/(6*C2) + (Ro2)/(12*c2) =0 (6 )

Equation (6) can be written in a quadratic form as:

A*Do2 + B*Do + C = 0

where:

Ro - Aj*hi - A2*h2 - An-l*hn_2 -- Ajj*Do + 4*cn*z = 0 (7)

where:

Aj = 4*ci - qo A2 = 4*C2 - qo

46

An = 4*cn - qo

Fran Equation (7) we have:

z = (Ai*^ + A2*h2 + ... + An-x^-i + An*Do - Ro)/(4*CN) (8)

As before, by taking the sum of moments about point o (EMo = 0).

Ro(Do + hi + h2 + ... + hn_i + yo) - Ai*hj(Do + + h2 + ... + hn—i + hi/2) — A2*h2(Do + h3 + ... + 1 + + h2/2) - ... - An_1*hn_1(Do + hn-i/2) - (l^A^Do2 + + (4/3)*Cn*z2 =0 (9)

Subtituing Equation (8) into Equation (9), we have:

T3"RO + T2*Do - L^A^hi - L2*A2*h2 - ... - Ln_2*AN„2*hn_2 " - An-i^ifhn-!^) - (l/2)*Ap*Do2 + (T12)/(12*cn) + + (Tl^DoJ/tS*^) + (An2*Do2)/(12*cn) = 0 (10)

Equation (10) can be written in quadratic form as:

A*Do2 + B*D + C = 0 (11)

where:

A = [(An2)/(12*Cn)] - [(An)/(2)] B = C(T1*An)/(6*cn)] + (T2) C = T3*Ro - L1*Ai*hi - L2*A2*h2 - ... - Ln-2*An_2*hn_2 -

" [(An-l*lin-l*hn-l)/(2)] + (1^/12*^

where:

— A^*hi + A2*h2 + ... + An_i*hn_i — Ro T2 - Ro - Ai*h! - A2*h2 - ... - An-i*!^-! T3 = hi + h2 + ... + hn-i + yo

= h2 + h3 + ... + hjj—1 + hj/2 L2 = h3 + h4 + ... + hn-i + h2/2

%-2 = hn-l + l^i-2/2

Cantilever Sheet Pile ffan in Multiple Ocheslve layers Below

Dredge Line (Special Case of Stability far z > Do). When the solution

equation (11) gives a value of Do less than z, a special case of

47

stability must be considered. As we can see from Figure 7, this

particular case occurs when 4*cn_i is greater than qo. Since the net

passive pressure below the pivot point d' is 4*cn + qo, equilibrium is

possible regardless of the value of 4*Cn with respect to qo, if and only

if Do is less than z.

Thus, for static equilibrium (EFh = 0):

Ho - AJL*h^ -A2*h2 - ... - An_i*hn-i + Area(abca) -- Area(bdofb) + Area(bdoecb) = 0 (12)

where:

Area(abca) = (x*(z - Do))/(2) = [(z - Do)2*^..! + An)]/(2*z) Area(bdofb) = An_j*Do Area(bdoecb) = [(a + b)/2]*h = [{An-! + An) - (An-! + An)/(2*z)]*Do

By taking the sum of moments about point o (IMo = 0):

T3*Ro + T2*Do - Li*Ai*hi - L2*A2*h2 - ... - Ln_2*hn_2*hn_2 " - An_i*hn_i(hn„i/2) + Area(abca)*yi - Area(bdofb)*y2 + + Area(bdoecb)*Y3 = 0 (13)

Since:

Area(abca)*y1 = Area(abca)*[Do + (l/3)*{z - Do)] Area(bdpfb) *y2 = Area (bdofb)* (Do/2) = (An-3.* Do2)/2 Area(bdoecb)*y3 = Area(bdoecb)*[(b + 2*a)/(a + b)]*{h/3)

= (b + 2*a)*(h2/6) = [3*(An-i + V " <2*(An-l + An)*Do)/(z)]*{Do2/6)

where:

a = x = [(z - Do)*{An_i + An)]/z b = AJ-J-I + An h = Do

by making the corresponding substitutions, Equation (13) becomes:

T3*RO + T2*Do - L1*A1*h1 - L2*A2*h2 - ... - IN_2*hn_2 -" An-l*hn-l(Vl/2̂ + (2*Ti2)/(3*T4) + (4*T1*Jf^_1*Do)/(3*T4) + (2*An-i2*Do2)/(3*T4) - (An_!*Do2)/2 = 0 (14)

Equation (14) can be written in quadratic form as:

48

A*Do2 + B*Do + C = 0

where:

A = [(2*(AN_1)2)/(3*T4)] - AN-X/2 B = [(4*T4*AN_1)/(3*T4)] + T2 C = RO*T3 - L1*A1*h1 - L2*A2*h2 - ... - (Ln 2)**n-2**n-2 ~

~ [{An-l*hn-l*J%i-l)/2] + [(2*(Ti)2)/(3*T4)]

where:

T4 = + An Ti,Tg,T3fLi.. .etc., are as previously defined.

Onpitlm the Mapri»w Bending Moment. To obtain the maximum

moment (Mnax) per unit length of the wall, one must determine the point

of zero shear Fran Figure 8, by taking the sum of moments about point

o, the maximum moment is computed as follows:

Mfcnax = RO*ZQ - Fj*ZI - F2*z2 - ... - Fi*z^

or:

or:

where:

Mnax = Ro(thf + h^ + h2 + ...+ h^_^ + yo) - Ai*hj[(thf + h2 + + h3 + ... + h^_2 + h^/2) - ... - Aj_i*hj[-i{thf + hj_i/2) -- AA*thf2/2

Mnax = thf*!?! + Ro*R2 - lah - (Ai»thf2)/2 (15)

thf = distance from the top of stratum i to the point of zero shear. R} = Ro - A^*h^ - A2*h2 - ... — A^_i*hi_j R2 = hi + h2 + ... + h^ + yo lah — A^*Li + A2*L2 + ... + A^_i*Lj[_j

= h2 + h3 + ... + hi—i + hj/2 L2 = h3 + + ... + hj_i + h2/2

I»i_l = (hj[_i)2/2

Applying the theory of maximum and minimum of one function, the point of

49

maximum moment or zero shear can be determined by setting the first

derivative of the Mnax with respect to thf equal to zero. Hence:

d(Mnax)/d(thf) = - thf*Ai = 0 (16)

and:

thf = Ri/Aj (17)

Therefore:

Mnax = [Ri2/Ai] + Ro*R2 - lah - [Ra2/2*Ai] (18)

If the point of zero shear occurs in stratum no. 2, Equation (17)

becomes:

thf = (Ro - A*hi)/A2

and Equation (15) becomes:

Mnax = Ro*thf + Ro*hi + Ro*yo - Ai*hi*thf + Ai*hi2/2 -- A2*thf2/2

iPPEXDIK B

User's Manual

50

UrmUJULTlGN

Hie follcwing manual is designed to assist users of program

SPILE. The program was written to aid in the design of cantilever sheet

pile walls in soil deposits containing up to 20 strata. Some

limitations of the program are mentioned in Section 3.5. The program

was written in FORTRAN 77 and compiled with the Microsoft FORTRAN

compiler version 3.2 or later. The program runs on a Sperry - XT

Personal Computer (which is an IBM PC-Compatible machine) with a DOS

2.11 operating system or later. The minimum PC configuration required is

one double-sided disk drive and the availability of 128k of memory.

51

52

Description of the lEPUt Data File. The input data file is a

group of lines of text in a given order that may be created with any

editor or wordprocessing system that produces an ASCII output file. The

SPILE program scans the input file sequentially ignoring all lines that

do not contain a slash character (/). In this manner the user can mix

data lines with canments throughout the entire file. Each entry must be

separated from the others by one or more blank spaces, and no other

punctuation symbols (ccrrmas, dashes, etc.) are allowed.

For each given line of the input file, the program expects a

certain number of numerical entries, and each entry is supposed to be of

a certain type and to fall within a certain range of values. Entries

not complying with these rules will be rejected, and a detailed error

message will be displayed.

Input FJi*' sugary . The input lines must be ordered in the

following manner:

Type Format / Description

Model size definition nstrat / Number-of-stratums

Stratum definition i prostr(1,1) prostr(2,i) prostr{3,i) (One line per stratum prostr(4,i) prostr(5,i) prostr(6,i) until all strata prostr(7,i) / Stratum, Unit Weight, Sat. U. are defined) Weight, Friction Angle, Cohesion, Active Earth

Pressure Coefficient, Passive Earth Pressure coefficient, Stratum Thickness

Dredge line and GWT DDL GWEL / Dredge line level, GWT level levels definition.

Surcharge definition SUR / Surcharge

53

All lines not containing a slash character ( / } will be treated as

comment lines and ignored. Each input line is described in detail as

follows:

Problem size definition. -

Input: nstrat / Description: nstrat is the number of strata in the soil deposit

Format : Integer or whole number Range : 2 <= nstrat <= 20 Units : None Remarks: For homogeneous deposits, stratum 1 and stratum 2

both have the same input data.

Strati* definition. -

Input: i prostr(l,i) prostr(2,i) prostr(3,i) prostr(4,i) prostr(5,i) prostr(6,i) prostr{7,i) /

Description: i is the stratum number defined by the subsequent properties

Format : Integer or whale number Range : 1 <= i <= 20 Units : None

prostr(l(i) is the total unit weight of the stratum (dry/wet/saturated)

Format : Real Range : 0 < prostr(l,i) < 10E18 Units : Force per cubic length

prostr{2,i) is the saturated unit weight of the stratum Format : Real Range : 0 < prostr(2,i) < 10E1B Units : Force per cubic length

prostr(3,i) is the friction angle of the stratum Format : Real Range : 0 <= prostr(3, i) <= 90 Units : Degrees Remarks: This value is used to obtain the earth pressure

coefficient only. In addition, it is input for strata above the dredge line only.

prostr(4,i) is the cohesion of the stratum Format : Real Range : 0 <= prostr(4,i) <= 10E18 Units : Force per square length

54

prostr(5,i) is the active earth pressure coefficient Format : Real Range : 0 <= prostr(5,i) <= 1 Units : None

prostr{6,i) is the passive earth pressure coefficient Format : Real Range : 0.1 <= prostr(6,i) <= 90 Units : None Remarks: This coefficient is reduced when the factor of

safety is considered

prostr(7,i) is the thickness of the stratum Format Range Units Remarks

Real 0 <= prostr(7,i) <= 10E18 Length If the thickness of the last stratum is unknown, it should be assumed.

Repeat this input line until all stratums are defined

Dredge Line and GWT Levels definition. -

Input: DDL GWTL / Description:

DDL is the level of the dredge line Format : Real Range : 0 <= DDL <= 10E18 Units : Length Remarks: This level defines the backfill height; therefore

the length is limited to moderate values (14 or 15 feet)

GWTL is the level of the ground water table Format : Real Range : 0 <= GWTL <= 10E18 Units : Length Remarks: For dry soil deposits, a large value for the GMT

level should be assumed (say 500 feet)

Surcharge definition. -

Input: SUR Description:

SUR is the vertical surcharge applied to the ground surface Format : Real Range : 0 <- SUR <= 10E18

55

Units : Force per square length Remarks: The applied surcharge must be uniformly distributed

Analyzing the Problem. Assuming that disk drove A is the

current drive, and that program SPILE is located on drive d, the

following conmand will cause the program to run:

A>d:SPILE i=inpfspec o=outfspec e s

The e and s parameters may be in any order including being mixed with

the input and output options. The e is used to print an echo of the

input data in the output file and s is used to list the output file cm

the screen at the same time that it is created.

