interactive design of braced excavations … personal computer program (called movex) has been...
TRANSCRIPT
INTERACTIVE DESIGN OF BRACED EXCAVATIONS
by
Sybil Elizabeth Hatch Goessling
Thesis submitted to the Faculty ofVirginia Polytechnic Institute and State University
in partial fulfillment of the requirementsfor the degree of
MASTER OF SCIENCE
in
Civil Engineering
APPROVED:
G. W. Clouah, Chairman
J. ä. Duncan
;/R.D. Krebs
December, 1985
Blacksburg, Virginia
INTERACTIVE DESIGN OF BRACED EXCAVATIONS
by
Sybil Elizabeth Hatch Goessling
Committee Chairman: G. Wayne CloughCivil Engineering
(ABSTRACT)
Construction of braced excavations in major urban areas
has increased over the last few decades. It is a major
concern of the designer to limit ground movement around an
excavation in order to prevent damage to adjacent structures,
utilities and roads. Existing design methods can accurately
predict ground and wall movement of a braced excavation, but
the calculations become complex when multiple construction
stages are considered, or if different design schemes are
compared.
This thesis presents an interactive personal computer
program (called MOVEX) to facilitate braced excavation
design. Using input variables for wall stiffness, strut
stiffness, and strut spacing, MOVEX includes four design
options that allow the designer to adjust the variables in
order to develop the optimal bracing design.
Details of the design theory, input and output data, and
a user's guide are included in this thesis. In addition, the
settlement of sand due to pile driving was investigated. A
predictive method is presented that relates sand densifica-
tion to the ground acceleration caused by pile driving.
ACKNOWLEDGEMENTS
My deepest and most sincere appreciation goes to
Professor G. Wayne Clough, a very stimulating instructor, and
a most generous, insightful, ana considerate advisor.
help and support I could not have done it.
-111
TABLE OF CONTENTS
äss1. INTRODUCTION .................... 1
2. EARTH PRESSURES AND THE FACTOR OF SAFETY ...... 3
2.1 Introduction ................. 3
2.2 Earth Pressures Acting On Excavations ..... 3
2.3 Calculation of Strut Loads .......... 10
2.4 Calculation of Bending Moment in Wall ..... 10
2.5 Factor of Safety Against Basal Heave ..... 12
2.6 Trends of the Factor of Safety With Depth . . . 19
2.7 Effects of Anisotropy on the Factor of Safety . 20
3. MOVEMENTS OF EXCAVATION SUPPORT SYSTEMS IN CLAY . . 24
3.1 Introduction ................. 24
3.2 Wall Movements and The Factor of Safety .... 24
3.2.1 Effect of Strut Stiffness ....... 31
3.2.2 Effect of Depth to a Firm Layer .... 34
3.2.3 Effect of Excavation Width ....... 37
3.3 Maximum Lateral Wall Movement ......... 37
3.4 Distribution of Ground Movement ........ 37
4. THE PROGRAM MOVEX ................. 42
4.1 Introduction ................. 42
4.2 Description of Input for MOVEX ........ 42
4.2.1 User Options .............. 43
4.2.1.1 Movement Option (MOPT) .... 43
4.2.1.2 Design Option (NOPT) ..... 43
4.2.2 Soil Data ............... 46
iv
TABLE OF CONTENTS (con't.)
4.2.3 Water Table Data ............ 47
4.2.4 Firm Layer Data ............ 47
4.2.5 Excavation Geometry .......... 48
4.2.5.1 Wall Stiffness ........ 48
4.2.5.2 Strut Stiffness ........ 50
4.2.5.3 Strut Spacing ......... 50
4.2.5.4 Maximum Wall Movement ..... 50
4.3 Suggestions for the Use of MOVEX ....... 50
4.4 Interactive Design .............. 53
5. SETTLBMBNT OF SAND DUB TO PILB DRIVING ....... 54
5.1 Introduction ................. 54
5.2 Vibration From Pile Driving .......... 61
5.3 Settlement of Sand due to Pile Driving .... 63
6. SUMMARY AND CONCLUSIONS .............. 70
BIBLIOGRAPHY ................‘ ...... 73
Appendix A. MOVEX Users' Guide ........ . . . . 77
Appendix B. Example Problem .............. 95
Appendix C. MOVEX Program Listing ........... 103
Appendix D. List of Variables ............. 128
Appendix B. Apparent Pressure Program ......... 134
Vita .......................... 139
V
LIST OF FIGURES
Number Page2.1 Failure Mechanism of Braced Walls ......... 4
2.2 Depth of Influence ................. 6
2.3 Apparent Pressure Diagrams ............. 8
2.4 Wall and Strut Geometry .............. 11
2.5 Factor of Safety Against Basal Heave ........ 14
2.6 Bearing Capacity Factor .............. 16
2.7 Factor of Safety for Layered Soil Profile ..... 17
2.8 Principle Stress Reorientation 21
3.1 General Movement Trends Around Braced Cuts ..... 26
3.2 Relationship between Factor of Safety andWall Movement ................... 27
3.3 Relationship between Factor of Safety, SystemStiffness, and Wall Movement ............ 30
3.4 Effect of Strut Stiffness ............. 32
3.5 Preload versus Strut Stiffness ........... 33
3.6 Effective versus Ideal Strut Stiffness ....... 35
3.7 Effect of Depth to Firm Layer ........... 36
3.8 Effect of Excavation Width ............. 38
3.9 Distribution of Vertical Ground Movement ...... 40
3.10 Distribution of Horizontal Ground Movement ..... 41
5.1 Acceleration versus Distance from the Pile ..... 62
5.2 Strain versus Acceleration ............. 65
5.3 Strain versus Distance from Pile, Loose Sands . . . 66
5.4 Strain versus Distance from Pile, Medium Sands . . . 67
5.5 Example of Settlement Calculations ......... 68
. vi
LIST OF FIGURES (con't)
Number Rage
A.1 Excavation Geometry ................ 85
B.l Example Problem — Soil Data ............ 97
B.2 Example Problem — Strut Geometry .......... 98
B.3 Example Problem — Measured Movements ........ 102
vii
LIST OF TABLES
äumbgr Page
3.1 Factors Affecting Movements Around Braced Cuts . . . 25
4.1 Input, Output, and Change Data for MOVEX ...... 44
4.2 Typical Wall Stiffness Ranges ........... 49
5.1 Case Histories of Vibration and SettlementIn Sand ...................... 56
A.l Input, Output, and Change Data for MOVEX ...... 90
B.1 Example Problem — Input Data ............ 99
B.2 Example Problem - Computer Output ......... 100
viii
CHAPTER 1
INTRODUCTION
Construction of deep excavations in major urban areas
has increased over the last few decades. New buildings
utilize more underground space for parking and other
facilities. Mass transit has moved underground to alleviate
above-ground traffic and congestion. The rehabilitation of
deteriorating sewer, storm, and water systems sometimes
requires excavations. Furthermore, sites underlain with poor
or troublesome soils that were previously overlooked are
being developed now.
Often, excavations are made directly adjacent to
existing structures and utilities. Excessive ground
deformation around the excavation has the potential of
causing damage: buildings can settle, pavement can crack, and
utility lines can break. Legal complications associated with
this damage add unanticipated costs to the project.
Formerly, the design of an excavation support system was
based solely on stability criteria: simply design the struts
and wall to withstand lateral earth pressures. Now, although
stability is still important, limiting ground movement has
become one of the primary concerns of bracing design.
Our understanding of braced excavation behavior has
expanded over the last decade. Routine use of the
inclinometer to monitor lateral wall and ground movement has
1
2
increased the amount of data available for analyses. These
data, in combination with finite element studies, have made
possible an accurate prediction of ground movement. In the
design method developed by Mana and Clough (1981), lateral
wall movement is related to the factor of safety against
basal heave, and such factors as bracing stiffness, soil
stiffness, and excavation geometry. However, some engineers
are still reluctant to use this method because the
calculations are more involved than those calculations based
on stability alone. To alleviate this problem, an
interactive personal computer program (called MOVEX) has been
written as part of this thesis for the design of bracing
systems to limit ground movement.
The program is designed for utility and ease—of—use to
the engineer. The ground deformations for each excavation
stage are calculated for almost any soil conditions and
excavation geometrya Or, given a maximum allowable ground
movement, the program will calculate the required bracing
stiffness to limit movement to that value. In addition, an
interactive design section is included to enable the user to
arrive at the optimum bracing design with the least effort.
Details of the calculations of earth pressures, the
factor of safety against basal heave, ground deformation,
and other quantities, descriptions of the computer input and
output, and helpful hints for the effective use of MOVEX are
included in the following chapters.
CHAPTER 2
EARTH PRESSURES AND THE FACTOR OF SAFETY
2.1 Intrgguggign
This chapter describes the state of stress and the
strength mobilized in the soil around an excavation. Two
major topics are discussed: earth pressures behind braced
excavations, and the factor of safety against basal heave.
2-2 äarshl-*.re.¤äs;.:.e.s.<LmAt°Ithas been found through field measurements of loads
on struts and excavation walls that the magnitude and
distribution of earth pressures acting on braced or tied-
back wall support systems differ from those predicted by
classical earth pressure theories. Rankine pressure
distribution is triangular whereas the measured pressures
on the struts and wall tend to be trapezoidal or
rectangular. Rankine theory predicts a smaller total
magnitude of earth pressures than field measurements
indicate.
Terzaghi addressed these discrepancies in 1936, and
proposed an idealized failure mechanism in braced
excavations, which is shown in Figure 2.1. In Rankine
theory, the wall rotates about the toe, which puts the
entire soil mass behind the excavation in an active state
of stress. In braced excavations, the toe of the wall
rotates about a hinge at the top of the wall created by the
3
4
rotationabout toe{‘
I\‘\
‘~ful|y active
I
Rcnkineearth pressure .
(a) Active State of Stress
II at rest
InIII ‘\active
x_/Parabane
mmtmn pressure distributionabout top
(b) Idealized Stress for Excavations
FIGURE 2.1 — Failure Mechanism of Braced Walls(after Terzaghi and Peck, 1967)
5
first strut. Only the soil near the toe experiences enough
deformation to mobilize the active state, with the
remaining soil mass in an at—rest state of stress. As a
result, the earth pressures in the upper section of the
wall will be larger than those in a fully active Rankine
state. The pressure distribution behind a braced wall
using Terzaghi's idealized failure mechanism is roughly
parabo1ically—shaped.
Bjerrum et al. (1972) compiled earth pressure data
from eleven braced excavation case histories. They conclude
that the magnitude of the total earth pressure on a braced
cut is equal to that predicted by earth pressure theory
only if the earth pressure is accounted for over the full
depth of soil that is straining, (Do in Figure 2.2). They
also found that the distribution of earth pressures depends
on the amount of movement in the soil below the excavation
relative to the movements in the struts. If there is
excessive soil deformation below the excavation, the earth
pressures will be transferred up into the stiffer struts,
resulting in higher measured strut loads.
The above findings explain why a straightforward
application of classical earth pressure theory does not
accurately model braced excavation .loading. Empirical
earth pressure diagrams based on extensive field
measurements and theory were developed and refined by
Terzaghi and Peck (1967), Peck (1969), and Peck, Hanson,
6
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7
and Thornburn (1974) for calculating strut loads. The
most recent versions of the diagrams, shown in Figure 2.3,
represent envelopes drawn around measured strut loads, and
are called apparent pressure diagrams. The use of apparent
pressure diagrams enables the designer to predict the
maximum strut load that any given strut will experience in a
braced excavation. The maximum bending moment in the wall
may also be determined from these diagrams, although the
magnitude of the pressures is reduced to account for arching.
The apparent pressure diagrams represent a statistical
maximum load, not the actual pressure distribution
acting on the wall and struts.
