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CANTILEVER SHEET PILE ANALYSIS FOR STRATIFIEDCOHESIVE SOIL DEPOSITS (COMPUTER PROGRAM, SPILE)
Item Type text; Thesis-Reproduction (electronic)
Authors Ibarra, German A., 1959-
Publisher The University of Arizona.
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Cantilever sheet pile analysis for stratified cohesive soil deposits
Ibarra Encinas, German Alberto, M.S.
The University of Arizona, 1987
Copyright ©1987 by Ibarra Encinas, German Alberto. All rights reserved.
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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