The i=inpfspec and o=outfspec parameters are also optional

inputs. The i=inpfspec option is used to set the input file name. The

o=outfspec option is used to specify the file to be used for all printed

output. The sequence of the i=inpfspec and o=outfspec options may be

reversed. If one or both of these parameter keys and associated

filenames are emitted, the program will ask for the missing file name

during the run. The inpfspec and outfspec files may be any valid DOS

file name, with an optional drive specification, directory path, and

type, if desired. If a file type is not specified, the program will use

.INP for the input file type and .OUT for the output file type. The

output file may be left completely unspecified (as long as 0= is

included), and the program will automatically use the same drive,

directory path and name as the input file and the .OUT extension. For

example:

B>B: SPILE I=A:TEST20 0= E => The program is in drive B which is

56

also the default drive since in this example B is the active drive. The

input file is named TEST20. INP and is contained in drive A. The output

file will be called TEST20.OUT and will be located in the same drive A:.

The echo option has been selected,

C>SPILE I=A:TEST 0=A: => The program is in the current default

drive C. The input file is named TEST.INP and is located in drive A. The

output file will be called TEST.OUT and will also be located in drive

A:. None of the echo or screen options have been selected.

Running the OcBpttter uruuiv.- After the logo of the program

is displayed on the screen the program will evaluate the parameters

passed in the command line —if any— and will prompt for the input and

output file names if they are missing. If the logo is not displayed on

the screen DON'T WDRRY, it just means that your canputer does not have a

graphics card. After the input file has been specified, SPILE will try

to locate it. If the file cannot be found, the following message will

be printed on the screen:

ERROR: File "inpfspec" cannot be found. Try again.

The program will then prcrnpt for the proper file specification again.

After the output file has been specified, SPILE will try to open it up.

If the output file cannot be opened, the following message will be

printed on the screen:

ERROR: File "outfspec" cannot be opened. Try again.

The program will then prompt for the proper file specification again.

Once SPILE has located the input file, it will proceed to read

its contents and will verify its validly. The screen will show the

57

progress as the data is read from the input file with a string of words

progressing across the screen as follows:

Size...Properties...Levels...Surcharge.. .End.

Each keyword corresponds to a block of lines in the input file. The

word "End" marks the completion of the process of reading the input

file.

After reading the input file, the program will start to solve

the resulting model. The entire process will take only a few seconds.

Once SPILE has solved the system, it will proceed to write the results

to the output file. The program then finishes by reporting the total

amount of time required to analyze the model and returning control to

the operating system.

Description of the Output File.- The SPILE program reports all

the information in single output file. The name and destination (both

drive and, directory path) of the output file are specified by the user

at the beginning of each run. The output file is a plain text file, in

ASCII format, and does not contain any special control characters other

than the standard carriage-re turn/line-feed at the end of each line.

The first lines of the output file generated by SPILE contain a header

that quickly identifies the run. For example:

SPILE CANTILEVER SHEET PILE ANALYSIS FOR STRATIFIED SOIL DEPOSITS Version 1.00 11/09/1986 22:24:13

Input data file : A:TEST.INP Output data file : A:TEST.OUT

58

The header shows the date and time of day when the file was created and

the data files involved.

An echo of the data is displayed in labeled tables as the

program progressively reads the input file. The program starts by

displaying the size of the model, and continues with the stratum

properties definitions. Next, the dredge line (DL) and ground water

table (GWT) levels are defined. Finally, the surcharge is specified:

SIZE OF THE DEPOSIT

Number of strata : 2

STRATUM PROPERTIES

Stratum Unit Satu. U. Friction Ka Kp Thickness Weight Weight Angle

1 125.00 135.00 0.00 1.00 1.00 9.00 2 125.00 135.00 0.00 1.00 1.00 500.00

DL AND GMT LEVELS

DL level GWT level 9.00 9.00

SURCHARGE

Surcharge 100.00

The information generated by SPILE about the solution of the

system is written to the specified output file with no options to be

specified. Again, to see the output data on the screen the user must

specify the s option in the command line. The data generated by the

59

program is the total length of the sheet pile and the maximum bending

moment. The data has the following form:

> Sheet Pile Size = 16.34 ft.

—> Maximum Moment = 8090.56 lb-ft

The following messages are displayed when they occur:

•** No pile is required. STOP. ***

*** Stratum 2 too weak, the system is unstable. STOP. ***

In addition, a table containing the total and effective stresses is also

generated. It is done in a table similar to the following example:

TOTAL AN) EEHEIHE aiKKWi {ACIKK)

SIR. ISB.(T) EXS.(T) EH3.(T) HH3. (T) 1VS. (B) EXS.(B) EH3. (B) EE.{B)

1 100.00 100.00 -1100.00 -1100.00 460.00 460.00 -740.00 -740.00 2 460.00 460.00 142.60 142.60 710.00 710.00 220.10 220.10 3 710.00 710.00 184.60 184.60 1055.00 1055.00 274.30 274.30 4 1055.00 1055.00 -145.00 -145.00 1555.00 1555.00 355.00 355.00 5 1555.00 1555.00 559.80 559.80 1775.00 1775.00 639.00 639.00 6 1775.00 1775.00 575.00 575.00 2450.00 2138.00 938.00 1250.00 7 2450.00 2138.00 1338.00 1650.00 2710.00 2273.20 1473.20 1910.00 8 2710.00 2273.20 1073.20 1510.00 3115.00 2491.00 1291.00 1915.00 9 3115.00 2491.00 1491.00 2115.00 68115.00 36291.00 35291.00 67115.00

TCHHL ND tohWl'LVE SHE3SS (BfiSSTVE)

SIR. US.(T) EV5.{T) EH3.{T) HB.(T) EW5.(B) EH3.{B) EE.(B)

6 .00 .00 1200.00 3200.00 675.00 363.00 1563.00 1875.00 7 675.00 363.00 1163.00 1475.00 935.00 496.20 1298.20 1735.00 8 935.00 498.20 1698.20 2135.00 1340.00 716.00 1916.00 2540.00 9 1340.00 716.00 1716.00 2340.00 66340.00 34516.00 35516.00 67340.00

(*) Tbtal end efferti\e sliumju at GWT lewsl.

60

The TVS(T), EVS(T), TVS(B), and EVS(B) parameters represent the

total and effective vertical stresses at the top and bottom of the

stratum, respectively. The THS{T), EHS(T), THS(B), and EHS(B)

parameters represent the total and effective horizontal stresses at the

top and bottom of the stratum respectively. The total and effective

stresses within a stratum at the GWT level are indicated by an asterisk

{*) in this table.

Program Messages.- There are two kinds of messages that the

SPILE program provides: (1) informative messages — ones the program

uses to keep you up to date about what it is doing, and {2) error

messages —diagnostics the program makes when it encounters a situation

it cannot handle, and that requires sane changes to be introduced by the

user. The following samples describe the error messages:

Message:

ERROR : INCOMPATIBLE TYPE OF NUMERIC ENTRY IN INPUT LINE. Encountered in line 6 of file A:ERRORS.INP.

1 | 5.2 110. 115. 25. 0. 0.36 1. 2. / |

, Reading stratum properties lines it was expected to find a stratum number - an integer between 1 and 6 - as the first entry.

Explanation: One of the entries in the line is of a type {integer, real,...) incompatible with the type of the expected data.

The arrows in the error message point to the character responsible for the type change and the following message states the required type for the entry.

Action: Check the input file and replace the entry with the correct type. Execute the program again with the modified input file.

Message:

ERROR : UNEXPECTED END OF INPUT FILE,

61

Encountered attempting to read line 8 of file A:ERR0R6.XNP.

Explanation: The program expects to find data in line 8 of the input data file.

Action: Check the input file and add the data corresponding to line number 8. Execute the program again with the modified input file.

Other messages given by the program are:

ERROR : ENTRY IS OUTSIDE THE PROPER NUMERIC BOUNDS.

ERROR : INPUT LINE CONTAINS LESS DATA THAN REQUIRED.

ERROR : ENTRY CANNOT EE INTERPRETED AS A NUMBER.

ERROR : DUPLICATED SPECIFICATION IN INPUT FILE.

Eaaule 1; Cantilever Sheet Pile {fall in Multiple Cohesive

Soil Strata Below Dredge Line with Maltiple Soil Strata Abowe Dredge

Line.- This example shows the program in one of its uses. The model

specified in file TEST60.INP represents a soil deposit with 9 strata.

Five of the strata are above the dredge line and the rest are below the

dredge line. The input file TEST60.INP is as follows:

9 / # stratums 1 120. 130. 0. 600. l. l. 3. / stratum properties 2 125. 135. 30. 0. 0.31 1. 2. / 3 115. 125. 35. 0. 0.26 1. 3. / 4 125. 135. 0. 600. 1. 1. 4. / 5 110. 115. 25. 0. 0.36 1. 2. / 6 125. 135. 0. 600. 1. 1. 5. / 7 120. 130. 0. 400. 1. 1. 2. / 8 125. 135. 0. 600. 1. 1. 3. / 9 120. 130. 0. 500. 1. 1. 500. / 14. 14. / dredge line and ground water levels in feet 100. / applied surcharge in pounds per square feet

The corresponding output file for this example problem is presented on

the following page. In order to obtain a similar format, the user must

62

set the printer for the correct number of characters per line and the

correct number of lines per inch. This can be done by setting the print

mode as follows:

A>MDDE LPT1:132,8

It means that the print mode was set for 132 characters per line and 8

lines per inch.

SEHE CSNHIEVER SJEET FILE AfTOVSIS KR SIRffllFTED FTTrr, EEKKITS Version: 1.0 11/09/1906 22:21:07

jfrput (Ma file Output data file

A:TESD50.IHP A:TESI60.CUr

SIZE CF HE LfcRKLT

NLnter cf strata 9

S3HSHM HOtKUJii {in fsf, pcf, ft)

Stratum thit Sactu. U. Erictim Cttesdcn Ki Vp Ihicknes Weight tfeirjht Argle

Vp Ihicknes

1 120.00 130.00 .00 600.00 1.00 1.00 3.00 2 125.00 135.00 30.00 .00 .31 3.22 2.00 3 115.00 125.00 35.00 .00 .26 3.88 3.00 4 125.00 135.00 .00 600.00 1.00 1.00 4.00 5 110.00 115.00 25.00 .00 .36 2.78 2.00 6 125.00 135.00 .00 600.00 1.00 1.00 5.00 7 120.00 130.00 .00 400.00 1.00 1.00 2.00 8 125.00 135.00 . .00 600.00 1.00 1.00 3.00 9 120.00 130.00 .00 500.00 1.00 1.00 500.00

EL Alt) GWT LEtfEIS

EL level G® level

14.00 14.00

9CK3BRGE

SuriiHryy

100.00

—> Slieet Pile siza =

—> ftennun Ntnanrt; =

30.124 ft.