The apparent pressure diagram for sand gives a
resultant force on the wall as
pa = 0.65kaö 'H2 (2.1)
where ka = coefficient of active earth pressure
= tanz (45 - 6/2)X' = effective unit weight of the soil
H = total height of wall
whereas classical Rankine earth pressure theory based on a
triangular pressure distribution gives the resultant as
pa = 1/2 ka 6* H2 (2.2)
Comparing the two resultants shows that the Peck diagram
for sand predicts a value 1.3 times that of classical earth
pressure theory.
6
HQZO HQJQO
=•>«
ä 2* LJE
6HQZOH 9°O H QZO gg
<DE—<$*2I >„ ~·¤>= c L46 ° ää«{» ^ ‘“ä6 E M
TSN8EDE(DO‘¤ EC
E SV
¤é’cn2O 3
I H|
9Thereare two possible apparent pressure diagrams for
clay. Figure 2.3b corresponds to the apparent pressure for
stiff-fissured clay, and Figure 2.3c is used for soft to
medium clay. Peck defines two excavation stability numbers
to determine which diagram to use:
NSu
Nb = lf- (2.3b)ub
where su = average undrained shear strengthadjacent to the cut
sub = average undrained shear strengthbelow the cut
Figure 2.3b is used if N is less than or equal to 4,
whereas Figure 2.3c is used if N is greater than 4,
provided that Nb does not exceed 7. No recommendations
were given for the case in which Nb is greater than 7,
except to say that basal instability is possible, and strut
loads as well as deformations are likely to be larger than
predicted from the conventional case (Figure 2.3b). The
reason for this is provided by the concept of Bjerrum,
et al. (1972).
For soft to medium clays, Peck's diagrams predict a
resultant of the earth pressure as
Pa = 0.875U'H2 — 3.5suH (2.4)
whereas Rankine theory for soft to medium clays gives the
resultant as
10
Pa = 1/2 Ö 32- 2suH (2.5)
Thus, Peck's empirical diagrams for clays predict a
resultant 1.75 times that of classical earth pressure
theory.
The pressure diagrams in Figure 2.3 can be used as
shown for simple problems of one soil layer. But to
account for more complex factors, such as surcharge next to
the excavation and layered soils, Rankine theory can be
used to calculate resultants of the earth pressure in each
layer, which are then multiplied by the appropriate factor
(1.3 for sand, or 1.75 for clay). The sum of these
resultants is then distributed over the height of the
excavation into apparent pressure diagrams similar in shape
to those in Figure 2.3.
2.3 Cglgulatign Q;ßtggtTo
determine the strut loads, the apparent pressure
diagram is divided into tributary areas equaling half the
vertical distance to the adjacent sets of horizontal
struts, and half the horizontal distance to the adjacent
vertical struts, shown as the dimensions'aJ and 's' in
Figure 2.4. The total strut load equals the apparent
pressure times the tributary lengths, 'a' and 'sk
2-4 9.£.§.B.L.9Bd'¤ Ls.tHm¤ inlflThe bending moment of the wall can also be found from
~
12
the apparent pressure diagrams by considering the wall as a
continuous beam supported by the struts. To account for
arching between the soil and the more rigid structural
supports, Peck, Hanson, and Thornburn (1974) recommend
using a design pressure of two-thirds of the apparent earth
pressure. The apparent earth pressure is treated as a
uniformly distributed load (w) in the beam equation:
M = 1/8 w L2 for a l—span (i.e. 2—strut) wall (2.6a)
M = 1/10 w L2 for a 3—span wall, and (2.6b)
M = 1/12 w L2 for more than 4 spans. (2.6c)
where L = longest span in the vertical directionw = uniformly distributed loadM = bending moment in a beam
The units for the bending moment thus calculated are
length-force per unit length of wall. In addition, if the
first strut is placed below the top of the excavation, the
cantilever moment about the top strut is calculated by the
formula
M = 1/2 w L2 (2.6d)
The maximum bending moment is
chosen from these two for structural design.
2-5 ;as$.o.1:9.fSaf.s.t.!A9.ai1;§1;ä§.al.H.e.a.v.e
Terzaghi (1943) compared basal heave of an
excavation in clay to general shear failure of a shallow
footing. The soil mass adjacent to the excavation acts
like a uniform load applied to a horizontal plane through
13
the bottom of the cut. If the load nears or exceeds the
bearing capacity of the soil below this plane, the adjacent
soil rotates down and in toward the excavation, producing
both basal heave in the the bottom, and settlement around
the excavation.
Terzaghi (1943) showed that basal heave in an
excavation in dry sand due to shear failure of the base
soil is independent of excavation depth, and depends only
on the sand's friction angle, Ö. The factor of safety
ranges from about 8 for d = 30°, to about 50 for d = 40°.
Thus, base instability is not a problem in dry sands. In
wet sands, however, bottom heave can be caused by the
upward flow of water that causes piping, or by hydrostatic
pressure in an aquifer below the excavation bottom. This
is a special problem, beyond the scope of this thesis.
For relatively wide and shallow excavations in
homogeneous soft clay, the factor of safety against basal
heave can be calculated using Terzaghi's original equation
(Figure 2.5). This can be written more conveniently as
N s LFS S ‘x’äEz‘?E;;gH (2-7)
where N = bearing capacity factorE = the smaller of D or 0.7B.
sub = average undrained shear strengthbelow the excavation
sus = average undrained shear strengthadjacent to excavation
It can be seen that (NC subL) is a bearing capacity term,
14
HL17
O.7 BH
O.7B
Factor of _ L _ 5.7 SuS¤f@ty H ts-S., /0.7B
‘H
L+5°
Factor of _ __L_ _ 5.7s„° Safety H Su / D·
FIGURE 2.5 — Factor of Safety Against Basal Heave(from Terzaghi, 1943)
15
GHL) is the weight of the soil mass adjacent to the
excavation, and (sus H) is the resistance to sliding
mobilized on the vertical failure plane.
Bjerrum and Eide (1956) studied the basal stability
of deep, narrow excavations in deep, soft clay. They also
expressed a factor of safety against basal heave in terms
of the bearing capacity of the soil below the excavation,
but assumed a different shape of yielding zone than
Terzaghi. They showed that the bearing capacity factor,
NC, is a function of the excavation geometry, as shown in
Figure 2.6.I
Equation 2.7 can be further modified to include a
layered soil profile of clay and a surcharge load adjacent
to the excavation. The factor of safety then becomes
N is LFS =iiä'E'l'§'E'§$Y§ä;'HY'‘‘‘‘‘‘‘‘‘‘‘ (*8)where the terms are illustrated in Figure 2.7.
Several details about the calculation of individual
terms in equation 2.8 are worth mentioning. First, when
the shear strength of the clay increases with depth, the
shear strength at middepth in the layer is found, which is
used as the average shear strength throughout the layer.
Second, for more than one clay layer, the term sush is
summed over each layer to obtain a total resistance to
sliding on the vertical failure plane. Similarly, the term
sub is a sum of the average clay strengths below the base
16”
L=L qth |()/ an _Sq¤¤r•(8/L=I)__8·‘
==” 6 Igéäll nn-
Z ?VlS1·;·1¤/¤·<>> II·i:¤·4.o ¤ 2 6 4 6
H/6.Foctor of
SofetyBottomHeove Anolysis for Deep Excovotions (H/B >t)—
BJERRUM 6 EIDE 0956)
FIGURE 2.6 - Bearing Capacity Factor(from Bjerrum and Eide, 1956)
17
ET X¤1$“• E
EH Z(S~«·E*) L| 26 x·»«>
L Lhß Xsyguö
FIGURE 2.7 — Factor of Safety for Layered Soils
18
of the excavation. Finally, the unit weight term is a
weighted average of all the total unit weights of the
soil layers adjacent to the excavation.
Theoretically, the bearing capacity factor, NC, will
be smaller for a long, narrow excavation than that for a
wide, short one. Skempton (1951) proposed the following
equation for the bearing capacity factor for a shallow
footing on clay.
NC = 5 (l + 0.2 E )(l + 0.2 E ) (2.9)B L
where D = depth of the footingB = width of the footingL = length of the footing
This equation can also be used in braced excavation design
to include the effects of excavation length. The depth, D,
is zero for excavations. The equation then becomes
NC = 5 (1 + 0.2 E ) (2.10)L
where B = width of the excavationL = length of the excavation
Terzaghi's factor of safety was found to be a useful
index to the movements around braced excavations (Mana and
Clough, 1981) for a wide variety of soils and excavations.
The factor of safety against basal heave is only an index
however, because it neglects the effect of any soil-
structure interaction, bracing stiffness, or wall
embedment below the excavation bottom. Mana and Clough
19
(1981) have shown that embedment of a flexible excavation
wall (such as a sheet pile system) below the base of the
excavation has little to no influence on the potential for
basal heave and subsequent ground movement. The embedment
of stiffer walls may have some effect on limiting ground
movement, however, but it is conservative to neglect it.
2•6 .'§!.L@9.§§.h§L§.Q§9L9iS§E$!H.i$.hD£2§h
For a deep clay layer, the factor of safety tends
to decrease as the excavation proceeds downward. If a firm
layer exists below the excavation, the factor of safety
will also decrease as the excavation proceeds until the
effect of the firm layer is felt H„e., when D'is less than
0.7B in Figure 2.5). Then, because the failure circle
becomes smaller, the term KH L decreases. However, the
resistance to sliding on the vertical failure surface
remains the same or increases. The denominator of the
factor of safety equation (weight minus side resistance)
becomes smaller, so the factor of safety tends to increase
as the excavation proceeds. In fact, if the excavation
bottoms out in the firm layer, the factor of safety is
infinite. In an excavation where a firm layer exists, the
minimum factor of safety will occur before the factor of
safety value is influenced by the firm layer. Since the
minimum factor of safety governs ground movements around an
excavation (Mana and Clough, 1981), it is this minimum
20
value that should be used for all subsequent excavation
stages.
· 2-7 Jsséßft 9;9n;.h.eLas.t.Qr9f.$.aJ_2ftAll clays are to some degree anisotropic. The
undrained shear strength of an anisotropic clay changes as
the major principal stress direction changes. For most
natural clays, the undrained shear strength is a maximum
when the principal stress is vertical, and decreases as the
stress direction approaches horizontal. „
Figure 2.8 shows the principle stress reorientation
that occurs along the failure plane around an excavation.
It can be seen that for the same excavation, the shear
strength mobilized in an isotropic clay will be greater
than that in an anisotropic clay. Furthermore, the factor
of safety against basal heave will be less in anisotropic
clay than in isotropic clay. The conventional factor of
safety against basal heave analysis in Section 2J5does not
account for anisotropy. The use of equation 2.7 for an
excavation in anisotropic clay will lead to an
overestimation of the factor of safety against basal heave.
Clough and Hansen (1981) presented a technique which
modifies the basal heave analysis to account for
anisotropy. First, an anisotropic bearing capacity factor
NQ, developed by Davis and Christian (1971) for footings on
anisotropic clay, is substituted into Equation 2.7 to
2 1
‘
$u451
K5u9OQ
SuoV
Su45
FIGURE 2.8 - Principal Stress Reorientation(from Clough and Hansen, 1981)
22
account for the stress reorientation and anisotropy below
the base of the excavation. Second, the shear strength at
45°, su45, is used in the term for resistance to sliding on
the vertical plane in the denominator. The equation then
becomes·k
N S OLps = --——E--E-———-- (2.11)KH L ' Su45H
where N* = anisotropic bearing capacity factorE = the smaller of D'or 0.7B.H = height of the excavation _
suo = average undrained shear strength .for vertical major principal stress
su45 = average undrained shear strengthfor major principal stress at 45°
su45 can be more conveniently expressed in terms of suo and
sugo as su45 = 1/2 (suo + sugo). By defining the ratio
KS = sugo/suo, su45 can be expressed in terms of suo alone
as su45 = (1/2)su0(l + KS). Then, the factor of safety
equation for anisotropic clays becomes
*N s Lrs = -———-----—E--B9---—-———-- (2.12)KH L - (1/2)suo(l + KS)H
In order to evaluate the effect anisotropy has on
excavation behavior, Clough and Hansen (1981) expressed a
ratio between the factor of safety of anisotropic soils to
the factor of safety for isotropic soils. This ratio, R, is3N; ÖHL - suou
R = ——-— ' -———-——---—-——-————-—--- (2.13)NC ÜHL - (1/2)su0(l + KS)H
Several important conclusions were drawn by Clough and
· 23
Hansen (1981) about the behavior; of excavations in
anisotropic clay. First, the basal heave factor of safety
may be overestimated by as much as 50% in strongly
anisotropic clays, and 10% — 30% in moderately anisotropic
clays if conventional analyses are used. This may lead to
unconservative predictions of the ground movements around
the excavation. Second, the discrepancy between isotropic
and anisotropic behavior is greatest when the factor of
safety is at or below 1.4. Finally, if anisotropy is
incorporated into the factor of safety, then movement
calculations will be the same for the anisotropic and
isotropic cases.
CHAPTER 3
MOVEMENTS OF EXCAVATION SUPPORT SYSTEMS IN CLAY
3.1 Introdugtign
The amount of earth movement around a braced cut is
dependent upon many factors, some of which the designer can
control. Clough (1985) lists 24 major factors affecting
ground movement in Table 3.1. The engineer has direct
control over the stiffness and geometry of the struts, the
wall stiffness, required preloads, and structural
connections. Soil and groundwater conditions can be
reasonably estimated using adequate subsurface exploration,
and are included in the factor of safety calculations. Thus,
about two thirds of the factors in Table 3.1 can be directly
incorporated into the movement calculations. Proper
construction techniques and quality workmanship will further
minimize earth movement.
3-2 t .o£§_¢.x¤ft
Vectors in Figure 3.1 show the general trend of soil
movement down and in toward the excavation, which produces
both lateral bulging of the wall, and basal heave (if the
factor of safety is low). There is a strong correlation
between the movement of the excavation wall and the factor of
safety against basal heave, as shown in Figure 3.2. This
diagram (Mana and Clough, 1981) was developed using selected
case histories of excavations in soft clay and finite element
24
25
Table 3.1.· ggggggs Affggging ggggggggg Argung Brgged ggg;(from Clough, 1985)
1. Excavation depth2. Excavation geometry: width, shape, berms, symmetry3. Duration of excavation4. Construction around excavation5. Wall stiffness6. Tie—back or brace stiffness7. Support spacing8. Type of support connections9. Amount of preload10. Preload maintenance proceduresll. Soil strength, sensitivity, and stiffness12. Soil stratification13. Soil property Variation with loading direction14. Presence or absence of a rigid base below soil strata15. Initial groundwater level16. Groundwater control system .17. Wall permeability18. Potential of ground water movement19. Support system construction sequence20. Wall installation technique21. Surcharge behind wall22. Quality of workmanship23. Weather24. Site topography25. Consolidation due to dewatering
26
• Q‘*¤'l:IAYgl*""""""’ '
i ///// /{1/ /
///11/ 1 / ///1//
' IIl, a’ ;/«/
/1 1,/fqvfl
l'&’
'HOITWOQGYTGOUS CÜGY
FIGURE 3.1 - General Movement Trends Around Braced Cuts(from Clough, 1985)
27
LGro
I <21 I 1 rd >1{ ‘ “ä LL| u-I
I I E äE
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28
studies that closely modeled field conditions. In the
parametric studies, a wall stiffness equivalent to that of a
relatively flexible sheet pile wall was used. Two important
conditions are shown. First, if the factor of safety is
greater than about 2.5, the maximum wall movement will remain
essentially constant at about 0.5% of the excavation depth.
Second, if the factor of safety approaches 1.0 and basal
heave is imminent, wall movements can be very large. This
diagram also indicates that there will always be some wall
movement associated with an excavation in clay, regardless of
the soil properties, the excavation geometry, or bracing
stiffness.
Excavations wholly in sands behave differently than
those in clay. For instance, Sunami (1981) showed that
movements around excavations in sand are independent of the
factor of safety against basal heave and depend instead on
the relative density. Consequently, the theories presented
in this thesis should not be used for excavations through a
soil profile consisting of cohesionless soil.
As mentioned above, the finite element curve in Figure
3.2 was found by using the stiffness modulus of a flexible
sheet pile wall. To account for the influence of other wall
stiffnesses, a correction factor, dw, is applied to the
lateral wall movement in Figure 3.2. Field observations of
the performance of slurry walls (of stiffness anywhere from
29 ‘
twice to sixty times that of sheet pile walls (Clough and
Buchignani, 1980)) indicate that ground movements tend to be
less than those from sheet pile walls. A study of the wall
movements of thirteen slurry wall projects in the San
Francisco area, as well as finite element studies, led to an
expansion and refining of the curve shown in Figure 3.2. The
results of this study are shown in Figure·3.3 as a family of
curves relating factor of safety to the non-dimensionalized
wall movements and the system stiffness, EI/ Kwhgvg. The
terms are definedbelow:E
= modulus of elasticity of the wallI = moment of inertia of the wall
Kw = unit weight of waterhavg = average strut spacing
In Figure 3.3, the correction factor for wall stiffness,
<xw, is incorporated directly into the curves through the
system stiffness term. The curves show that for unstable
systems (factors of safety near 1.0), the system stiffness
plays a large role in controlling movements. For higher
factors of safety (3.0 or more), movements remain almost
constant regardless of the support stiffness.
Wall and ground movements depend not only on the factor
of safety against basal heave and wall stiffness, but also on
the bracing stiffness and the excavation geometry. Parametric
studies were performed by Mana (1978) in conjunction with the
factor of safety/movement relationship in Figure 3.2 to
determine the effects of strut or tie-back stiffness, depth
30
I
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to firm layer, and excavation width.These same factors can
be applied to the curves in Figure 3.3. The effects of the
parameters are discussed below.
3-2-1 §.tie.@séTheideal strut stiffness is defined as
Ki = Ö3-g-- (3.1)where A = strut cross—sectional area
E = strut modulus of elasticityL = strut length
The strut stiffness is nondimensionalized by dividing it by
the final height of the excavation and the unit weight of
water. Figure 3.4 illustrates the influence of ideal strut
stiffness on wall movements. A higher strut stiffness
results in smaller wall movements, but very high stiffnesses
show diminishing returns. The term de is a ratio of wall
movement for a particular strut stiffness to that of the
nondimensionalized strut stiffness of 133.3.
When defining the ideal strut stiffness, it is assumed
that all slack in the bracing system is eliminated with
proper jacking and preloading techniques. Any slack in the
system can lead to a sizable reduction in the actual strut
stiffness. The relationship between preload and the ratio of
effective to ideal strut stiffness (Ke/Ki) is shown in Figure
3.5 (O'Rourke, 1981) for excavations during the construction
of the Washington D.C. Metro. The effective stiffness Ke is
32
OOV
OON
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I—$ I “
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8 E 6•;I8
666‘°
5„. gg?
gO :s
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AI
MI
g
Eli!
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KI9
l—— °CO
N-
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IIIJo; Q)/ggsx,
33
I.0Q ••-•
XIX
::„-C 1/
n- ~•- ¢(D *0-
ev-Z.2
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3 3322¤> 0
70 90 IIO(aus) (405) (495)
Prelood, kips (kN)
FIGURE 3.5 - Preload versus Strut Stiffness(from O'Rourke, 1981)
34
defined as
Ke = ·Ä—1?·§•·· (3.2)
where P = average preloadA S = average apparent deformation
at each strut level
For this excavation, a preload of about half the strut design
load resulted in effective stiffnesses of about 0.5 to 0.75
of the ideal stiffness.
Figure 3.6 shows that the ratio Ke/Ki decreases as the
ideal strut stiffness increases. This is because ineffective
preloading and slack in the system (which tend to lower the
ratio Ke/Ki) is more predominant at larger values of Ki
(Hansen, 1981). The designer should be aware of the
possibility that the specified strut stiffness may not
necessarily be equal to the strut stiffness in the actual
excavation. It is recommended that a preload be required
during construction to reduce slack in the strut system. The
performance of the struts should then approach that shown in
Figure 3.4.
3•2-2 FäsfgfaepfhfgaäimhamxThe influence of the depth to a firm layer as a
function of the excavation height is illustrated in Figure
3.7. As explained in Section 2.5, the existence of a firm
layer near the base of the excavation limits the amount of
soil that can yield and cause ground and wall movement. It
35
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• macsureddisplocements
U)•
.U)ev ga)
: _.5 30.6 \j•; ••-
*6**5 •2
"’.
L: E ° gQ • ‘:::9 • Q
0 IO 4 20Ideal stiffness IO kN/m/m
FIGURE 3.6 — Effective versus Ideal Strut Stiffness(from Hanson, 1981)
I 36
I.O 0
N
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E 0.6HI 7
6; D„ • M0x.W0ll Detlection _l_go o M0x.Gr0und Settlement 7 _
OI.OH |.5H 2.0H 25H
DEPTH TO FIRM LAYER, D
FIGURE 3.7 - Effect of Depth to Firm Layer(from Mana and Clough, 1981)
37
appears that a depth to firm layer of more than twice the
excavation height has no influence on wall movement, whereas
a value of D less than 2H tends to lessen the amount of wall
deflection. The term O(D is defined in a similar manner to
ds : it is the ratio of the maximum wall movement for any
particular depth of firm layer to that wall movement for
D = 2H.
3.2.3 Effect QiExcavatiggThe
wall and ground movements for a wide excavation
tend to be substantially larger than those for a narrow
excavation, simply because for wider excavations more soil is
yielding around the cut. The influence of excavation width
on wall movement is shown in Figure 3.8, in terms of the
ratio (XB.
3.3 Meg;mum Lagergl gel; Movement
The maximum lateral wall displacement (€HI;ax) is found
using Equation 3.3 , which incorporates all factors
described in previous sections:
Sßßax = Sßmax°‘s°‘¤°‘B (3-3)
where€Hmax
is obtained from Figure 3.3, O/5 is from Figure3.4, OKD from Figure 3.7, and0(B from Figure 3.8.
3.4 Distgvibutign g; gggund Mgvegent
Up to this point, all equations and graphs have been
expressed in terms of the maximum lateral wall movement. But
38
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39
the ground surface movement (both lateral and vertical) is of
major interest to the engineer due to the possibility of
damage to adjacent buildings, roads, or utilities. Mana and
Clough (1981) have found that maximum vertical ground
settlement behind the wall can range from 0.5 to equal to the
maximum lateral wall movement. For all practical purposes,
however, the two are assumed to be equal.
The distributions of both the vertical and lateral
ground surface movements with respect to distance from the
excavation wall can be found from the value of maximum
vertical ground movement using the curves in Figures 3.9
(Mana and Clough,l98l) and 3Jß (Clough, 1985). As seen in
Figure 3.9, the maximum vertical ground settlement occurs at
the excavation wall. This is the case for a soldier beam and
lagging wall, because the soil closes up the gap that is left
behind the lagging. However, for a sheet pile or slurry
wall, the maximum vertical ground settlement may occur at
some small distance from the excavation wall. The curve in
Figure 3.9 thus represents an envelope of the possible
vertical ground settlement distributions for several types of
walls.
40
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DUHOJQ
CHAPTER 4
THE PROGRAH MOVEX
4.1 Inggodugtign
An interactive computer program, called MOVEX, has been
written as part of this thesis to aid in the design of
excavation bracing. It has several useful features that will
be described in detail in the following sections.
(l) Any combination of horizontal clay layers, watertable, excavation geometry and stiffness can beused.
(2) Several design options are available for theconvenience of the user.
(3) The factor of safety against basal heave and thecorresponding ground movement around the excavationis calculated at every construction stage.
(4) The distribution of both lateral and verticalground movements with distance from the excavationis calculated.
(5) The program includes an interactive design sectionin order to quickly arrive at the optimalcombination of strut and wall stiffnesses tocontrol movement.
All the calculations in MOVEX are based on theory
described in the previous chapters, which will be referenced
when necessary.