17421.720 Ib-ft

TOERL iSC HEFEDIIVE aiMjAKj (^CTOE)

SIR. TVS. (T) ESS.{T) HB.(T) HB.(T) T\E.(B) ESS.(B) EH5.(B) 3H3.(B)

1 100.00 100.00 -1100.00 -1100.00 460.00 460.00 -740.00 -740.00 2 460.00 460.00 142.60 142.60 710.00 710.00 220.10 220.10 3 710.00 710.00 184.60 184.60 1055.00 1055.00 274.30 274.30 4 1065.00 1055.00 -145.00 -145.00 1555.00 1555.00 355.00 355.00 5 1555.00 1555.00 559.80 559.80 1775.00 1775.00 639.00 639.00 6 1775.00 1775.00 575.00 575.00 2450.00 2138.00 938.00 1250.00 7 2450.00 2138.00 1338.00 1650.00 2710.00 2273.20 1473.20 1910.00 8 2710.00 2273.20 1023.20 1510.00 3115.00 2491.00 1291.00 1915.00 9 3115.00 2491.00 1491.00 2115.00 68115.00 36291.00 35291.00 67115.00

TDIBL PiD EHFECUVE aiHftfcKB (EfiSSIVE)

SIR. 2V5.{T) EXE.{T) EH3.(T) US. (T) 1V5.(B) HE.(B) EH3.(B) TH3.(B)

6 .00 .00 1200.00 1200.00 675.00 363.00 1563.00 1875.00 7 675.00 363.00 1163.00 1475.00 935.00 498.20 1298.20 1735.00 8 935.00 498.20 1696.20 2135.00 1340.00 716.00 1916.00 2540.00 9 1340.00 716.00 1716.00 2340.00 66340.00 34516.00 35516.00 67340.00

{*) Tbtal and effective stmuuuLt at GWT level

Bfnitim time : 20.60 seocrris.

APPBHDIX C

Listing of Counter Program SPUE

64

65

SLINESIZE: 132 SPAGESIZE: B1 SSTORAGE: 2 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCGCCCCCCCCCCCGCCCCCCCCCCCCCCCCCCCCCCCCCCC c c C U N I V E R S I T Y o f A R I Z O N A C C Department of Civil Engineering C C C C S P I L E C C Cantilever Sheet Pile Analysis for C C Stratified Cohesive Soil Deposits C C 1st Part C C Version : 1.0 C C C C by GERMAN IBARRA C C Fall 1986 C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

PROGRAM spile CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDCCCCCCC c c C TYPE SPECIFICATION C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

INTEGER pppiuqq)ofnflglechfl9,scrflo,ascstr ,ddrive,odrive,nstadl, + flagul, fstbdl,flagwt,np,flag,flagan,flagby,kk CHARACTER inpfi1*78,outfil*78,toufi1*78,txtdisp*24,comand*127,

+ space*2,string*5,datext*ll,tirotxt*12,intgst«25,dash*l, + prompt*63,diamsg*l10,reaclb*8,arrow*1,elipss*4, + blank*l,ifdriv*6,ifpath*64,i fname*9,i fextn*5,f1 spec*78, + ofdriv*6,ofpath*64,ofname*9,ofextn*5,toextn*5 REAL prostr,ddl,gut 1, po,yo,qo,thw,thd,nst,dth,qij,s,tl,t2,t3,a,b, + c,cl,d,z,ths,pth,lah,1,mmax,dz LOGICAL ffound

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C c c ARRAY DIMENSIONING C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

DIMENSION entry(8 ),pth< 20 ),1(20,20) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C COMMON SPECIFICATION C c c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

COMMON /filenm/ inpfil,outfil COMMON /dskrom/ serflg,odrive COMMON /propet/ prostr(7,20) COMMON /levels/ DDL.GWTL COMMON /surcha/ SUR COMMON /stress/ sgavtt(20) ,sgavet(20 ),sgahet(20 ),sgahtt(20 ), + sgavbt< 20 ),sgaveb< 20),sgahebt 20),sgahtb(20),

G6

+ u<20> COMMON /staguil/ sgavdt(20 ),sgavedC20 ),Bgahed(20 ),sgahtd(20 ), + sgavut ( 20 ), Bgavewt 20 >, sgaheui( 20 ), sgahtuit 20) COMMON /pastrd/ sgpvtt<20>,sgpvet<20 ),sgphet<20 ),agphtt(20),

-I- sgpvbt (20 >, sgpvebf 20 ), sgpheb( 20 ), agphtb< 20 ), + up(20) COMMON /stpgwl/ sgpvdt(20 ),sgpved<20 ),sgphed(20 ),sgphtd<20>, + sgpvwt (20 ), sgpvew< 20 ), sgphew( 20 ), sgphtu( 20 ) COMMON /netprs/ s(20)

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C c C GENERAL INITIALIZATION C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

call time (inithr,initmn,initsc,iniths) call datstr (datext) call timstr (timtxt)

C C Show logo on the screen. C

call logo C C Initialize variables. C

serflg=0 space**1 ' call setstr (2,space) toextn='.OUT ' call setstr (5,toextn> el ipss5^ ... ' call setstr <4,elipss) call defdrv (0,ddrive)

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C READ THE COMMAND TAIL C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

ierror=ppmuqq (0,0,comand ) length=ascstr (l,comand)+2 if (length .ne. 2) then

call setstr (127,conand) call endstr <length,conand) call inovstr (comand, 1,0, space, 1,1 > call upestr (cociand) string-1 1= ' call setstr <4,string) locatn=locstr (1,conand,string)+3 if (locatn .ne. 3) then

nxtloc^locstr (locatn,conand,space) if (nxtloc .eq. 0) nxtloc=length nunchranxtloc-locatn

G7

inpfil=' + •

call setstr <78,inpfil) call movstr (inpfil,1,0,comand,locatn,numchr ) call resstr (inpfil) ifnflgBl

endi f call rnodstr < string,2,79 ) locatn=locstr (1,comand,string)+3 if <locatn .ne. 3) then

nxtloc=locstr (locatn,comand,space ) if (nxtloc .eq. 0) nxtloc*=length numchr=nxt loc-locatn outfil-'

+ '

call setstr (78,outfil) call novstr (outfil,1,0,comand,locatn,nunchr) call resstr (outfil) ofnflg=l

endi f 5tring=' E '

call setstr (3,string) locatn=locstr (1.coroand,string) if (locatn .ne. 0) echflg=l call nodstr <string,2,83) locatn=locstr (1,comand,string ) if (locatn .ne. 0) scrflg=l

endi f CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c c C SET INPUT AND OUTPUT FILES 'C C C cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

65 if (ifnflg .eq. 0) then WRITE (*,70)

70 FORMAT (' Input data file name [.INP17 '\> READ (*,'<A>' ) inpfil

else WRITE (*,72 ) inpfil

72 FORMAT <* Input data file name I.INP]' ',a78) endi f flspec=inpfil call parafn ( flspec,ddrive,ifdriv,idrive,ifpath,ifname,ifextn ) inpfil=flspec if {lenstr(ifextn) .eq. 0) then

ifextn*'.INP ' call setstr (5,ifextn) call constr (inpfil,ifaxtn)

endi f call resstr (inpfil) inquire (FILE«inpfil,EXIST=ffound)

G8

i f ( f f o u n d ) t h e n OPEN <1,FILE=inpfi1)

else call setstr (78,inpfil) call pakstr (inpfil ) lengthBlenstr (inpfil) call expstr (Inpfil) call resstr <inpfil> call wrfstr (float(length ),intgst ) length=lenstr (intgst) prompt^C'' ERROR = File '"',a , cannot be found. Try agai

+n."> •

call setstr (63,prompt) call movstr (prompt,21,0,intgst,1,length) write (*,prompt) Inpfil i fnflg=0 goto G5

ENDIF 74 toufil=inpfil

call setstr <78,toiifil) locatn=locstr (1, toufi1,ifextn) call movstr (toufil,locatn,1,toextn,1,4 ) length»lenstr (toufil) call expstr (toufil) call resstr (toufil) call wrfstr (float(length ),intgst ) length=lenstr (intgst) prompt®'^' Output data file name E'',a ,''3s 1',a78 )

+ *

call setstr (63,prompt) call movstr (prompt,30,0,intgst,1,length) if (ofnflg .eq. 0) then

call modstr (prompt,3B,63) string='\ '

call setstr (5,string) call movstr (prompt,38,0,string,1,4) call resstr (prompt) WRITE (*,prompt) toufil READ (*,'(A)' ) outfil

else call resstr (prompt) WRITE (*,prompt) toufil,outfil

endif flspec^outfil call parsfn (f1 spec, idrive-1,ofdriv,odrive,ofpath,ofname,ofextn) outf i 1 •=• f lspec IF (lenstr(ofdriv) .le. 2) then

call setstr (78,outfil) call endstr (1,outfil) if (lenstr( of driv ) .eq. 0) of drivifdriv if (lenstr(ofpath ) .eq. 0) ofpath=ifpath

69

if (lenstrCofname) .eq. 0) ofname^ifname if (lenstr(ofextn) .eq. 0) ofextn=toextn call constr (outfi1,ofdriv) call constr (outfil,ofpath) call constr <outfil,ofnaroe) call constr (outfil,ofextn)

endi f call resstr (outfil) call opnfil (ierror) if (ierror .ne. 0) then

ofnf1Q=0 goto 74

endi f cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c C START THE OUTPUT FILE C C C cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

call diskroom (0) C C Header title C

call diskroom <331) WRITE (2,80,err=2000) datext,timtxt,inpfil,outfil

8 0 F O R M A T ( ' S P I L E C A N T I L E V E R S H E E T P I L E A N A L Y S I S F O R ' , +' STRATIFIED SOIL DEPOSITS'/' Version: 1.0',3x,al0,lx,a8// +/' Input data file : ',A/' Output data file '• ',A/)

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C c C START READING THE INPUT FILE C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

diamsg='Reading model data from file + '

call setstr (110,diamsg ) call setstr (78,inpfil) call novstr (diamsg,30,0,inpfil,1,77) call resstr (inpfil) call pakstr (diamsg) call constr (diamsg,elipss ) call expstr (diamsg) call resstr (diamsg) call resstr (ofdriv) if (ofdriv .eq. 'CON: '> scrflg=-l

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C c C READ AND PROCESS THE DEPOSIT SIZE LINES C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c C Size header

70

if (echflg .oq. 1) then if (scrflg .eq. 1) then

WRITE (*,85) 85 FORMAT (/' SIZE OF THE DEPOSIT'/)

else if (scrflg .eq. 0) write (*,87) diamsg

87 format </IXfA/1 Size...'\) endif call diskroon (30) WRITE (2,85,err«2000)

else write (*,87) diamsg

endif C C Number of strata C

CALL verify?1.entry,ierror> IF (ierror .NE. 0) GOTO 994 nstrat=entry( 1) if (echflg .eq. 1) then

if (scrflg .eq. 1) WRITE (*,90) nstrat 90 FORMAT (' Number of strata :',I4)

call diskroon (48) WRITE ( 2, 90,err*=2000 ) nstrat

endi f cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c C READ AND PROCESS THE PROPERTIES OF STRATUMS LINES C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c C Properties of the strata C

if (echflg .eq. 1) then if (scrflg .eq. 1) then

WRITE (*,125) 125 FORMAT (//' STRATUM PROPERTIES'//' Stratum Unit

+ 'Satu. U. Friction Cohesion Ka Kp Thickness') WRITE (*,126)

126 FORMAT (' Weight Weight Angle'/) else

if (scrflg .eq. 0) urite (*,130) 130 format (' Properties...'\)

endif call diskroon (G8) WRITE (2,125,err=2000) WRITE (2,12B,err»2000 )

else urite (*,130)

endif

71

180 FORMAT (F8.2,3X,F8.2 ) call diskroom (39) WRITE (2,180,err,o2000 ) entry(1 ),entry(2)

endif 190 CONTINUE

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c C C READ AND PROCESS THE APPLIED SURCHARGE C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c C Surcharge C

if (echflg .eq. 1) then if (scrflg .eq. 1) then

write (*,200) 200 FORMAT (//' SURCHARGE'//' Surcharge'/)

else if (scrflg .eq. 0) write (*,205)

205 format ('Surcharge..."\ ) endi f call diskroom (114) WRITE (2,200,err=2000)

else write (*,205)

endif call chkdup (0,ierror) CALL verify(4,entry,ierror) SUR = entry(l) if (echflg .eq. 1) then

if (scrflg .eq. 1) WRITE (*,210) entry( 1) 210 FORMAT (F9.2)

call diskroom (92) WRITE (2,210,errs2000) entry(l)

endi f CLOSE <1 ) if ((echflg .eq. 0) .or. (scrflg .eq. 0)) WRITE (*,500)

500 format ('End') CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c c c SOLVE THE SYSTEM C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c C Calculate number of strata above dredge line C

nstadl » 0 nst •» 0.