4-2 VEX
This section describes the input required for the
program MOVEX. A condensed version appears in the Users'
Guide in Appendix A.
. 42
43
4.2.1 gg; Ogtigns
The user inputs one value each for MOPT and NOPT.
4.2.1.1 Hgvgmgnt Qpjjgg (HQPT)
If MOPT = 0, both the lateral and vertical distributions
of movement with respect to distance from the wall are
calculated based on the methods described in Section 3.4.
For MOPT = 1, they are not calculated. If NOPT = 0 ( find
wall movement), the movement distribution will be calculated
at each excavation stage. For NOPT = 1,2, and 3, the
distribution is based on the maximum allowable lateral wall
movement, and is calculated for the final excavation stage.
4.2.1.2 Dgsign Qpjgjgg QQQPT)
The input and output for each design option are
summarized in Table 4.1. A description of the actual
quantities to be input is found in Section 4.2JL For NOPT =
O, the user inputs the entire excavation design: wall
stiffness, strut stiffness and spacing. The program
calculates the factor of safety against basal heave and the
maximum lateral wall movement at each stage of the
excavation. For NOPT = 1, the user inputs the strut spacing
and stiffness, and the maximum allowable wall movement. The
program calculates the factor of safety at every stage, and
picks the minimum. Then the wall stiffness required to limit
ground movement is found. For NOPT = 2, the user inputs the
wall and average strut stiffnesses, and the maximum allowable
44
Table 4.1 Input, Output, and Change Data fo; HOVEX
I I I I IINOPTI Input I Output I Changes II____I___._........_.__I......_.._________I_______________II I I I II I wall stiffness I factor of safety I wall stiffnesslI I I at every stage I II 0 I strut stiffness I I no. of struts II I I maximum lateral I II I strut spacing I wall movement I strut spacing II I I I II I I Istrut stiffness!I—···I·———··—···•·*·•··I*··•*'**·•··•····—I··———·······—·—II I maximum allow. I factor of safety I no. of struts II I lateral wall I at every stage I II I movement I I strut spacing II 1 I I required wall I II I strut spacing I stiffness Istrut stiffnesslI I I I II I strut stiffness I I II———·I·······—·······—·I—·——····—·—·—··——·I···—·—····————·II I maximum allow. I minimum factor I wall stiffness!I I lateral wall I of safety I II I movement I I strut spacing II I I required strut I II 2 I wall stiffness I spacing I average strut II I I I spacing II I average strut I I II I stiffness I I II———·I····———·————·····I—····—·····'·•·••·I•··*—*·—··**—··II I maximum allow. I factor of safety I wall stiffness!I I lateral wall I at every stage I II I movement I I no. of struts II 3 I I required average I II I wall stiffness I strut stiffness I strut spacing II I I I II I strut spacing I I II____I________________.I.._._.............I.............._I
45
lateral wall movement. The program divides the final
excavation into five fictitious stages and calculates the
factor of safety at each one in order to find the minimum
factor of safety for the entire excavation. The average
strut spacing required to limit movements is then calculated.
For NOPT = 3, the user inputs the wall stiffness, strut
spacing, and maximum allowable wall movement. The program
calculates the factor of safety at every excavation stage,
selects the minimum, and then computes the required average
strut stiffness to limit ground movement.
Equation 3.3 is used to calculate the maximum lateral
wall movement for NOPT = 0. This equation is manipulated to
solve for other variables in the excavation bracing design.
For example, to find the strut stiffness required to limit
movements to a predetermined value (NOPT = 3), solve for 0%:
and work backward through Figure 3.4 to find Ki. This is
also done in MOVEX to find the required wall stiffness (for
NOPT‘= l) and the required average strut spacing (for NOPT =
2).
It should be noted that in MOVEX, upper and lower limits
have been placed on the curves in Figures 3.3, 3.4, 3.7, and
3.8, so that the program does not crash when a very large or
small value is encountered. For Figure 3.3 (factor of safety
46
— stiffness — movement relationships), if the limits on the
curves are exceeded, the program will not calculate the
movement (or stiffness, depending on NOPT). Instead, an
error statement is printed to warn the user that the limits
have been exceeded, For Figures 3.4, 3.7, and 3.8, if the
limits on the curves are exceeded, the upper or lower limit
is automatically used in the calculations.
The program can handle up to twenty (20) different clay
layers adjacent to, or below the excavation. If the
properties of the clay layer vary considerably with depth,
the layer can be divided into two or more sublayers, each
with its own properties. The user inputs the thickness of the
layer, the total unit weight of the soil, and the shear
strength profile. The soil layers are assumed to be
horizontal. Since braced excavations are generally temporary
structures, clay layers are assumed to be undrained during
the life of the project. Thus a "phi = O" analysis is used.
The total unit weight is always used in the calculations.
The theory used in MOVEX was developed for use with
excavations in soft clay. However, sand layers may be
included in the soil profile by calculating an “equivalent
cohesion" using equation 4.2:
47
Usu = O"3 tan ¢ (4.2)
where0“3
= horizontal effective stressin the sand layer
¢ = angle of internal friction ofthe sand
The "equivalent cohesion” can be calculated at both the top
and bottom of the sand layer to obtain an increasing shear
strength with depth. Or, the "equivalent cohesion" can be
found at mid-layer to obtain an average shear strength
throughout the layer. Either way, the sand layers can then be
treated the same as clay layers in the input data. The
methods used in this program do not provide for mixed soils,
such as clayey sand or silty clay. Engineering judgement is
required to classify these mixed soils and identify their
predominant shear strength.
4-2-3The
depth to the water table from the ground surface,
and the unit weight of water are self—explanatory input. The
water table is assumed to be horizontal, and the water is in
hydrostatic equilibrium, i.e., no seepage forces exist.
4-2-4 Lim Luc.: Las;As explained in Section 3.2.3, the depth to a firm layer
is an important factor in limiting ground and wall movement.
The firm layer is defined as that surface below which the
soil will not fail. If the firm layer is deeper than H +
0.7B, where H = final height of the excavation and B =
48i A
excavation width, it will have no effect on the factor of
safety against basal heave. If the depth to firm layer is
more than twice the final excavation height (2H), it will
exert no influence on movements.
4-2-5 SssmltzxsadAnyexcavation width or height may be used, but the
number of struts (or tie—backs) is limited to ten (10). It
is assumed that the excavation is long enough so that
boundary conditions do not affect the behavior of the
excavation. The user inputs the total width, total length,
and final height of the excavation, and the surcharge
adjacent to the excavation, if one exists, expressed in terms
of force/lengthz.
Depending on the NOPT design option selected, the user
will input the following quantities, which are also outlined
in Table 4.1.
4.2.5.1 ggg], Sgiffngsg
The wall stiffness is expressed in terms of EI (in units
of force lengthz per unit length of wall), where E = modulus
of elasticity of the wall (in force /length2), and I is the
wall's moment of inertia (length4 per unit length of wall).
Sheet pile walls, reinforced slurry-concrete tremie walls,
and soldier beam and lagging walls are commonly used. Ranges
of typical stiffnesses for these walls are given in Table
4.2.
49
1a.Ql.a.,.42 i1.‘3z2i3;1¤.lEal.l§.t.1'f¤ S.ä.9s§R¤
I lower I upper I___....._lI_._._..._i_|_l______iI
I 6 2 I 7 2 ISoldier beam I 5 x 10 lbft I 5 x 10 lbft Iand lagging I per ft. wall I per ft. wall I__._._l_I___._i_______|.l__l_____I
I 7 2 I 7 2 Isheet pile wall I 4 x 10 lbft I 6 x 10 lbft I
(PZ Sections) I per ft. wall I per ft. wall |—————I———···——I·—··—————·'I
I 3 x 108 1bft2 I 3 x 109 lbftz ISlufry wallsI per ft. wall I per ft. wall I__________;_I._____i__l_I_________l_____l
Note: E steel = 4.3 x 109 lb/ftz
50
4.2.5.2 ßggut gtiffngss
The ideal strut stiffness, Ki, equals A E/L (in force
per length per unit length of wall) where E is the strut
modulus (force/lengthz), A is the strut's cross-sectional
area (in lengthz), and L is the unbraced length of the strut
(length).
4.2.5.3 gtrut gpggjgg
The strut spacing is defined as the distance from a
particular strut to the one above it. The theory used to
calculate movements in MOVEX does not apply to a cantilever
stage at the top of the excavation. Thus, if the first strut
is placed below the top of the excavation, this stage is
ignored, and the program·skips to the next stage. In MOVEX
it is also assumed that, during construction, the strut is
placed near the bottom of the cut at each excavation stage
(within about 4 feet (1.2 m)). The program also skips the
cantilever at the bottom of the excavation if no strut is
placed there for the final stage.
4.2.5.4 Mgxigug Allgwgplg Latggal Displagement
As explained in Section 3.4, the maximum lateral wall
displacement is assumed equal to the maximum vertical ground
surface movement, so that settlement limitations on adjacent
structures or utilities may determine this quantity.
4.3 gugggstions fg; ggg ggg gg ggggg
As explained in previous sections, the design of the
51
support system for a braced excavation consists of two major
requirements: stiffness and stability of the wall and
struts. Other variables to consider are the horizontal and
vertical strut spacing, the spacing of intermediate
stiffeners within the excavation, the maximum allowable
ground movement, etc. Often, one or more of these variables
is fixed. For instance, the construction contractor may
already have sheet piles left from another project to be used
for the wall. Or, local building codes may specify certain
limits on movements, or other safety requirements. But even
if none of these variables are known, the problem of
designing an excavation "from scratch" is a complicated
process.
The following guidelines are given to help in the
efficient design of the excavation bracing. The general idea
is to set all but one of the variables, then run to program
to find the missing parameter. Once a structural section is
selected from this parameter, the program is run again to
determine its influence on the other variables.
(l) Calculate (by hand) the strut loads and bending moment
in the wall based on earth pressure theory.
(2) Select a bracing design based on the values calculated
in Step l.
(3) With NOPT = 0, run MOVEX to determine the wall and
ground movements associated with the bracing design.
52
(4) If the wall movement exceeds the maximum allowable wall
displacement, run the program again with NOPT = l or 2 to
determine the appropriate wall and strut stiffness to limit
ground movement.
(5) If any of the sections (strut or wall) seem excessively
large or small, try changing the strut spacing to compensate.
Note that samll changes in the strut spacing have a large
influence on the other variables.
53
4.4 Interactive Design
The interactive design portion of MOVEX permits the user
to easily change certain variables in the bracing design, and
then observe the impact of the change upon the other
variables. In this way the engineer can readily perform a
small parametric study for the variables to arrive at the
optimum bracing design. This feature eliminates the need to
modify the original data file repeatedly using a line editor
or word processor; the program does this automatically.
The interactive portion of the the program uses a series
of screen prompts. The first prompt asks if the user wants
to change the variable. If the answer is 'yes', the second
prompt asks for the new value. If 'no', the process is
repeated for the next variable. The quantities that can be
changed depend on the design option in the original data
file. A complete list of variables that can be changed for
each design option is shown in Table 4.1.
CHAPTER 5
SETTLEMENT OF SAND DUE TO PILE DRIVING
5.1 Intggductign
Previous chapters have discussed ground movement around
braced cuts due to the shear failure of clay below the base
of the excavation. However, there are many other causes of
movement. Table 3.1 listed some major factors affecting
ground movements. Many of these are directly related to
construction activities for, in, and around the excavation.
In this chapter, emphasis will be given the settlement of
sand due to pile driving.
Often, sheet piles are used for the walls of a braced
excavation. Commonly, they are driven through a layer of
loose, sandy rubble fill into some other deposit, such as a
soft clay. This is a particularly common situation in the
San Francisco Bay area. It is a well known fact that loose
sands and silts tend to densify upon vibration. Sheet pile
driving through the rubble fill will cause settlements thatU
are additive to those caused by deep—seated movements in the
clay. The total settlement from the entire excavation
construction may be twice that predicted from the clay alone.
It would be useful to be able to predict how much a sand
layer would densify if vibrated at a certain frequency.
Troublesome sites could be identified easier, specifications
could be better written, and, if a potential settlement
54
‘55
problem exists, an alternative construction procedure could
be used altogether.
The most commonly specified limit on vibrational level,
2 in/sec (51 mm/sec), was developed by the U.S. Bureau of
Mines (1971) with reference to the damage from blasting.
They claim that residential structures are 'safe' from any
sort of damage if subjected to vibrations less than 2 in/sec.
However, there are several case histories (see Table 5.1)
that show that vibrational levels of much less than 2 in/sec
causing excessive settlement in cohesionless soil that in
some instances led to great damage to adjacent structures.
For instance, in Case 8 from Table 5.1, a peak particle
velocity of 0.2 in/sec (one-tenth of the USBM criteria)
caused sand densification and more than 3 inches of
settlement to adjacent buildings, which were subsequently
demolished because of excessive damage. In Case 9, a maximum
of 0.1 in/sec vibration caused about 2.4 inches of settlement
in an adjacent structure. Cases 10 and ll give similar
results.
Obviously the USBM criteria for structural damage from
vibrations is inadequate when applied to the problem of
settlement of sands due to pile driving. The objective of
this chapter is to develop a predictive method that relates
pile driving vibrations and sand densification as a function
of distance from the pile and the relative density of the
sand.
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Numerous measurements of Vibrations due to pile driving
have been made (case numbers 1,2, 4,7, 11,14, and 18 from
Table 5.1). A11 the data are combined in Figure 5.1 into a
single plot of acceleration (in g's) versus distance from the
pile (in metersL
Figure 5.1, plotted on log — log scale, shows
exponentially decreasing acceleration with distance from the
Vibration source, which in this case, is the tip of the pile
as it is being driven through the cohesionless soil. This
plot is consistent with the general trend of attenuation of
ground Vibration for all types of construction activity given
by Wiss (1970). Three levels of acceleration are shown in
Figure 5.1 : high, mdium, and low. The medium acceleration
line was found from a linear regression of all the data
points. The high and low lines envelope most of the data on
either side. High acceleration corresponds to hard driving,
for instance that which occurs when boulders or dense soil
are encountered. Conversely, low acceleration is the result
of easy driving, such as driving piles in loose sands or soft
clays. It has been found that acceleration tends to increase
with depth of pile penetration (see for instance Cases 1 and
16 from Table 5.1). For all practical purposes, however, it
may be taken as a constant. Also, it has been found that
Vertical and horizontal Vibrations are not significantly
62
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different.
Most of the vibration data in the literature was
presented as peak particle velocity versus distance from the
pile (with the exception of 1 and 2, which gave acceleration
versus distance).The particle velocities were transformed
into accelerations by assuming simple harmonic motion. The
relationship between velocity (v), acceleration (a), and
frequency (f) is
a = 21rf v
A convenient nomograph is given in Richart, Hall, and Woods
(1970) to make this conversion.
Frequencies for vibratory hammers are in the range of 15
to 30 cycles per second (cps), with an average of about 18
cps. For resonant hammers, the range is about 70 to 100 cps.
Impact hammers generally operate at about 40 to 60 blows per
minute, or about 0.8 cps.
5-3 9§$§B§Dil.Q@El§D ' in
Relationships between strain and acceleration have been
investigated by Lambe and Whitman (1985) in a centrifuge,
Seed and Silver (1972) in the laboratory, and by Clough and
64
Chameau (1980) in the field. The data in Clough and Chameau,
measured directly from sheet pile driving, is similar to that
observed in other testing environments. The data from all
three are combined in Figure 5.2. Here, strain is defined as
the total amount of settlement divided by the total
thickness of the layer (for field data) or total thickness of
the sample (for laboratory data). The upper and lower bounds
on the strain were established based on the relative density
of the sand.
Using acceleration as a common denominator, Figures 5.1
and 5.2 were combined to obtain the relationship between
strain and distance from the pile for low, medium, and high
accelerations for loose to medium, and medium to dense soil.
The results are shown in Figures 5.3 and 5.4. A comparison of
these figures shows that not only will a loose sand settle
more than a medium dense sand at a given acceleration, but
that loose sand will settle at a greater distance from the
vibrating pile than dense sand. Figures 5.3 and 5.4 enable a
prediction to be made for the settlement of a sand layer due
to pile driving. An example of the use of this method is
given in Figure 5.5. It may be noted that if a vibratory
hammer is operated at the standard vibrational criteria of 2
in/sec (-0.5 g's) in loose sand, anywhere from 0.12 to 1.6
percent strain may occur at a distance of 3 m (10 ft) from
the pile, depending on driving conditions.
65
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(UJUJ) LNEWB-l.L.LES
CHAPTER 6
SUMMARX AND CONCLUSIONS
The major objective of this thesis was to develop
personal computer software to facilitate the design of
excavation bracing. To this end, the program MOVEX was
written. Previous chapters have described the theories used
in MOVEX. A summary of its main features is given below.
The calculations in MOVEX are based on the design method
by Mana and Clough (1981). In this method, the ground
movements around an excavation are directly related to the
factor of safety against basal heave. The method is intended
for the the analysis of braced excavations in homogeneous
soft clay. However, it has been expanded by the writer to
include a multi-layered soil profile. The sequence of
calculations in the program is briefly listed below:
(1) Find the factor of safety against basal heave atevery construction stage and find the minimumfactor of safety for the entire excavation.
(2) Calculate the corresponding ground movement,considering the effects of strut stiffness, wallstiffness,soilstiffness,andexcavation geometry.
(3) Make changes to the original design, if necessary.
several design options have been included in the program
for maximum flexibility to the user. The details of these
options are given in previous chapters, so they will not be
repeated here, except in a general way; the user inputs a
limit on the ground movement and the program will calculate
70
7l
the required value of the bracing stiffness to limit movement
to that level.
Effective computer software should meet several
standards: it should be easy to use, it should perform
calculations that are ordinarily too long or involved to do
by hand, and it should be accurate with the range of accuracy
of the input data.
The program MOVEX meets these criteria. First, the
program has several features that make it easy to use. The
input data file is relatively short. The user has a choice
of design options. The user has a choice as to where the
output is sent. And, an interactive design section enables
the user to quickly change variables to see the effect on the
bracing design as a whole. Second, the program has been made
as general as possible in order to accommodate almost any
excavation geometry and soil profile. The resulting
calculations are too long to do by hand for repeated design
trials at every excavation stage. Third, the program has
been tested against many example problems and case histories,
one of which is given in Appendix C. In all cases, the
results were very reasonable, and, for the case histories,
the calculated values fell close to the field measurements.
MOVEX calculates the ground movement due solely to basal
instability. In a somewhat related topic, the settlement of
sands due to pile driving was investigated by the writer.
Sheet piles are often driven through cohesionless soil to be
72
used as the walls of a braced excavation. So it would be
useful to be able to predict the amount of settlement that
might occur due to pile driving alone. An extensive
literature search was made for data that would show the
relationship between pile driving Vibration and densification
of sands. Vibration data from the literature were applied to
laboratory and field measurements of strain due to Vibration,
to obtain the relationship between strain versus distance
from the pile for several acceleration levels and soil
densities. This relationship can be used toward the main goal
of this thesis: to further identify and predict ground
movement around excavations.
BIBLIOGRAPHY
Attwell, P.B.and Farmer, I.W.(1973),"Attenuations ofGround Vibrations from Pile Driving," groundEngineering, July, p. 26.
Bjerrum, L. and Eide, O. (1956), "Stability of StruttedExcavation in Clay,' Qeotechnigue, Vol. 6, No. 1,pp. 32 -47.
Bjerrum, L„,C1ausen, X„ and Duncan, J.(1972),"EarthPressures on Flexible Structures - A State of the ArtReport," Preceedings, Fifth European Cenference epSeil Mechaniee and Feundation Engineering, Vol. 1, pp.169 - 196.
Brand , E. W. , and Brenner, R. P.(l981), Seft ClayEngineering, New York, Elsevier Scientific APublishing Co„ p.399 - 633.
Clough,<L W.,and Buchignani, A.(l980),"Slurry Walls inthe San Francisco Bay Area,' preprint.
Clough,CL W.,and Chameau, J.I„ (1980), "Measured Effectsof Vibratory Sheetpile Driving," ASCE Journal er thegeetechnical Engineering Division, GTl0, October, p.1081 - 1099.
Clough, G. W., and Hansen, L. A. (1981), 'Clay Anisotropyand Braced Wall Behavior," ASCE Journal er thegeoteehnical Divisien, GT 7, July, pp. 893 - 913.
Clough, G. W. (1985), "Effects of Excavation—InducedMovements in Clays on Adjacent Structures", llthInternationel Qenferenee ep Soil Mechanies andFoundation Engineering, Mexico. Session 5A.
Dalmatovq B.I.,Ershov,\L A.and Kovalevski, E.D.(1968), "Some cases of Foundation Settlement inDriving Sheeting and Piles." Properties of EarthMaterials, Universtiy of New Mexico, Albuquerque,NM, p.607 - 613.
Davidson, Richard R. (1977), "Effects of Construction onDeep Excavation Behavior," p. 177, Thesis presentedto Stanford University in partial requirement for therequirements for the Degree of Master of Science.
73
74”
Fawcett, A. , (1973), "The performance of the Resonant PileDriver", 8th International Conference QQ SoilMeehenics and Foundation Engineering, Moscow,pp. 89 - 96.
Hansen, L., (1982), 'Ground Movements Caused By BracedExcavations: Discussion," ASCE Journal er theGeotechnieal Engineering Division, GT9, September.
Heckman, William S. (1975), "A Study of the Effects ofPile Driving Vibrations on Nearby Structures." MastersThesis, University of Louisville, p.62.
Heckman, W. S., and Hagerty, D. J. (1978), 'VibrationsAssociated with Pile Driving', ASCE Journal er theConstruction Divisien, CO4, December, p. 385 -394.
Hol1oway,IL M., Moriwaki,Y., and others,(1980),"Fie1dStudy of Pile Driving Effects on Nearby Structures", rMinimizing Detrimental Construetion Vibrations,ASCE National Convention, April, p. 63 — 100.
Lambe, P.C., and Whitman„ R.V.(l985),"DynamicCentrifugal Modeling of a Horizontal Dry Sand Layer".ASCE Journal ef Qeetechnical Engineering Division,March, p 265 — 287.
Lynch, T. J. (1960), "Pile Driving Experiences at PortEverglades', A§CE Jeurnal er the Soil Mechanics andFoundation Division, SM2, April, p. 41 - 62.
Mana, A. I. (1978), 'Finite Element Analyses of DeepExcavation Behavior in Soft C1ay," Thesis presented toStanford University in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy.
Mana„ A.I., and Clough,<L W.(l98l),'Prediction ofMovements For Braced Cuts in Clay', A§CE Journal erthe Qeotechnicel Divisien, GT6, April, p. 759 — 777.
O'Rourke, T. D. (1981), 'Ground Movements Caused ByExcavations," ASCE Journal of the GeotechnicalEngineering Division, GT9, September, p. 1159 — 1177.
Richart, F. E., Hall, J. R., and Woods, R. D. (1975),Vibrations er Soils and Foundations, (EnglewoodCliffs, NJ: Prentice — Hall IncJ
Peck, R. B. (1969), 'Deep Excavations and Tunnelling —
State of the Art', 7th Internationai Conference QßSoil Mechanics, Mexico, p. 259 - 290.
75
Peck, R. B., Hanson, W. E.,and Thornburn, T.EL (1974),Foundation Engineering, New York, J. Wiley and Sons,
2nd Edition.
Sandqvist, G. , (1972), 'Back—tied Sheet Pile Wall inFriction Soil. Deformation and Drag Forces Due toPilling and Freezing', 5th European Conference QQ SoilMeehenics and Foundatien Engineering, Madrid, Vol. 1,April, p. 293 — 298.