DO 300 i • ltnstrat net ® nst + prostr(7,i) IF (DDL .eq. nst ) THEN

72

nstadl = nstadl + 1 goto 302

ELSE nstadl = nstadl + 1 goto 295

ENDIF 295 CONTINUE 300 CONTINUE

C 302 CONTINUE

C C Compute stresses above dredge line C

flagwl «• 0 thw B 0. thd a 0. po » 0. yo = 0. qo = 0.

DO 310 i =1,nstadl CALL gutlev (i , flagwl,thu,thd) IF (flagwl .eq. 0) THEN

CALL sigmaa <i,qo,flagwl) goto 305

ELSE if (flagwl .eq. 1) then

CALL sgmiaa <i ,qo,thw,thd) goto 305

else CALL sigmaa (i,qo,flagwl) goto 305

endi f ENDIF

305 CONTINUE 310 CONTINUE

C C Compute stress distribution above dredge line C

CALL stradl (nstadl,po,yo> if (po .eq. 0.) goto 224

C C Calculate number of strata below dredge line C

nstbdl =• nstrat - nstadl fstbdl » nstadl + 1

C C Locate GWT level and compute stresses in front and behind the sheet C pile wall below dredge line C

qd •= 0. qw = 0.

•thu = 0. thd = 0. flagut = 0 flagan = 0 flagst K 1 flagin «= 1 s(nstadl> = 0. t1 = -po t2 « p0 t3 « yo lah = 0. p t h ( 0 ) = 0 . DO 320 i ° l,nstbdl k " nstadl + i CALL gwtlev (k , f lagwl, thui, thd) IF (flagwl .eq. 0) THEN

CALL sigmaa (k,qd,flagwl ) goto 306

ELSE if (flagul .eq. 1) then

CALL sgmiaa (k,qd,thw,thd) goto 30G

else CALL signaa (k,qd,flagwl) goto 306

endif END1F

306 CONTINUE C

CALL locgwt (k,fstbdl,flagut,thw,thd,qw) IF (flaguit .eq. 0) THEN

qui = 0.

CALL slgnap (k,fstbdl,flagul,qui, flagin ) goto 307

ELSE if (flagwt .eq. 1) then

CALL sigmap { k, fstbdl, flaguit ,qu, flagin goto 307

else CALL sgmiap ( k, fstbdl, flaguit, thui, thd) flagin = 0 goto 307

endi f ENDIF

307 CONTINUE C C Compute sheet pile size C

s(k) = sgphtt(k) - sgahtt(k) flag = 0

311 IF (s(k) .gt. 0.> THEN

74

if (flag .eq. 1 ) then s< k) » -s< k ) if ((i .eq. 1) .or. (s(k-l) .le. 0.)) then

if ((pth <i-1 ) .eq. 0.) .and. (k .eq. nstrat)) then WRITE (*,229) k WRITE (2,229,err=2000) k flagst - 0 goto 353

else goto 308

endif else

if (pth(i-l) .gt. ths) then if ((flagby .eq, 1) .and. (k .eq. nstrat)) then

WRITE (•,229) k WRITE (2,229,err»2000) k

229 FORMAT (/' *«* Stratum ',12,' too ueak,the system1

+ ,' is unstable. STOP. ##•',/) flagst = 0

goto 353 else

if (flagby .eq. 0) then flag ° 2 goto 308

else goto 308

endi f endi f

else flag = 1 flagan = 1 goto 308

endi f endi f

else goto 308

endif 308 if (i .eq. 1) then

tl = tl t2 = t2 t3 * t3 goto 312

else ti = tl + s(k-1 )»prostr(7,K-l ) t2 • t2 - s(k-1 )«prostr(7,k-l ) t3 = t3 + prostr(7,k-1) goto 312

endif 312 if (flag .eq. 1) then

goto 314 else

75

goto 313 endi f

313 A = s< k )**2/(12.*proatr(4,k )) - s(k>/2. B - tl»s(k )/<6.*prostr(4,k )) + t2 if (k .eq. fstbdl ) then

C = t3«po + 1l**2/(12.*prostr(4,k )) goto 345

else goto 314

endi f 314 CONTINUE

n = 0

DO 330 j = 1,1-1 n =• i - 1

if (J .eq. n) then 1(j,i ) = prostr(7,k-l)/2. goto 333

else Kj,i> = prostrt7,k-1) + l(J,i-l) goto 315

endi f 315 CONTINUE 330 CONTINUE 333 CONTINUE

if < flag .eq. 1 ) then goto 31E

else goto 335

endi f ELSE

flag = 1 s< k ) «= -s(k)

goto 311 ENDIF

335 CONTINUE C

CI = t3*po + tl**2/(12.*prostr(4,k)) 31B m = 0

lah « 0. DO 340 j = 1,i-1 n = natadl + J lah »= lah + 1( j , i )*s(n )*prostr( 7,« )

340 CONTINUE if (flag .eq. 1) then

goto 318 else

goto 317 endi f

317 C = CI - lah C C Solve the quadratic equation

c 345 NP = 2

CALL quad(A,B,C,XR1,XII,XR2,XI2,NP) D - XR2 if (D .It. 0.) then

WRITE (*,219) 219 FORMAT ( ' D is negative, the system is unstable. STOP1/)

flagst * 0 goto 353

else goto 341

endi f 341 z = (tl + s<k )*D )/(4.*prostr(4,k ) >

if (z .le. D) then bmz = D - z

if (bmz .It. prostr(7,k)) then flagby = 0

" goto 34G else

flagby = 1

goto 346 endif

el se WRITE (*,217) WRITE (2,217)

217 FORMAT (/' > z > than D'/) flag = 2

goto 34G endi f

346 CONTINUE C C Solve the quadratic equation for (z > D) C

if (flag .ne. 2) goto 347 t4 = 4.*(prostr(4,k-1 ) + prostr(4,k)) A » 2.»s(k-l )#*2/(3.*t4) - s(k-1 )/2. B = 4.*tl*s(k-l)/(3.*t4) + t2 CI = t3*po + 2.*tl**2/(3.»t4 > C ™ CI - lah NP = 2

CALL quad(A,B,C,XRl,XIl,XR2,XI2,NP) D = XR2

if (D .It. 0.) then WRITE (*,219) goto 353

else z = 2.*< 11 + s(k-1 )*D)/14 WRITE (*,22G ) 0,2 if (flagan .eq. 1) then

pth (i) = ths - prostr(7,k) + D goto 352

else pth < i > = ths + D goto 352

endi f end! f

347 CONTINUE 318 m - 0

ths = 0. DO 350 j = 1,1 m = nstadl + j ths = ths + prostr(7,m)

350 CONTINUE if ((flag ,eq. 1) .and. (flagan .eq. 1)> then

flag = 2

goto 346 else

if (flag .eq. 1 ) then goto 351

else goto 319

endi f endi f

319 if (i .eq. 1) then if (D .le. ths) then

pth (i ) = D

goto 352 else

pth < i) - D goto 351

endi f else

pth (i) - ths - prostr(7,k) + D if (pth(i) .le. ths) then

goto 352 else

goto 351 endi f

endi f 351 CONTINUE 320 CONTINUE 352 CONTINUE

psize = DDL + pth(i ) WRITE (•,218 ) pth (i) WRITE (*,225) psize WRITE <2,225terr»2000) psize

218 FORMAT (//' pile size from dredge line = ',F15.5,/) 225 FORMAT <//' > Sheet Pile size - \F1S.3,' ft.',/) 353 CONTINUE

if (flagst .eq. 0) goto 224 kk - i

78

if (z .gt. D) then dz = prostr(7,k-l) - 2 + D goto 354

else dz = 0 - z

goto 354 endi f

354 CONTINUE C C Compute maximum moment C

CALL MAXMO (kk,nstadl,nstbdl,fstbdl,po,yo,dz,mmax) WRITE ( « ,222 > mmax WRITE (2,222,err=2000 ) mmax

222 FORMAT (' —> Maximum Moment = \F15.3,' lb-ft',/) 224 CONTINUE

C C Write the active and passive stresses C

CALL uirtsdi (nstadl,nstrat ) if (po .eq. 0.) goto 800 CALL uirtpsd ( fstbdl,nstrat )

800 CONTINUE C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC c c c REPORT THE EXECUTION TIME C C C cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c C Report the execution time C 994 cpusec=0.

call time <lasthr,lastmn,lastsc,lasths> if (lasthr .It. inithr) cpusec«86400. cpusec=cpu5ec+3G00.*(lasthr-inithr >+60.*(lastmn-initmn)+lastsc-+ initsc+.01«(lasths-iniths) if (scrflg .ge. 0) write (*,995) cpusec

995 format (//• Execution time * 1,f8.2,' seconds.') if (ierror .ne. -1) then

call diskroom (43) write (2,995,err=2000 ) cpusec

endi f write (*,999)

999 format (' 1)

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

STOP

C c c

REPORT UNSPECIFIED I/O ERRORS DETECTED C C C

1000 write (#,1010)

1010 format <//* ERROR : CANNOT READ INPUT FILE.'/ + ' The program cannot continue.') goto 994

2000 write <«,2010) 2010 format (//' ERROR : CANNOT WRITE OUTPUT FILE.'