Seed, H.B. ,and Silver, M.L., (l972),'Sett1ement ofDry Sands During Earthquakes', ASCE Journel ef theSoil Mechanics and Feundations Division, SM4, April,p. 381 - 397.
Sunami, Susumu. (1981), "Designing Excavation SupportSystems for Deformation Control," Thesis presented toStanford University in Partial Fulfillment of theRequirements for the Degree of Engineer.
Swiger, W. F. (1948), 'Effect of Vibration on Piles inLoose Sand,' Proceedings, Seeond InternationalConference er Soil Mechanics and FeundationEngineering, V.II, Rotterdam.
Terzaghi, K. (1943), Theoretical Soil Meehenies, (New York:John Wiley)
Terzaghi, K.and Peck,IL B.(l968), Seil Mechanics_ihEngineering Preetice. (New York: John Wiley and Sons),p. 587.
Theissen, John R.and Wood, J.C. (1982), 'Vibrations inStructures Adjacent to Pile Driving," EngineeringBulletin, Vol. 60, July, p.5 — 21.
Tschebotarioff, Gregory P. (1973), Feundations, Retainingang Eerth Structures, (New York: McGraw Hill, 2ndedition), p. 62.
U.S. Army Engineer Waterways Experiment Station, Corps ofEngineers, (1962), 'Review of Soils Design,Construction and Performance Observations, Low-SillStructure, Old River Control, Technical Report No. ·3 - 602, June.
U.S. Army Corps of Engineers, Huntington District, (1975),Tug Fork Valley, Williamson Flood Wall Feature DesignMemorandum No. 5, January.
76
United States Steel Sheet Piling Handbook (l976),"ReferenceData on Shapes, Materials, Performance and Applications."
Wiss, J. F. (1970), "Damage Effects of Pile DrivingVibration," Minimizing Detgimgntal ConstructionVibrations, ASCE National Convention, April.
APPENDIX A
MOVEX User's Guide
_ 77
78
INTRQDUCTIQ§
The program MOVEX computes the ground movements around
braced excavations. It has several useful features:— Any combination of horizontal soil layers, water table,
and excavation geometry and stiffness can be used.
- Several design options are available for the convenience
of the user.
— The factor of safety against basal heave and the
corresponding ground movement around the excavation is
calculated at every construction stage. .
— The distribution of both lateral and vertical ground
movements with distance from the excavation is calculated.
— The program includes an interactive design section in
order to quickly arrive at the optimal combination of strut
and wall stiffnesses to control movement.
The program is based on the design method by Mana and
Clough (1981). The first version was developed by Sunami
‘ (1981). Expansion and modification was made by Goessling
(1985) under sponsorship of the Nikken-Sekki Corporation,
under the direction of Professor G. W. Clough at Virginia
Polytechnic Institute.
79
$Y$TEH.EEQQIREME§E§
This program has been written to run under MS—DOS.
Hardware requirements include 64 to 128 kilobytes of RAM
memory and at least one disk drive. It is not necessary for
the user to have a copy of the FORTRAN compiler in order to
execute this program; however, it would be necessary if
modifications were made to the program.
The accompanying diskette contains the following files:
Cgntents Eile ßige (kilobytes)
Source file _Executable fileData File for ExampleOutput File for Example
The file sizes shown are based on MS-DOS operating
system and Microsoft FORTRAN — 77 version 3.2 compiler.
The user should make a backup copy of the program
diskette and store the original. It is not necessary to copy
the source file if the program is not going to be changed.
80
LßäßßThe
program consists of a main section, MOVEX, and
several subroutines: FSHEAV, SDISP, COEFS, SOLVE, DECOMP,
DSTRB, AND CHNG. Their functions are briefly explained
below.
MOVEX is the main segment of the program. It reads all
the input, and for each excavation stage, calls the
subroutines FSHEAV and SDISP. It also controls the overall
execution of the program.
FSHEAV calculates the factor of safety against basal
heave.
SDISP finds the lateral wall displacement, and the terms
0fS, OIB, and GID.
COEFS, DECOMP, and SOLVE are curve—fitting subroutines.
DSTRB calculates the distribution of lateral and
vertical ground movement for various distances from the wall.
CHNG controls the interactive change section.
V8l
PROGRAH EXECUTION ‘ P
Prior to running the program, it is necessary to create
a data file using a text editor or a word processor. For a
single—disk system, the data file should be saved on the\
program disk. For dual-disk system, the data file can be
saved either on the program disk, or on a separate data disk.
Once the data file has been created, and the system
prompt ( A> ) appears, simply type MOVEX followed by a
return, and the program will begin. A title page like the
one shown below will appear on the screen. Input the name of-
the data file, and select the output destination.
*******************«+**********«***********# Movrx * _**
* A program for the design of ** excavation bracing to limit ground ** movement. ***
NAME OF INPUT FILE:(e.g. b:xyz.dat) ——>
OUTPUT DESTINATION:
0 = Screenl = Printer2 = Disk
PLEASE SPECIFY -->
82
.D.E.S§„.QERIP'1‘I QL LEELQBIt
is not necessary to type the input data in formatted
columns. The numbers can be typed one after another
separated by one or more commas. Decimal points need only be
typed for numbers having fractional parts, such as 5.32 or
0.08. Blanks are not interpreted as zeros. Zeros must be
typed. Any system of units (SI, British, etc.) may be used,
but units must be consistent. Units are shown in this manual
in square brackets [ ], using the following notation (or a
combination thereof): _
[L] = length[F] = force
A. PROBLEM IDENTIFICATION
TITLE - (maximum of 72 characters), any desiredidentifying information.
B. USER OPTIONS
MOPT, NOPT, where
MOPT — movement distribution option
MOPT = 0 : vertical and lateral distribution ofmovement with respect to distance fromwall calculated.
MOPT = l : movement distribution not calculated.
NOPT — design option
NOPT = 0 : entire excavation geometry andstiffness is input; maximum lateralwall movement calculated for each° excavation stage.
NOPT = l : excavation geometry and maximumallowable lateral wall movement input;wall stiffness (EI) calculated.
83
NOPT = 2 : excavation geometry and stiffness, andmaximum allowable lateral wall movementinput; required strut spacingcalculated.
NOPT = 3: excavation geometry, and maximumallowable lateral wall movement input;required strut stiffness calculated.
C. CONTROL DATA
NLAY, NSTRT, where
NLAY - total number of soil layers in the vicinityof the excavation. Include layers thatextend either to a firm layer below theexcavation bottom, or to a distance oftwice the final excavation height belowthe bottom of the excavation. Maximumof twenty (20) soil layers.
NSTRT — total number of struts in the excavation.Maximum of ten (10) struts (or tie-backs).
D. SOIL DATA - One line for each soil layer. There should. be NLAY line(s).
J,H,GT,C0,DC, where
J — layer number, starting with the topmost layer asnumber 1. [L]
H — thickness of layer J. [L]
GT — total ugit weight of the soil in layer J.[F/L ]
C0 - undrained shear strengfh (cohesion) at the topof the clay layer. [F/L ]
DC — change in undrained sheai strength with depthin the clay layer. [F/L ]
E. FIRM LAYER DATA
DF, where
DF - Depth to a firm layer from the ground surface[L]. For a very deep clay layer, input anynumber greater than (H + 0.7B) where H = final
84
excavation height [L1 and B = total excavationwidth. [L1
F. WATER TABLE DATA
GW,WT,where A
GW - unit weight of water [F/L3]
WT - depth to the ground water table from theground surface. [L1
G. EXCAVATION GEOHETRY (see Figure A.l)
B,ELN,HW,Q , where
B — total excavation width [L]
ELH - total excavation length [L] .
HW — final excavation depth [L]
Q — surcharge next to the excavation. [F/L2]
STRUT—WALL-DEFLECTION DATA Choose the appropriate input,based on the value of NOPT.
Fo; NQPT = 0 (find maximum displacement),
H. WALL STIFFNESS
EI , where
BI - bending stiffness of the wall [F L2 per unitlengäh of wa111,where E = moduluä of the wall[F/L 1, and I = moment of inertia [L per unitlength of wall].
I. STRUT DATA — One line for each strut; there should beNSTRT lines of data.
J,HS,S, where
J - strut number, starting with topmost strut asnumber 1.
HS — strut spacing [L1, distance between strut Jand thestrut above it. For the top strut, HS isthe distance between the strut and the groundsurface.
854
G2 62IUIlÄH]*—**—*[[[[[Huse
WT 1 L.A‘/EZT.éz .. _. — —.
HS2
uw 2 4
HSB L..A‘/EK 23
DF H544 4 1.A~/ez 6
FIQURE A.1 · EXCAVATIOM ÖEOMETIZY
86
S — strut stiffness [F/L per unit length of wall]— AE/L, per unit length of wall, wheäeA = cross-sectional aria of strut [L 1,E = strut modulus [F/L 1, andL = effective length [L].
Fg; §QPT = l (find wall stiffness)
H. DISPLACEHENT DATA
DL!, where
DL! — maximum allowable lateral movement ofthe wall. [L]
I. STRUT DATA — One line for each strut; there shouldbe NSTRT line(s) of data.
J,HS,S , where I r
J - Strut number, starting with the topmost strut asnumber 1.
HS- Strut spacing [L], distance between strut Jand the strut above it. For the top strut,HS isthe distance between the strut and theground surface.
S — Strut stiffness [F/L per unit length of wall]AE/L per unit length of wall, where
2A = cross-sectional aräa of strut [L 1,E = strut modulus [F/L 1,L = effective strut length [L].
Fgr §QPT = 2 (find average strut spacing)
H. DISPLACEHENT DATA
DL! ,where
DL! - maximum allowable lateral movement ofthe wall [L].
I. WALL STIFFHESS
EI, where
EI - bending stiffness of the wall [F L2 per unitlengiéh of wall], where E = modulus of 4the wall[F/L 1, and I=moment of inertia [L per unitlength of wall].
87
J. AVERAGE STRUT STIFFNESS
SAVG, where
SAVG = AE/L per unit length of wall [F/L per unitlength of wal}] , where A = cross-sectional area ofthe Etruts [L ], E = average modului of the struts[F/L ], and L = effective strut length [L].
Fo; NQPT = 3 (find strut stiffness)
H. DISPLACEHENT DATA
DLH, where
DLH — maximum allowable lateral movement of thewall [L].
I. WALL STIFFHESS ·
EI, where
BI - bending stiffness of the wall [F L2 per unitlengäh of wall], where E = modulus og the wall[F/L ], and I = moment of inertia [L per unitlength of wall].
J. STRUT SPACING — One line for each strut; there shouldbe NSTRT line(s) of data.
J,HS, where
J — Strut number, starting with the topmost strut asnumber l.
HS - Strut spacing [L], distance between strut J andthe strut above it. For the top strut,HS isthe distance between the strut and the groundsurface.
88
DEQQRIPTIQN Q; QUTPUT_§gQg ggggg
In the computer output, the first six major items:
title, soil layer data, water table data, excavation
geometry, and strut data, are all values that were read from
the data file. The format of these data remains virtually
the same, regardless of the values of MOPT or NOPT. The
calculated output, however, depends on the design options
specified. The output for Example l is shown in Figure A.3.
If MOPT==0 (calculate the distribution of movements),
both the vertical and lateral displacements (in length) are
found for various distances from the wall (length).
The output for each design option (NOPT) is summarized
in Table A„l. The maximum lateral wall movement is given in
units of length, the required wall stiffness, EI, in units of
force-lengthz per unit length of wall, the required strut
stiffness in force/length per unit length of wall, and the
required strut spacing (in the vertical direction) in length
units.
89
INQEMCTIVE DESIQN
After the program has been run with the original data
file, the user is given three options: make changes to the
design, run a new program, or exit to DOS. If the first
option is selected, changes can be made to the original data
file by responding to prompts from the screen as follows.
The user inputs a new input data file name. The name
can either be the same as the original file, in which case
all original data will be written over, or the name can be
different from the original name, in which case a totally new.
file will be created. In either case, the new data file will
automatically be used to run the program over again. The
data that can be changed depends on the design option used in
the original data file. It is summarized in Table A.l.
For NOPT = 0 (find maximum wall movement), the following
prompts will appear on the screen:
Change wall stiffness? (yes/no) -—>
New wall stiffness -—>
Change number of struts? (yes/no) -->
New number of struts -—>
Change strut spacing? (yes/no) -—>
New spacing for strut l ——>
New spacing for strut (NSTRT) ——>
Change strut stiffness? (yes/no) -->
90
Table A.l. Input; Qu;gu;„ ggg Change Dgtg fg; Mgygx
I I I I IINOPTI Input I Output I Changes II____I____________..___I________._________I_________________II I I I II I wall stiffness I factor of safety I wall stiffness II I I at every stage I II 0 I strut stiffness I I no. of struts II I I maximum lateral I II I strut spacing I wall movement I strut spacing II I I I II I I I strut stiffness II·——·I———········—·—·—·I·····•——·•········I·——····—·——·—·———II I maximum allow. I factor of safety I no. of struts II I lateral wall I at every stage I II I movement I I strut spacing II l I I required wall I II I strut spacing I stiffness I strut stiffness II I I I II I strut stiffness I I II—···I·—·——··········—·I·—······—·—····—··I·········—····—·—II I maximum allow. I minimum factor I wall stiffness II I lateral wall I of safety I II I movement I I strut spacing II I I required strut I II 2 I wall stiffness I spacing I average strut II I I I spacing II I average strut I I II I stiffness I I II—···I·······—·———·····I······—·——···—···—I·—————··——····—··II I maximum allow. I factor of safety I wall stiffness II I lateral wall I at every stage I II I movement I I no. of struts II 3 I I required average I II I wall stiffness I strut stiffness I strut spacing II I I_ I II I strut spacing I I I
91
New stiffness for strut 1 —->
New stiffness for strut (NSTRT) —->
For NOPT = l (find wall stiffness), the following
prompts will appear on the screen:
Change number of struts? (yes/no) —->
New number of struts —->
Change strut spacing? (yes/no) -·>
New spacing for strut]. —->
New spacing for strut (NSTRT) —-> _
Change strut stiffness? (yes/no) -->
New stiffness for strut l -->
New stiffness for strut (NSTRT) -—>
For NOPT = 2 (find strut spacing), the following prompts
will appear on the screen:
Change wall stiffness? (yes/no) -—>
New wall stiffness -—>
Change average strut stiffness? (yes/no) -->
New average strut stiffness -—>
For NOPT = 3 (find strut stiffness), the following
prompts will appear on the screen:
Change wall stiffness? (yes/no) ——>
New wall stiffness -—>
92
Change strut spacing? (yes/no) —->
New spacing for strut l —->
New spacing for etrut (NSTRT) ——>
93
ETIN@lB£.§S§QEThe
design of the support system for a braced excavation
consists of two major requirements: stiffness and stability
of the wall and struts. Other variables to consider are the
horizontal and vertical strut spacing, the spacing of
intermediate stiffeners within the excavation, the maximum
allowable ground movement, etc. If none of these variables
are known, the problem of designing an excavation "from
scratch" is a complicated process.
The following guidelines are given to help in the
efficient design of the excavation bracing using MOVEX.The
general idea is to set all but one of the variables, then run
to program to find the missing parameter. Once a structural
section is selected from this parameter, the program is run
again to determine its influence on the other variables.
(l) Calculate (by hand) the maximum bending moment in the
wall and the strut loads based on earth pressure theory.
(2) Select a bracing design based on the values calculated
in Step 1.
(3) With NOPT = 0, run MOVEX to determine the wall and
ground movements associated with the bracing design.
(4) If the wall movement exceeds the maximum allowable wall
displacement, run the program again with NOPT = 1 or 2 to
determine the appropriate wall and strut stiffness to limit
ground movement.
94
(5) If any of the sections (strut or wall) seem excessively
large or small, try changing the strut spacing to compensate.
Note that samll changes in the strut spacing have a largeI
influence on the other variables.
APPENDIX B
Example Prcblem
95
96
EXAHPLE: Compare MOVEX calculations with field measurements
of movements of a braced excavation. Case history is
from 'Measured Behavior of Braced Wall in Very Soft
C1ay,' (Clough and Reed, 1984). Soil conditions are
shown in Figure B - 1. Excavation is shown in Figure
B — 2. Calculate the wall movements associated with the
braced excavation construction.
sßgrxgy 1>go1>gg•1·1E§:
ehee; eige PZ 32 E = 4.2 x 109 psf
I = 382 in4 per pile= 220.6 in4 per foot wall
EI = 4.2 x 109 ° 0.011 ft4/ft wall= 4.5 x 107 lb - etz/et
eeeel sgguts HP l2x74 E = 4.2 x 109 psf
A = 21.8 1¤z = 0,15 etzL = 25 ft
. 9K: 7-7 6 l°“eääéäii
ggg ggg E = 2.5 x 108
A = 1 etzL = 25 et
K1 6-7 6 *65 eääéäiiMOVEX input shown in Table B — 1. Computer output shown
in Table B — 2. Measured wall movements are shown in
Figure B - 3.
97 VRenlln
0ev1o•en Avenue I $"'**' I Cute: Anne;O B.*lF4ä‘-;€'1]l$H¥; O'¤·•" ·* =·=·······‘° usw uv uuo *0
—_ ~_;_‘,:·:·f.{é_-;.Z;_;§';::>•I·é"; I:
E 80 _ IU-_&.·J~‘ ." 80 é• 1 °— K
E *5; '· oto an nunE}._ (SIIH) · uzo
°§'·1&··=§<€:·„_‘
Reel *_ '_{*_‘“ _
_IsoS: * ‘ *: :. ‘“·r·············‘.
~_**_ . ISO
I400 1200 I000 800 600 400 EO 0‘ DISTANCE F••r
‘—SoII Profile along Cuhrert Axis (1 ft
-0.305 m)
—ComperIson of Propertles of Bay Mud from Custer Avenue end RsnldnStreet and Dsvldson Avenue
AverageAverage Unlt Weight. In AverageWater Pounds per Shear Strength.
Content, Oublc Foot In Pounds per PI, as LL asmm as a Per- (Kßograms per Square Foot s Per- e Per-
, in fw; centage Cublc Meter) (Pascats) Sensitrvity centage oentage(meters)D‘C° c0(1)(2) (3) (5) (6) (7) (8) (9) (10) (11) (12) (13) (15)0-30 95 91 92 350 500 1.4 1.5 15 105 95
(0-9) (1,460) (1,470) (16,770) (24,000)30—55 75 96 104 60 800 1.0 1.5 10 85 68(9-17) (1,540) (1,670) (21,600) (38,300)
'D-
Davidson Avenue.tc • Custer Avenue and Rankin Street. .‘OCR - overcoruolidation ratio.‘8ased on effective pressures with allowances for artesian pressu.re.Note: 1 psf
- 47.9 N/mz; 1 pd-
0.157 kN/¤1’.
FIGURE B.l — Example Problem — Soil Data
(from Clough and Reed, 1984)
' 98
Notu: Struta an Blt horizontal o•nt•nEach strut 9r•|ood•d by 2.8 tip;
I Z5' Il2°•a.
wood mut Ihö3%G?-‘=:•'-'-'-‘-‘·==‘-1-1er-2;:-at-:-:-:+:4-:-;:rar? · 5.
STAGE 2Chmnab ta pr•v•nt valar 9-rotat•an(u••¤•¢e•e•••¢1t••)Ä!I1l-I"FZ
STAGE 3 Io_
STAGE 6 6'
rz' au.Thrownmvayvood strut I5· ,
lnlarlachnq•h••lpd•
FIGURE B.2 - Example Problem - Strut Geometry
(from Clough and Reed, 1984)
99
Tgblg B.1 Example Problgm — Input Data
Islais Creek Excavation (after Clough and Reed, 1984)1 02:21,30,91,350,02,25,96,450,010062.4,625,500,30,04.52+71,0,6.7E+52,l4,1.7E+63,10,l.7E+6
100
Table B,2 Example Pggblgm - Cgmputer Output
Program MOVEX
Islais Creek Excavation (after Clough and Reed, 1984)CONTROL DATA
Number of soil layers 2Number of struts 3Design Option 0
SOIL LAYER DATALayer number 1
Thickness 30.00 Cohesion 350.00Unit Weight 91.00 Coh. Increase .00
Layer number 2
Thickness 25.00 Cohesion 450.00Unit Weight 96.00 Coh. Increase .00
Depth to firm layer from ground surface 100.000WATER TABLE DATA
Unit weight of water 62.40Depth to groundwater table 6.00‘
EXCAVATION GEOMETRY
Total width of excavation 25.00Total length of excavation 500.00Final height of excavation 30.00Surcharge next to excavation .00Wall Stiffness .450E+08
STRUT DATAStrut Spacing Stiffness
IOO
1 .6700E+0614.00
2 .l700E+0710.00
3 .l700E+076.00
MOVEMENT CALCULATIONSExcavation stage 2
Height of excavation = 14.000Factor of safety against basal heave = 1.8217Max. lateral wall movement = .172
101
Tgglg B.2 Example Pgoglgm — Comgutg; Qutput (con't)
Excavation stage 3
Height of excavation = 24.000 -Factor of safety against basal heave = 1.2320Max. lateral wall movement = .383
Excavation stage 4
Height of excavation = 30.000Factor of safety against basal heave = 1.0669Max. lateral wall movement = .471
II
102
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APPENDIX C