+ ' The program cannot continue.') ierror=-l goto 994 END

80

$LINESIZE: 132 SPAGESIZE: G1 SSTORAGE: 2 cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c C U N I V E R S I T Y o f A R I Z O N A C C Department of Civil Engineering C C C C S P I L E C C Contiliver Sheet Pile Analisys for C C Stratified Soil Deposits C C 2nd Part C C Version • 1.0 C C C C by GERMAN IBARRA C C Fall 1986 C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

SUBROUTINE parsfn <flspec,ddrive,fldriv,driven,flpath,fInane, + flextn)

C C Parse a file specification and get drive, path, name and extension C

IMPLICIT INTEGER (a-z) CHARACTER fldriv*6,flpath*64,fInane*9,flextn*5,f1spec*78,colon*2, + bslash*2,period*2

C C Initialization. C

call setstr (78,flspec) call pakstr (flspec) call upcstr (flspec) fldriv0' ' call setstr <6,fldriv) flpath=1

+ •

call setstr (64,flpath) flnane®' ' call setstr (9,flname) flextn=* '

call setstr (5,flextn) colon®': ' call set6tr (2,colon) bslash='\ '

call setstr (2,bslash) period™'. ' call setstr (2,period)

C C Determine the drive specification C

locatnalocstr (1,flspec,colon ) if (locatn .eq. 0) then

driven=ddrive+l else

call movstr (fldriv, 1,1,flspec,1,locatn> drivenaascstr (locatn-1,flspec )-B4

endi f C C Determine the path specification C

f irstc*locatn+l lastoc=locatn

10 locatn=locstr (lastoc+l,flspec,bslash> if (locatn .ne. 0) then

lastoc=locatn goto 10

else call movstr (flpath,1,1,flspec,firstc,lastoc-firstc+l)

endi f C C Determine the extension specification C

length=lenstr(flspec ) locatn=locstr (lastoc+l,flspec.period ) if (locatn .ne. 0) then

call movstr (flextn, 1,1,flspec,locatn,length-locatn+1) else

locatn=length+l endi f

C C Determine the name specification C

call movstr <flname,1,1,flspec,lastoc+l,locatn-lastoc-l> C C Pack the return strings C

call pakstr (fldriv) call pakstr (flpath) call pakstr (flname) call pakstr (flextn) RETURN END

$PA6E SUBROUTINE opnfil (ierror)

C C Open a file for output with verification C

LOGICAL ffound CHARACTER lnpfi1*78,outfi1*78,prompt*55,intgst*25 common /filenm/ inpfil,outfil inquire (FILE=out fil,EXIST=ffound ) if (.not.(ffound ) > then

call setstr (78,outfil)

82

call pakstr (outfil) length*lenstr( outfil)+l call expstr (outfil) call resstr (outfil) call setstr (length,outfil) call chopur (outfil,ierror ) if (ierror .ne. 0) then

call resstr (outfil) length*=length-l call wrfstr (float(length ),intgst ) length=lenstr (intgst) prompt®'('' ERROR : File "'^a cannot be open. Try a

+gain. " ) ' call setstr (55,prompt) call movstr (prompt,21,0,intgst,1,length ) call resstr (prompt) write (*,proPipt) outfil return

endi f call resstr (outfil)

endi f OPEN (2,FILE=outfil,STATUS='new') ierror=0

return END SUBROUTINE diskroom (nbytes)

C C Update count of characters in output file to avoid disk full errors. C

INTEGER frespc*4,odrive, scrflg,asc i ic COMMON /dskrom/ serflg,odrive

C if (nbytes .eq. 0) then

call dskspc (odrive,frespc) frespc=frespc-1

else C

20 frespc^frespc-nbytes C

if (frespc .It. 0) then close (2) asciic=odrive+64 write (*,30)

30 format (//' ERROR : Output file disk is full.') 32 write (*,35) char(asciic) 35 format (' Change the disk in drive *,al, + ' and press any key to continue.' )

call confrm if (scrflg .eq. 0) write (*,40)

40 format (lx\ ) call opnfil (ierror)

83

C C c

If <ierror .ne. 0) goto 32 call dskspc <odrive,frespc ) frespc=frespc~l goto 20

endi f end! f return end SUBROUTINE verify (idline,entry,ierror>

Verify input data

implicit integer (a-z) real prostr,entry,boulow,bouhig,ftcons,fltstr CHARACTER buffer*126,slash*2,space*2,stcon5*25tline*79,inpfi1*78, + out f i1*78,period*2,grafch*1,tabchr*2,typpar*14,ordinl*8, + errmsg*50,lintyp*27,1inent*30,txtpar*30,nessge*80 DIMENSION nunpar(4 ),itypar(4,8),boulow(4,8 ),bouhig(4,B>, + itxtpr(4,8),typpar(2 ) ,errmsg(6 ),lintyp(4 ),1inent(4), 4 ordinl(8 ),txtpar<12 ) ,messge(3 >.entry(8) common /propet/ prostr(7,20) common /filenm/ inpfil,outfil

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C ARRAY INITIALIZATION C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

DATA numpar /l,8,2,1/ /2*1,30*2/ /2*1.,19*0.,0.1,3*0.,0.1,6*0./ /20.,0.,11*10E18,100.,7*10E18,1.,3*10el8,90.,G*10E1B/

DATA DATA DATA DATA DATA

itypar boulou bouhig typpar errmsg

/' - an integer » i

+ + + + + [ +

+

+ [ + + + C

+

+

+

+

DATA lintyp

DATA 1inent

DATA ordinl

- a number '/ /'UNEXPECTED END OF INPUT FILE. 'INPUT LINE CONTAINS LESS DATA THAN REQUIRED. 'ENTRY CANNOT BE INTERPRETED AS A NUMBER. 'INCOMPATIBLE TYPE OF NUMERIC ENTRY IN INPUT LINE. 'ENTRY IS OUTSIDE THE PROPER NUMERIC BOUNDS. 'DUPLICATED SPECIFICATION IN INPUT FILE. 'model size ' 'stratum propeties ' 'dredge line and 6WT levels ' 'surcharge '/ • 1

'propeties of stratum ' 'levels of dredge line and SWT ' 'applied surcharge ' / 'first 'second 'third 'fourth 'fifth

84

+ +

+

,'sixth ' , 'seventh ' ,'eighth */

DATA itxtpr /i,Z,10,12, + + + + + + +

0,3,11,0, 0,4,0,0, 0,5,0,0, 0,6,0,0, 0,7,0,0, 0,8,0,0, 0,9,0,0/

stcons=' ' line='

+ slash='/ '

call setstr(2,slash ) space=' *

call setstr(2,space ) grafch=char(9) tabchr-' ' call setstr(2,tabchr) call novstr( tabchr,1,0,grafch,1,1) chrerr=0 idparn=l locatn=l if (idline .eq. 1) linurnb=0

10 linumb=linumb+l ierror=l READ (1,20,END=70,ERR=1000 > buffer

20 FORMAT (A126 ) call setstr(12B,buffer) ierrorB0 ENDSEP=locstr(1,buffer,slash ) IF (ENDSEP .eq. 0) goto 10 call endstr (endsep+1,buffer )

25 itcon5*locstr(locatn,buffer,tabchr) if (itcons .ne. 0) then

call movstr <buffer,itcons,0,space,1,1) locatn=ltcons+l goto 25

endi f locatn=l

30 IF (locatn .ge. ENDSEP) THEN chrerrHENDSEP lerror=2 GOTO 70

endi f seprtrBlocstr(locatn,buffer,Bpace > IF (seprtr .eq. locatn) THEN

locatn=locatn+l GOTO 30

85

endi f IF {(seprtr .eq. 0) .OR. (aeprtr .gt. ENDSEP)) seprtr^ENDSEP ierror=0 decpop=0

EXPFLG-0 EXP5GN-0 seploc=seprtr-locatn do 50 positn=l,SEPLOC index=1ocatn+positn-1 asciic^ascstrt index,buffer) IF ((asciic .gt. 47) .AND. (asciic .It. 58)) goto 40 IF ((positn .eq. 1) .AND. ((asciic .eq. 43) .OR.

+ (asciic .eq. 45))) goto 40 . IF ((asciic .eq. 4B> .AND. (decpop .eq. 0)) THEN

decpop=locatn+positn-1 GOTO 40

endi f IF (((asciic .eq. B8) .OR. (asciic .eq. 69) .OR. (asciic .eq. 100) + .OR. (asciic .eq. 101)) .AND. < EXPFLG .eq. 0)) THEN

EXPFLG=locatn+positn GOTO 40

endif IF (((asciic .eq. 43) .OR. (asciic .eq. 45)) .AND. (EXPFLG .ne. 0) + .AND. (EXPSGN .eq. 0)) THEN

EXP5GN=1ocatn+positn if (asciic .gt. 43) expsgn=-expsgn GOTO 40

endi f ierror=3 chrerr=locatn+positn-1 goto 60

40 continue 50 continue 60 continue

IF (ierror .eq. 3) goto 70 call setstr(25,stcons ) cal1 movstr(stcons,1,1.buffer,locatn.SEPLOC ) call resstr(stcons ) ftcons=fltstr(stcons) IF ((ftcons .It. boulow(idline,idparn )) .OR.

+ (ftcons .gt. bouhig(idline,idparn ))) THEN ierror=5 chrerr=locatn GOTO 70

endi f IF ((itypar(l d line,idparn) .eq. 1) .and. + (ftcons .ne. float(int<ftcons )))) then

ierrorM IF (decpop .ne. 0) THEN

chrerrBdecpop GOTO 70

86

ELSE IF (EXPSGN .It. 0) THEN

chrerr=-EXPSGN GOTO 70

ELSE chrerr=locatn GOTO 70

endi f endi f

endi f entryt idparn)=ftcons if ((idparn .eq. 1) .and. (idline .gt. 1) .and. (idline .It. 4)) + then

itcons=INT( ftcons) CALL CHKDUP (itcons,ierror) IF (ierror .ne. 0) THEN

ierror=6

chrerralocatn

goto 70 endi f

else if ((idparn .eq. 2) .and. (idline .eq. 4)) then

itcons=INT(3*entry(1 )+ftcons-3 ) CALL CHKDUP (itcons,ierror ) IF (ierror .ne. 0) THEN

ierror=6

chrerr^locatn

goto 70 endi f

endif endi f locatn=seprtr+l idparmBidparn+l IF (idparn .gt. nunparfidline)) THEN

if (idline .eq. 1 ) then bouhig(idline+1,1)Bentry( 1)

endi f goto 3000

ELSE goto 30

endif 70 txtpar(1 )=1nunber of strata 1

txtpar(2 )='stratun nunber ' txtpar(3 )='unit weight of the stratun 1

txtpar(4)='subn. u. ui. of the stratum ' txtpar(5)='friction angle of the stratun ' txtpar(6^'cohesion of the stratum ' txtpar<7 )=*active coeff. of the stratum ' txtpar(8 )='passive coeff. of the stratun 1

txtpar(9)='thickness of the stratum ' txtpar(10 )='DL level in the deposit '

txtpar( 11 )«•' GWT level in the deposit ' txtpar< 12 )•='surcharge * write (#,80) errnsg( ierror )

80 FORMAT <//' ERROR « \A50) call diskroom (67) write <2,80,err=2000) errmsg(ierror ) messge(1>•'

+ * messge< 2 )=»'

+ '

messge(3 )=' + '

call setstr (240,MESS6E(1)) stcons^'Encountered ' call rnovstr (messge<1 ),1,1,stcons,1,11 ) IF (ierror .eq. 1) THEN

stcons=' attempting to read 1

ELSE stcons=' in '

endif call setstr (25,stcons) call constr (messge<1 ),stcons ) call pakstr <nessget1)) stcons=' line ' call setstr (6,stcons) call constr (messgef1),stcons ) call pakstr (messge(l>) call constr {messge(1 ),space) call wrfstr (float(linumb>,stcons ) call constr <messge(1 ),stcons ) call pakstr (messge(l)) stcons=' of file ' call setstr (9,stcons) call constr (messge(1),stcons ) call constr (rnessget 1 ),space ) call setstr (78,inpfil) call pakstr (inpfil) call constr <messge<1 ),inpfil) period®'. ' call setstr (2,period) call constr <messge(1 ),period) call writxt (messge) IF (ierror .eq. 1) goto 3000 grafchachar(218) call setstr <79,line) call filstr (19B,line) call rnovstr (line,1,0,grafch,1,1) if (chrerr .ne. 0) then

grafch=char(25)

call rnovstr (line,chrerr+l ,0,grafch, 1,1 ) endif

lengthalenstr (buffer)+2 grafch^charf191 ) call movstr (line,length,©,grafch,1,1 ) length"length+l call endstr (length,line) call resstr (line ) write (»,90) line format (lx,A7S> call diskroom (82) write (2,90,err=2000 ) line length=length-3 call setstr (79,line) QrafchBchar(179) call movstr (line,1,0,grafch,1,1 ) call movstr (line,2,0,buffer,1.length ) length=length+2 call movstr (line,length,0,grafch,1,1> length°length+l call endstr (length,line) call resstr (line) write (*,90) line call diskroom (82) write (2,90,err=2000) line grafch=char( 192) call setstr (79,line) call filstr (19G,line) call movstr (line,1,0,grafch,1,1) if (chrerr .ne. 0) then

grafch=char(24) call movstr (1ine,chrerr+l,0,grafch,1,1)

endi f length=lenstr (buffer )+2 grafchsschar(217) call movstr (line,length,0,grafch,1,1) length=length+l call endstr (length,line) call resstr (line) write (»,90) line call dlskroom (82) write (2,90,errB!2000) line call filstr (32,messge(1)) if (ierror .eq, G) then

5tcons=1 The ' call movstr (messge(1),1,0,stcons,1,5) call pakstr (messge(l)) call constr (messge(1),space) call setstr (30,1inent(idline )) call constr (messge(1),linent(idline)) call resstr (linent(idline )) call pak&tr (messge(l)) call constr (nessge(1 ),space)

call uirfstr ( entry{ 1 ), stcons ) call constr (messge(1),stcons) stcons=' appear twice. ' call setstr <15,stcons> call constr (messge<1),stcons) call writxt (messge) goto 3000

endi f stcons0' Reading * call novstr <messge(1 ),1,0,stcons,1,8) if (idparm .eq. 1) then

call movstr <messget1),10,0,lintyp(idline ),1,27) call pakstr (nessge(l)) stcons=' lines ' call setstr (7,stcons> call constr (messge<1 ),stcons>

else call movstr (messge(1 ),10,0,linent(idline ),1,30) call pakstr (messge(l)) call constr (messge(1),space) call wrfstr <entry(1 ),stcons ) call constr (messge<1),stcons )

endi f 5tcons=' it was expected to find ' call setstr<25,stcons ) call constr<messget1),stcons ) if ((idparm .eq. 1) .and. (idline .gt. 1)) then

stcons=' a * else

Btcons=' the 1

endi f call setstr (5,stcons) call constr (messge(1 ),stcons) call pakstr (messge(l)) call constr (messge(1),space) index°itxtpr(idline,idparm > call setstr (30,txtpar<index)) call constr (messge(1),txtpar(index)) call resstr (txtpartindex)) call pakstr (messge(l)) index=itypar< idline,idparm) call setstr (14,typpar<index>) call constr (messget1) ,typpar<index)) call resstr (typpar(index>) call pakstr (messge(l)) Btcons®' between ' call setstr <10,stcons) call constr (messge(1),stcons ) call wrfstr ( bouloui( idline, idparm ),stcons ) call constr (meBsge(1),stcons) stcons53' and '

90

call setstr (6,stcons) call constr (messge(1 ),stcons) call wrfstr (bouhig(idline,idparm),stcons) call constr (messge(1 ),stcons ) stcons=' - as tho ' call setstr (11,stcons) call constr (messge(1),stcons) call setstr (8,ordlnl(idparm)) call constr (messget1>,ordlnl(idparm)) call resstr <ordinl(idparm)) call pakstr (messge(l)) stcons**' entry. ' call setstr (8,stcons) call constr <messge(1 ),stcons ) call uiritxt (messge) goto 3000

1000 write (»,1010 ) 1010 format <//' ERROR s CANNOT READ INPUT FILE.'/

+ ' The program cannot continue.') lerrora-l goto 3000

2000 write (*,2010) 2010 format (//' ERROR s CANNOT WRITE OUTPUT FILE.'/

+ ' The program cannot continue.1) ierror=-l

3000 return end SUBROUTINE writxt (messge)

C C Write text on the screen formatting to avoid breaking words C

IMPLICIT INTEGER (a-z> CHARACTER messge«80, line»79,endwrd*3,space*2 DIMENSION messge(3) line='

+ •

call setstr <79,line) endwrd=' '

call setstr (3,endwrd) space=* '

call setstr (2,space) call expstr (messge(l)) startp=l endtxt^locstr (1 ,(nessge< 1 ),endurd )

110 index1=startp+79 IF (ENDTXT .ge. index) THEN

spcpos^startp-l 120 nxtspc=spcpo5+l

length^locstr (nxtspc,messge(1 ),space ) IF (length .It. index) THEN

spcpos^length

GOTO 120 endi f length=spcpos-startp call movstr (1ine,1,1,messge(1),startp,length) call resstr (line) write (*,90) line

90 format (lx,A79) call diskroom (82) write (2,90,err=2000) line call setstr (79,line) startp^spcpos+l GOTO 110

endi f endtxt=endtxt-l call movstr (1ine,1,1,messge(1 ),startp,ENDTXT) call resstr (line) write (*,90) line call diskroom (82) write < 2,90,erra:2000 ) line goto 3000

2000 write (*,2010) 2010 format (//' ERROR : CANNOT WRITE OUTPUT FILE.'/

+ ' The program cannot continue.') ierror=-l

3000 return end

$PAGE SUBROUTINE datstr(string)

C C Write the date in a string. C

IMPLICIT integer (a-z) CHARACTER string*ll ,blank*2,buffer*10 call date (day,month,year ) write (buffer,10) month,day,year

10 FORMAT (i2,'/',i2,'/•,i4) READ (buffer,20) string

20 format (al0) call setstr (11,string) asciic=ascstr(4,string ) if (asciic .eq. 32) call modstr (string,4,48)

RETURN END

SPAGE SUBROUTINE timstr(string)

C C Write the time-of-day in a string. C

IMPLICIT integer (a-z) real realsc CHARACTER string*12,blank*2,buffer*!1

92

call time (hour.minute,second,secl00) realsc=float<second )+float( sec100 )/100. write {buffer,10> hour,Minute,realsc

10 FORMAT READ (buffer,20) string

20 fornat (all ) call setstr (12,string) asciic°ascstr(4,string) if (asciic .eq. 32)'call modstr <string,4,48) asci ic=ascstr(7,string ) if (asciic .eq. 32) then

call nodstr (string,7,48) asci icBascstr<8,string ) if (asciic .eq. 32) call nodstr (string,8,48)

endi f RETURN END

SPAGE FUNCTION fltstr (string)

C C Calculate the floating point value of a string. C

CHARACTER buffer*2E,string*25 write (buffer,*) string READ (buffer,10,ERR=300) intstr

10 format (bn,i25) fltstr®float(intstr) goto 500

300 fltstr=0 READ (buffer,310,ERR=500) fltstr

310 format (bn,f25.0) E00 RETURN

END $PAGE

SUBROUTINE urfstr (real,string ) C C Write a real in a string. C

implicit integer (a-z ) real real CHARACTER string*25,expnnt*5 if (real .eq. 0. ) then

string='0 ' call setstr (2E,string) call endstr (2,string)

el se if ((abs(real) .ge. l.ell) .or. (abs(real) .It. l.e-5)> then

write (string,10) real 10 format (E12.6E2)

call setstr (25,string) call pakstr (string)

93

expnnt^'E * call setstr (5,expnnt) call endstr (2,expnnt) l=locstr (1,airing,expnnt) call movstr <expnnt,1,1,string,1,4)

30 1-1-1 if <ascstr<1,string) .eq. 48) goto 30 call movstr (string,1+1,1,expnnt,1,4)

else write <strina,40) real

40 format <F19.10) call setstr <25,string) call pakstr {string) l=lenstr <string)+l

50 1=1-1 if <ascstrC1,string ) .eq. 48) goto 50 if <ascstr<1,string ) .eq. 4E ) 1=1-1 call endstr (1+1,string)

endi f endif RETURN END

C SUBROUTINE gwtlev (i,flagwl,thu,thd)

C C Locate GUT level C

INTEGER flagwl REAL prostr,thta,dth,thw,thd COMMON /propet/ prostr(7,20) COMMON /levels/ DDL.GUTL

C if < i .eq. 1 ) then

thta = 0.

goto 12 else

goto 12 endif

12 continue C

IF (GWTL .gt. 0. ) THEN thta = thta + prostr(7,i)

if (GWTL .ge. thta) then flagwl ° 0 goto 15

else dth - thta - GWTL

if (dth .ge. prostr(7,i)) then flagwl = 2 goto 15

else

thu = thta - GWTL thd = prostr(7,i) - thw flagwl H 1 goto 15

endi f endif

ELSE flagwl ** 2

ENDIF IS RETURN

END 0

SUBROUTINE sigmaa <i,qo,flagul ) C C Calculate total and effective stresses due to active presssure C

INTEGER flaguil REAL prostr»sq,soiluu COMMON /propet/ prostr(7,20>

COMMON /surcha/ SUR COMMON /stress/ sgavtt(20),sgavet(20 ),sgahet<20>,sgahtt(20 ) + sgavbt< 20 ),sgaveb< 20 ),sgaheb< 20 ),sgahtb(20) + u(20)

C uuui = 62.4 if (flagwl .eq. 0) then

u{i )=0.

soiluu = prostr(l,i)

goto 14 else

soiluu = prostr(2,i) u( i )=uuu»prostr( 7, i ) goto 14

endi f 14 sq = sqrt(prostrt5,i ))

IF (i .eq. I) THEN sgavt t(i )=SUR sgavet(i )=sgavtt(i ) sgahet(i )=prostr(5,i )*sgavet(i) - 2*prostr(4, i )*sq sgaht t(i )=sgahet(i ) sgavbt<i>=sgavtt(i ) + soiluu*prostr<7,i> sgavebti )=sgavbt(i ) - u<i ) sgaheb<i )«prostr(5,i )*sgaveb(i) - 2»prostr<4,i )*sq sgahtbti )»sgaheb(i> + u(i ) goto 15

ELSE sgavtt(i )»sgavbt< i-1) sgavet< i )=»sgavtt ( i ) - u(i-l) sgahet(i )=prostr(5,i )*sgavet(i) - 2*prostr(4,i )*sq sgahtt<i )=sgahet(i) + u(i-l)

u(i )=u< i-1> + u(i )

95

sgavbt(i )=sgavbt(i-1) + soi luu)»pro3tr (7, i )

sgaveb(i )»sgavbt(i ) - u<i) agaheb(i)=prostr<5,i )*sgaveb(i ) - 2*prostr<4,i )*sq sgahtb(i )=sgaheb<i ) + u(l) goto 15

ENDIF 15 qo a sgaveb( i )

RETURN END

C SUBROUTINE sgmiaa (i,qo,thu,thd)

C C Calculate total and effective stresses due to active presssure C considering arbitrary GWT level. C

REAL proatr,sq,soiluw COMMON /propet/ prostr{7,20) COMMON /surcha/ SUR COMMON /stress/ sgavtt(20>,sgavet<20 ),sgahet<20>, sgahtt(20 ), + sgavbtt 20 ),sgaveb(20 ),sgaheb(20 ),sgahtb(20 ), + u<20> COMMON /stagwl/ sgavdt(20 ),sgaved(20 ),sgahed<20 ),sgahtd(20), + sgavut (20 ), sgavew< 20), sgaheu)( 20 ), sgahtw< 20 )

C uww - B2.4 sq = sqrt(prostr(5,i))

IF (i .eq. 1) THEN sgavtt(i)=SUR sgavet(i )nsgavtt(i ) sgahet( i )«=prostr(5, i )*sgavet< i ) - 2*prostr(4,i )*sq sgahtt(i >=sgahet< i)

C soiluw = prostr(l,i>

C sgavdt(i )=sgavtt(i ) + soiluw*thd sgaved(i)asgavdt(i) sgahed(i )=prostr(5,1>»sgaved(i) - 2»prostr<4,i )*sq sgahtd(i)Bsgahed(i >

C sgavut< i )=sgavdt(i) sgaveu< i )*sgavut(i > sgaheuti )=prostr(5,i)*sgavew( i) - 2+prostr(4, i )«sq agahtw( i )=sgahew( i )

C soiluw • prostr(2,i)

C sgavbtti^sgavwtti) + 5oiluw*thw

u( i )=uwui*thu sgaveb( i >"»sgavbt< i ) - u( i ) agahebt i )|=prostr(51 i >*agaveb{ i ) - 2*prostr(4,i )*sq agahtb( i)"sgaheb(i ) + u(i )

goto 15 ELSE

sgavtt(i )»sgavbt(i-l> sgavet< i )=sgavtt< i ) sgahetti>»prostr(5,i>*sgavet(i) - 2»prostr(4,i>*aq sgahtt( i )#,sgahet< i )

soiluw = prostr(l,i)

sgavdt(i )=sgavtt(i ) + soiluw*thd sgaved< i )a=sgavdt< i ) sgahed( i )=prostr(5,i )*sgavedCi > - 2#prostr(4,i )»sq sgahtd(i )=sgahed(i )

sgavuit < i J^sgavdt ( i ) sgaveui( i )=sgavujt< i ) sgahew(i )=prostr(S,i )*sgavew(i ) - 2*prostr(4,i )»sq sgahtw(i )=sgahew( i )

soiluw = prostr(2,i)

sgavbt(i )=sgavdt(i ) + soiluu*thw u( i )-uuw«thw

sgaveb<i )=sgavbt(i ) - u(i) sgaheb<i )=prostr(5,i )»sgaveb(i ) - 2*prostr(4,i )*sq sgahtb<iJ^sgahebti> + u< i )

ENDIF IB qo « agaveb(1)

RETURN END

SUBROUTINE stradl (nstadl,po,yo}

Calculate the resultant (po) of the stress distribution above dredge line

INTEGER nstadl,flagwl DIMENSION a(20),y(20),ydl(20 >,ad(20 ) ,yd< 20 ) ,yddl(20), + aw(20),yw<20 ),ydul(20 )

REAL prostr,a,y,po,ap,at,th,ydl,ad,au,yo,yd,yui,yddl,ydwl,thw,thd, + x COMMON /propet/ prostr(7,20) COMMON /stress/ sgavtt(20 ),sgavet(20 ),sgahet(20 ),sgahtt(20 ), + sgavbt(20 ),sgaveb(20 ),sgaheb(20 ),sgahtb(20), + u< 20)

COMMON /stagul/ sgavdt(20),sgavedt20 ),sgahed<20),sgahtd<20), + sgavuit < 20), sgaveui( 20 ), sgaheui( 20), sgahtui< 20 ) COMMON /levels/ DDL,GWTL

flagwl • 0 thui = 0.

97

thd = 0.

ap e 0. at = 0.

th = DDL

DO 20 i » 1.nstadl CALL guitlev( i , flagwl, thui, thd )

IF ((flagwl .eq. 0) .or. (flagwl .eq. 2)) THEN if (sQahet(i) ,le. 0.) then

if (sgaheb(i) .la. 0.) then th = th - prostr(7,i) WRITE (*,151 ) th goto 16

else x = abs(sgahet(i))«prostr(7,i)/(sgahebti)

+ + abs(sgahet(i ))) a<i ) = sgaheb(i )»(prostr(7,i> - x)/2. y(i ) = (prostr(7,i) - x>/3. th a th - prostr(7,i) ydl(i > = th + y(i )

goto 15 endif

else a(i) = ((sgahet(i) + sgaheb(i>>/2. )*prostr(7,i) y(i) " (prostr(7,i>/3, )*((sgaheb(i) + 2.»sgahet(i ) ) >

+ /(sgahet(i) + sgaheb(i)) th = th - prostr(7,i ) ydl<i ) = th + y(i ) goto 15

endi f ELSE

if (sgahet(i) .le. 0.) then if (sgahed(i) .le. 0.) then

if (sgaheb(i) .le. 0.) then th e th - prostr(7,i) goto 16

else x = abs( sgahew( 1 )*thui) / <sgaheb(i)

+ + abs(sgahew(i )) ) aw( i ) = sgaheut i )*( thui - x) / 2. yw( i) =• (thw - x) / 3. th = th - prostr<7,i > ydwl(i ) = th + yw(i) goto 15

endi f else

x e abs(sgahet<i )*thd) / (sgahed(i) + + abs(sgahet(i )))

ad<i ) = sgahed<i>*(thd - x> / 2. yd( i ) = (thd - x) / 3.

th • th - thd yddl(i ) B th + yd( i)

98

aw<i ) = ((sgaheu(i) + sgaheb(i)) / 2.>*thu yw(i) = (thu / 3. )*<(sgahebCi ) + 2.«sgahew(1 )))

+ / (agahewfi) + sgaheb<i)> th = th - thu ydul(i ) = th + yu< i )

goto 15 end! f

else ad( i > = ((sgahet(i) + sgahed(i )) / 2.)*thd yd(i ) = (thd / 3.)*((sgahet<i> + 2,«sgahed(i ) ))

+ / <sgahet(i) + sgahed(i)) th = th - thd yddl( i ) « th + yd( i)

C au( i ) = Usgaheu(i) + Bgaheb(i)) / 2. )*thw yu(i) = (thui / 3.)*<(sgaheb(i ) + 2. *agaheu(i)))

+ / (sgahew(i ) + sgahebfi)) th = th - thui ydwl(I) = th + yu( i) goto 15

endi f ENDIF

15 CONTINUE C

If ((flagul .eq. 0) .or. (flagwl .eq. 2)) then po = po + a(i )

ap B ap + a(i )*ydl( i) at e at + a( i ) goto 16

else po = po + ad(i ) + aw(i) ap «= ap + ad( i )*yddl (1 ) ap =• ap + au( i )»ydiul< i ) at B at + ad(i > at « at + au( i )

endi f IB CONTINUE 20 CONTINUE

if ((ap .eq. 0.) .or. (at .eq. 0.)) then WRITE (•,150) WRITE (2,150)

150 F0RMAT(/,' **» No Pile is required. STOP. ***'/) po = 0.

goto 17 else endif yo • ap / at

17 CONTINUE RETURN END

99

SUBROUTINE urtsdi (nstadl,nstrat) C C C

INTEGER nstadl,nstrat COMMON /stress/ sgavtt<20),sgavet(20),5gahet(20),sgahtt{20), + sgavbt<20 ),sgaveb( 20),sgaheb(20),sgahtbf 20), + u(20) COMMON /staguil/ sgavdt ( 20 ), sgavedC 20 >, sgahed( 20 ), sgahtd( 20 ),

+ sgavuit(20),sgavew(20),sgahBw(20),sgahtu( 20)

C WRITE (2,99) WRITE (2,100) DO 50 i = l.nstrat if (sgahtd(i) .ne. 0.) then

WRITE (2,200) i,sgavtt(i ),sgavet(i ),sgahet(i ),sgahtt(i ), + sgavbt(i ),sgaveb(i ),sgaheb(i ),sgahtb(i)

WRITE (2,201) i,sgavdt(i ),sgaved(i),sgahed(i ),sgahtd(i) goto 49

else WRITE (2,200) i,sgavtt(i ),sgavet(i ),sgahet(i ),sgahtt(i ),

+ sgavbt(i ),sgaveb(1),sgaheb(i),sgahtb(i) goto 49

endi f 49 CONTINUE 50 CONTINUE 99 FORMAT (' TOTAL AND EFFECTIVE,

+ STRESSES (ACTIVE)'/) 100 FORMAT (/,IX,1STR . ' ,GX,'TVS.(T )',6X,'EVS.(T )*,6X,'EHS.(T )',BX,

+'THS.{T )',BX,'TVS.(B )',BX,'EVS.(B )',6X,'EHS.(B >',GX,'THS.< B)'/) 200 FORMAT <I3.3X.8F13.2> 201 FORMAT (13,1(* )',4F13.2 )

RETURN END

C C C

SUBROUTINE urtpsd (fstbdl,nstrat)

INTEGER fstbdl,nstrat COMMON /pastrd/ sgpvtt(20),sgpvet(20 ),sgphet(20 ), sgphtt(20 ), + sgpvbt(20 ),sgpveb(20 ),sgpheb(20 ),sgphtb(20 ), + up(20) COMMON /stpgul/ sgpvdt(20),sgpved(20),sgphed(20 ),sgphtd(20), + sgpvut (20), sgpveui( 20 ), sgpheu< 20 ), sgphtw< 20 )

WRITE (2,99) WRITE (2,100)

100

j a nstrat - fstbdl + 1 DO 50 k - l,j i = fstbdl + k - 1 If (sgphtd(i) ,ne. 0.) then

WRITE (2,200) i,sgpvtt(i ),sgpvet(i ),sgphet(i ),sgphtt(i ), + sgpvbt(i ), sgpveb(i ),sgphebC1 ),sgphtb(i)

WRITE (2,201) i,sgpvdt(i ),sgpved(i ),sgphed(i),sgphtd(i) goto 49

else WRITE (2,200) i,sgpvtt(i ),sgpvet<i ),sgphet(i ),agphtt(i ),

+ sgpvbt< i ),egpveb(1),sgpheb(i ),sgphtb< i ) goto 49

endif 49 CONTINUE 50 CONTINUE

WRITE (2,202) 99 FORMAT (///' TOTAL AND EFFECT, + IVE STRESSES (PASSIVE )'/)

100 FORMAT (/,IX,'STR. ',6X, 'TVS.(T )1,6X,'EUS.(T ) •,6X,'EHS.(T )',BX, +1THS.(T )',EX,•TVS.(B )',6X,1EVS.(B ) •,GX,'EHS.(B )',6X,'THS.(B )'/ )

200 FORMAT (13,3X,8F13.2 ) 201 FORMAT (13,'(* )',4F13.2 ) 202 FORMAT (//,' (») Total and effective stresses at GWTL'//)

RETURN END

C SUBROUTINE locgut (k,fstbdl,flagut,thu,thd,qw )

C C Locate 6WT level in front of the sheet pile C

INTEGER fstbdl,flagutfflag REAL ddl,gut1,thtp,thu,thd COMMON /propet/ prostr(7,20) COMMON /levels/ DDL,GWTL

C uuw = B2.4 if (k .eq. fstbdl) then

thtp = 0. flag = 0

goto 15 else

goto 15 endi f

15 continue locutl - DDL - GWTL IF (locutl .eq. 0. ) THEN

flagut * 0 goto 17

ELSE if (locutl ,gt. 0.) then

qu = locwtl«uuw

101

flagwt = 1 goto 17

else thtp « thtp + prostr(7,k) dthp « abs(locuitl) - thtp

If (dthp .ge. 0.) then qui = 0. flagwt = 1 goto 17

else if ((abs(locwtl) .gt. thtp) .or. (flag .eq. 2)) then

qui = 0.

flagwt = 1 goto 17

else thw = thtp - abs<locwtl) thd = prostr(7,k) - thw flagwt = 2 flag = 2 goto 17

endi f endif

endif

ENDIF 17 CONTINUE

RETURN END

C SUBROUTINE sigmap (i,fstbdl,flagwt,qw,flagin )

C C Calculate total and effective stresses due to passive presssure C

INTEGER fstbdl,flagwt,flagIn REAL sq,qw, soiluui,thw COMMON /propet/ prostr(7,20) COMMON /pastrd/ sgpvtt(20),sgpvet(20),sgphet(20),sgphtt(20), + sgpvbt(20),sgpveb(20),sgpheb(20 ),sgphtb(20), + up(20)

C uwu = B2.4 if ((flagwt .eq. 1) .and. (qw .ne. 0.)) then

soiluw • proatr(2,i) if (i .eq. fstbdl) then

up(i) = uww*prostr(7,i ) + qw goto 14

else up(i ) • uww»prostr( 7,1) goto 14

endi f else

if ((flagwt .eq. 1) .and. (flagin .eq. 1)) then

102

soiluw = prostr(l,i) up{ i) e 0. goto 14

else soiluw = prostr(2,i) up(i) = uww«prostr<7,i) goto 14

endl f endi f

C 14 sq * sqrt(prostr<6,1 ))

C IF (i .eq. fstbdl) THEN

SQPvtt(i )=qw

sgpvet(i )=sgpvtt(i ) - qu sgphet ( i )=,prostr< G, i )*sgpvet ( i ) + 2#prostr(4,i )*sq sgphtt<i )»sgphet<i ) + qw

C 15 sgpvbt(i)=sgpvtt(1> + soiluw«pro5tr<7,i )

sgpveb(i )=sgpvbt(1 ) - up(i ) sgpheb( i )»=prostr( 5,1 >*sgpveb( i ) + 2*prostr(4, i )*sq sgphtb(i)<=sgpheb(i ) + prostr<6,i )*up(A ) goto 26

ELSE sgpvtt(i )=sgpvbt(i-1) sgpvet(i>=sgpvtt<i ) - up(i-l) sgphet(i )=prostr(6,1 )*sgpvet(i) + 2*prostr(4,i )*sq agphtt(i )=sgphet<i ) + prostHG,i )*up<i-1)

C up(i )=up(i-1 ) + up(i>

sgpvbt(i)=sgpvbt<i-1> + soiluw»prostr(7,i ) sgpveb<i )=sgpvbt(i ) - up(i) sgphebti )=prostr(B,i )*sgpveb(i ) + 2»prostr<4,i )*sq sgphtb<i )=sgpheb(i ) + prostrCG,i )*up(i )

ENDIF 2G RETURN

END C

SUBROUTINE sgniap (i , fstbdl,flagwt,thw,thd) C C Calculate total and effective stresses due to passive presssure C considering arbitrary GWT level below dredge line C

INTEGER fstbdl,flagwt REAL thd,thw,sq,soiluw COMMON /propet/ prostr(7,20) COMMON /pastrd/ sgpvtt(20 ),sgpvet<20),sgphet(20),sgphtt(20>, + sgpvbt(20 ),sgpveb(20),sgpheb< 20 ),sgphtb(20 ), + up< 20) COMMON /stpgwl/ sgpvdt(20),sgpved(20),sgphed<20),sgphtd(20), + sgpvwt(20),sgpvew(20),sgphew< 20 >,sgphtu(20)

uuw = 62.4 sq = sqrt<prostrtE,i)) IF < i .eq. fatbdl ) THEN

sgpvtt(1)"0. sgpvet C1)«*sgpvtt( i > sgphet(i )=prostr(6,i )*sgpvet( i) + 2»prostr(4,i )»sq sgphtt(i )=sgphet(i)

soiluui = prostr(l,i)

agpvdt(i )=sgpvtt(i ) + soiluw*thd

sgpved( i )«5gpvdt(i )

5gphed<i )=prostr(G,i )*sgpved(i ) + 2*prostr(4, i )«sq sgphtd(i )«sgphed(i)

sgpvwt( i )=sgpvdt(i ) sgpvew(i )Bsgpvut(i ) sgpheu<i )=prostr(B,i )*sgpveu(i ) + 2*prostr(4,i )*sq sgphtw< i )=sgpheuj( i )

soiluu = prostr<2,i>

sgpvbt(i )=sgpvwt< i ) + solluw«thui up( i )euuiw*thu>

sgpveb(1 )=sgpvbt<i> - up(i)

sgpheb(1 )=prosir(B,i>«sgpvob(i ) + 2*prostr<4,1 )*sq sgphtb( 1 )=sgpheb( 1 ) + prostH 6, i )*up( i > goto 16

ELSE sgpvtt(i )=sgpvbt<1-1 ) sgpvet{i )-sgpvtt(1 ) sgphett1 )=prostr(6,1 )*sgpvet(1) + 2»prostr(4,i )*sq sgphtt(1 )=sgphet(i )

soiluui * prostr(l, i )

sgpvdt(i )=sgpvtt(1 ) + soiluui»thd 5Qpved(i ) -agpvdt(1 ) sgphed( i )=»prostr( 6, i )»sgpved< i ) + 2*prostr( 4, i )*sq sgphtd<1)=sgphed( 1)

sgpvut(1 )=sgpvdt(i ) sgpveuit 1 )=sgpvwt( i ) Bgpheut1)-prostr(G,i )*sgpveu(1 ) + 2«prostr(4,i )»aq sgphtwt 1 )=sgpheui< 1)

solium a prostr(2,i)

sgpvbt(1 )=sgpvdt(i ) + soiluw*thw

up( 1 )»uuiuj*thui

104

sgpveb(i )=sgpvbt<i ) - up(i) 5gpheb(i )=prostr(B,i )*sgpveb(i ) + 2*prostr(4,i )*sq sgphtb(1)=5gpheb(i* + prostr(6,i )*up(i )

ENDIF 16 RETURN

END C

SUBROUTINE quad*A,B,C,XRI,XI1,XR2,XI2,NP ) C C C

if (np .gt. 0) then OPEN (4,FILE=' A •• ROOTS. DAT', STATUS«=1 new' > WRITE (4,1000) goto 20

else goto 20

endif 20 IF ((A .ne. 0.) .or. <B .ne. 0.)) THEN

if (A .eq. 0.) then XRI = -C / B

if (np .gt. 0) WRITE (4,1002) A,B,C,XR1 elseif (B .eq. 0.) then

D = -C / A

if (D .It. 0. ) then XII = sqrt(-D) XI2 = -XII if (np .gt. 0) WRITE (4,1003) A,B,C,XI1,XI2

elseif (D .eq. 0.) then XRI = 0. XR2 =0.

if (np .gt. 0) WRITE (4,1002) A,B,C,XR1,XR2 else

XRI - sqrt(D) XR2 = -XRI if (np .gt. 0) WRITE (4,1002) A,B,C,XR1,XR2

endi f ELSE

D = B**2 - 4.*A*C A2 = 2.*A XRI = -B / A2 XR2 = XRi

if (D .It. 0. ) then XII » sqrt (-D > / A2 XI2 = -XII if (np .gt. 0) WRITE (4,1004) A,B,C,XRI,XI1,XR2,XI2

elseif (D .eq. 0.) then if (np .gt. 0) WRITE (4,1002) A,B,C,XRI,XR2

else E - sqrt (D) / A2 XRI = XRI + E

105

XR2 = XR2 - E if <np .gt. 0) WRITE (4,1002) A,B,C,XR1,XR2

endi f endi f

ENDIF 1000 FORMAT (' SOLUTION OF QUADRATIC EQUATION'//

+5X,'A1,10X,'B',10X,'C',15X,'XI',20X,'X2'/ +3BX,'REAL',8X,'IMG',7X, 'REAL',8X,'IMS'/)

1002 FORMAT <1X,4E11.4,11X,E11.4) 1003 FORMAT <1X,3E11.4,2(11X,E11.4>) 1004 FORMAT (1X.7E11.4)

C CLOSE (4) RETURN END

C SUBROUTINE MAXMO (kk.nstadl,nstbdl,fstbdl,po,yo,dz,r>max )

C C C

INTEGER kk.nstadl,nstbdl REAL po, yo, mnax ,tol,JJ,lah,dz,tshl,tBhh DIMENSION 1(20,20 ), t sh(20 ) COMMON /propet/ prostr(7,20> COMMON /netprs/ s<20) rl «= po rZ = yo ahd = po tol = 0.001 Jj = 0.001 DO 100 i = 1, kk k • nstadl + i if (i .eq. 1) then

rl •= rl

r2 B r2 goto 120

else rl = rl - s(k-1 )*prostr(7,k-1 ) r2 = r2 + prostr(7,k-1 ) goto 120

endi f 120 CONTINUE

if (i .eq. kk) then tsh(k) = dz

goto 125 else

tsh(k) = prostr<7,k) goto 125

endi f 125 IF < s(k > .It. 0. ) THEN

shd 3 ahd - tsh(k)*s(k)

106

goto 210 ELSE

shd = shd - tsh(k)*5(k) If (abs(shd) .eq. tol) then

thf = tsh(k)

goto 220 else

if (shd .It. 0.) then thf = rl / s(k)

goto 220 else

goto 210 endi f

endi f ENDIF

210 CONTINUE 100 CONTINUE 220 CONTINUE

if (k .eq. fstbdl) then lah = 0.

goto 316 else

goto 212 endif

212 n = 0 DO 300 J = l,i-l m « nstadl + j + 1 n = i - 1

if (j .eq. n) then Kj,i) = prostr(7,m-l) / 2. goto 315

else l(J,i) = prostr<7,m-1 ) + l(j,i-l) goto 215

endi f 215 CONTINUE 300 CONTINUE 315 CONTINUE

m = 0 lah = 0.

DO 350 j = 1,i-1 m = nstadl + j lah = lah + 1<j , i )*s(n )*prostr<7,n)

350 CONTINUE 316 CONTINUE

mmax • thf»rl + po»rZ - lah - s<k)«thf«*2 / 2.

RETURN END

REFERENCES

Cernica, J. N. (1982), Geotechnical Engineering, Holt, Rinehart and Winston, New York.

Gere, J. M. and Timoshenko, S. P. (1984), Mechanics of Materials, Brooks/Cole Engineering Division, Monterrey, California.

Head, J. M. and Wynne, C. P. (1985). Designing Retaining Walls Embedded in Stiff Clay, Ground Engineering, Vol.18, No.3, pp.30-33.

Teng, W. C. (1962), Foundation Design, Prentice-Hall, New Jersey

United States Steel (1969), Steel Sheet Piling Design Manual.

107