HOVEX Program Listing
103
104
$Uo66PROGRAM MOVEX
CC PROGRAM MOVEX - 1985Cc Program for design of excavation bracing to limitc ground movement. Based on the design method ofc Mana and Clough (1981), and Clough andc Buchignani 1981). First version of program writtenc by Susumu Sunami (1981); current versionc written by Sybil Goessling (1985).C
DIMENSION h(20),c0(20),dc(20),gt(20),1(20),j(20),1 fS(20),diSp(20),d(8,20),S(20),dV(8,20),2 d1(8,20),hS(20)
CHARACTER fin*14,fout*14,tit1e*72COMMON de,hw,b,q,io,e1n
Cc........................TITLE PAGE........................C
150 WRITE(*,8001)80011
15X,' * *'/2 15X,' * MOVEX *'/3 15X,' * *'/4 15X,' * A program for the design of *'/5 15X,' * excavation bracing to limit ground *'/6 15X,' * movement. *'/7 15X,' * *'/
8C
WRITE(*,8010)8010 FORMAT(///20X,'NAME OF INPUT FILE:'/
1 20X,' (e.g. b:xyz.dat) -—> '\)READ(*,8800) fin
8800 FORMAT(A14)8002 WRITE(*,8020)8020 FoRMAT(//20x,' OUTPUT UESTINATIUN: '//
1 20X,' 0 = Screen '/2 20X,' 1 = Printer'/3 20X,' 2 = Disk '//4 20X,' PLEASE SPECIFY ——> '\)READ(*,8810) io
8810 FORMAT(IS)IF(io.LT.0.0R.io.GT.2) GO TO 8002IF(io.LT.2) WRITE(*,8040)
8040 FORMAT(//20X,' Press "RETURN' to continue. '//)IF(io.EQ.2) WRITE(*,8030)
8030 FORMAT(//20X,' NAME OF OUTPUT FILE: '/1 20X,' (e.g. b:xyz.out) ——> '\)READ(*,8800) fout
105
C ÄIF(i0•EQ.l) OPEN(1,FILE='PRN')OPEN(5,FILE=fin,STATUS='OLD',ACCESS='SEQUENTIAL')IF(iO•EQ.2) OPEN(2,FILE=fout,STATUS='NEW',
1 ACCESS='SEQUENTIAL')REWIND 5
1 WRITE(i0,8045)8045 FORMAT(lHl,T5,'Program MOVEX'/)
CC...„„..•..„.„..„„....READ AND WRITE THE INPUT DATA......C
READ(5,99) title99 FORMAT(A72)100 FORMAT(1H,' ',A72)
WRITE(io,l00) titleREAD(5,*) mopt,noptREAD(5,*) nlay,nstrtWRITE(io,l01) n1ay,nstrt,nopt
101 FORMAT(lH0,TS,'CONTROL DATA'//l 1H,T10,'Number of soil layers',T40,I5,/2 lH,Tl0,'Number of struts',T40,I5/3 1H,Tl0,'Design Option',T43,I2)
CWRITE(io,102)
102 FORMAT(1H0,T5,'SOIL LAYER DATA',)READ(5,*) (j (i) ,h(i) ,qt(i) ,<=0 (i) ,d¢(i) ,i=lmlay)READ(5,*) dfde=0DO 50 i=l,n1ay
WRITB(io,120) iWRITE(i0,l2l) h(i),C0(i)WRITE (i0,122) gt(i),dC(i)de=de+h(i)
50 CONTINUEWRITE(io,1l0) df
110 FORMAT(lH0,Tl0,'Depth to firm layer from ground1 surface',T50,F9.3)
120 FORMAT(lH0,Tl0,'Layer number ',I2,/)121 FORMAT(Tl5,'Thickness',T30,F6.2,T40,'Cohesion',
1 T60,F6.2)122 FORMAT(Tl5,'Unit Weight',T30,F6.2,T40,'Coh. Increase',
1 T60,F6.2)C
READ(5,*) gw,wtWRITE(io,l04) gw,wt _
104 FORMAT(1H0,T5,'WATER TABLE DATA',//1 lH,T10,'Unit weight of water',T40,F7.2/2 lH,Tl0,'Depth to groundwater tab1e',T40,F7.2)IF(gw.EQ.0.) gw=l.0
C
106
READ(5,*) b,eln,hw,qWRITE(io,l05) b,eln,hw,q
105 FORMAT(1H0,T5,'EXCAVATION GEOMETRY'//1 1H,T10,'Tota1 width of excavation',7X,Fl0.2,/2 1H,Tl0,'Tota1 length of excavation',6X,Fl0.2/3 1H,Tl0,'Fina1 height of excavation',6X,F10.2,/4 lH,T10,'Surcharge next to excavation',5x,F8.2,)
chstrt=0.0shs=0.0havg=0.0savg=0.0sss=0.0ms=nstrt
cIF(nopt.EQ.0) GOTO 200IF(nopt.EQ.1) GOTO 210IF(nopt.EQ.2) GOTO 220IF(nopt.EQ.3) GOTO 230
‘
cc ...........nopt=0 input ............c
200 READ(5,*) eiREAD(5,*) (1(i),hs(i),s(i),i=1,nstrt)WRITE(io,l06) ei
106 FORMAT(T10,'Wa11 Stiffness',18X,El2.3) ‘
205 WRITE(io,l07)107 FORMAT(1H0,T5,'STRUT DATA',/
1 1H0,T10,'Strut Spacing Stiffness')DO 52 i=1,nstrt
WRITE(io,ll1) hs(i)WRITE(io,l08) l(i),s(i)hstrt=hstrt+hs(i)
52 CONTINUE
IF(hstrt.LT.hw) THENms=ms+lhs(ms)=hw-hstrtWRITE(io,ll1) hs(ms)
ENDIFlll FORMAT(T20,F5.2)108 FORMAT(T11,I2,T30,E13.4)
c174 WRITE(io,*)' '
IF(nopt.EQ.0) WRITE(io,*)' MOVEMENT CALCULATIONS'IF(nopt.EQ.1) WRITE(io,*)' WALL STIFFNESS CALCULATIONS'GOTO 400
c
1
107
C OOIUOOI•O•lnopt=l inputIOOIIOlIlI•¢C
C210 READ(5,*) dlm
WRITE(io,l09) dlm109 FORMAT(Tl0,'Maximum allowable vert. displacement',
1 2X F12„3)READ(5,*)'(l(i),hs(i),s(i),i=l,nstrt)GOTO 205
C
CC
220 READ(5,*) dlmWRITE(iO,109) dlmREAD(5,*) eiWRITE(i0,106) GiREAD(5,*) SavgWRITE(io,224) savg
224 FORMAT(T10,'Average stzut stiffness',7X,El3.4)WRITE(io 113)
113 FORMAT(1é0,T5,'STRUT SPACING CALCULATIONS')mS=5DO 222 i=1,5
hs(i)=hw/5222 CONTINUE
GOTO 400C
C OIOOOOOOt=·3 inputIOO•OOOlOO
C230 READ(5,*) dlm
WRITE(io,l09) dlmREAD(5,*) eiWRITE(io,106) eiREAD(5,*) (l(i),hs(i),i=l,nstrt)WRITE(io 234)
234 FORMAT(lé0,T5,'STRUT DATA',/1
232lH0,T10,'Strut Spacing',/)
DO i=1 nstrtWRITE(ié,ll1) hs(i)WRITE(iO,112) 1(i)hstrt=hstrt+hs(i)
232 CONTINUE112 FORMAT(Tll,I2)
IF(hstzt.LT.hw) THENms=ms+lhs(ms)=hw—hstrtWRITE(io,lll) hs(ms)
ENDIFWRITE(iO,*)' STRUT STIFFNESS CALCULATIONS'
C
108
c...............INTERACTIVE CHANGES IN THE DESIGN.........c
300 WRITE(*,310)310 FORMAT(//20X,'NAME OF INPUT FILE TO BE REWRITTEN:'/
1 20X,' (e.g. b:xyz2.dat) --> '\)READ(*,8800) finOPEN(5,FILE=fin,STATUS='NEW',ACCESS='SEQUENTIAL')CALL CHNG(mopt,nopt,ei,nstrt,hs,s,tit1e,n1ay,df,gw,wt,
1 dc,gt,h,j,c0,1,d1m,savg)GOTO 8002
C CALC€1F(h5(1)_EQ_9_9) TEEN
C i_ IF(m.EQ.1) THEN400 DO 402 m=l,mS g9T9 492ELSE
[ nx=m—·1j ENDIF
IF(nopt.EQ.2) GOTO 116 ENDIFWRITE(io,ll5) m —
115 FORMAT(1H0,T10,'Excavation Stage ',I2/)116 k=m-l
CALL FSHEAV(hS,m,k,wt,gw,n1ay,h,c0,dc,gt,fs,gm,he,1 df,ncpt)
cIF(nopt.EQ.2) GOTO 402
shs=Shs+hs(m)havg=shs/nxIF(nopt.EQ.3) GOTO 402SsS=SSS+S(m)savg=SsS/m
IF(m.EQ.1) GOTO 402IF(nopt.EQ.1) GOTO 402
CALL SDISP(fs,diSp,d1m,gm,he,ei,havg,savg,df,m,1 nopt,gw)
IF(mopt.EQ.0) CALL DSTRB(m,fS,he,diSp,d,dv,dl)402 CONTINUE
cIF(nopt.EQ.0) GOTO 405IF(nopt.EQ.1) THEN
CALL SDISP(fs,disp,d1m,gm,hw,ei,havg,savg,df,mS,1 nopt,gw)
IF(mopt.EQ.O) THENdisp(ms)=d1mCALL DSTRB(ms,fs,hw,diSp,d,dv,d1)
ENDIFGOTO 405
ENDIFIF(nopt.GE.2) THEN
IF(nopt.EQ.2) THENWRITE(io,408) fs(ms)
109
IF(fs(ms).LT.1.0) WRITE(io,409)ENDIF
408 FORMAT(lHO,T15,'Min. factor of safety for the1 excav. = ',F7.4)
409 FORMAT(/,Tl5,'**CAUTION: Factor of safety is less1 than l.0**')
CALL SDISP(fs,disp,d1m,gm,hw,ei,havg,savg,df,ms,1 nopt,gw)
IF(mopt.EQ.0) THENdisp(ms)=d1mCALL DSTRB(ms,fs,hw,disp,d,dv,d1)
ENDIFENDIF
c405 CLOSE (5)
IF(io.EQ.2) CLOSE (2)WRITE(*,600)
600 FORMAT(lH0,20X,' ')WRITE(*,8070)
8070 FORMAT(/////20X,' 1. MAKE CHANGES TO THE DESIGN'//1 20X,' 2. RUN A NEW RRoELEM'//2 20x,' 3. Ex1T TO Dos '///3 20X,' Please Specify 1, 2, or 3 -—-> '\)READ(*,88l0) ioptIF(iopt.EQ.l) GOTO 300IF(iopt.EQ.2) GOTO 150
c410 STOP
END
cc....................SUBROUTINE FSHEAV......................c
SUBROUTINE FSHEAV(hs,m,k,wt,gw,n1ay,h,c0,dc,gt,fs,gm,1 he,df,nopt)
cDIMENSION hs(20),h(20),c0(20),dc(20),Qt(20),fs(20)COMMON de,hw,b,q,io,eln
cht=0pe=0iend=0rc=Ohe=0cml=0cm=0fsk=fs(k)
c
ll0c .......incremental excavation depth ..........C
DO l i=l,m1 he=he+hS(i)
CIF(he.GE„df) THEN
fs(m)=fskGOTO 400
ENDIFCc ........side resistance .........C
DO 2 i=l,nlayht=ht+h(i)hl=h(i)IF(h€•GT.ht) GOTO 3h1=h(i)—(ht-he)iend=lIF(he.EQ.ht) iend=2
3 CONTINUEC
:c=rc+(c0(i)+dc(i)*hl/2.0)*hlpe=pe+gt(i)*hlIF(iend.NE.0) GOTO 6
C2 CONTINUE6 CONTINUE
Cgm=pe/he
b7=0.7*bd=df-heIF(b7.GE.d) fdb=dIF(b7•LT•d) fdb=b7
Cc ..find equivalent c below the bottom of the excavationC
l=iIF(ie¤d.EQ.2) l=i+1hb=he+fdb
CDO 10 k=l,nlay
j=kIF(iend.EQ.2) GOTO llIF(j.NE•l) GOTO ll
Ccl=c0(j)+dc(j)*hlc2=c0(j)+dc(j)*h(j)IF(ht.GE.hb) c2=c0(j)+dc(j)*(hl+fdb)IF(ht.GE.hb) iend=3dl=h(j)-hl
4 lll
IF(ht.GE.hb) d1=fdbcm=(cl+c2)/2-0 ’cm1=cm1+cm*d1pe=pe+gt(j)*d1GOTO 12
C
11 cl=c0(j)ht=ht+h(j)d1=h(j)IF(ht.GE.hb) d1=h(j)—ht+hbc2=c0(j)+dc(j)*dlIF(ht.GE.hb) iend=3cm=(c1+c2)/2.0cm1=cm1+cm*dlpe=pe+gt(j)*d1
C12 IF(iend.EQ.3) GOTO 1310 CONTINUE13 CONTINUE
C
C••••••••••••b€ati¤gC
bcf=5*(l.0+0.2*(b/eln))C
Sa.f€ty••••••••••••••
CIF((gm*he*fdb+q*fdb).LE.rc) THEN
fs(m)=fskGOTO 400
ENDIF.
fs(m)=(bcf*cml)/(gm*he*fdb+q*fdb—rc)C
IF(*“-E¤·l) GOTO l6° 11·‘(hs(1).1·:o.o.o> ·rx-muIF(fs(m).GT.fsk) fs(m)=fsk 1F(m_EQ_2) G9T9 159
160 CONTINUE ENDIFC
400 IF(nopt.EQ.2) GOTO 615'
610 WRITE(io,611) he611 FORMAT(T15,'Height of excavation = ',F10.3)
WRITE(io,116) fS(m)116 FORMAT(T15,'Factor of safety against basal heave = ',
1 F7.4)IF(fs(m).LT.1.0) WRITE(io,117)
117 FORMAT(1H0,T15,'**CAUTION: Factor of safety is less1 than 1.0**')
C
615 RETURNEND
112
cc........SUBROUTINE SDISP - FINDS DISPLACEMENT............c
SUBROUTINE SDISP(fs,disp,dlm,gm,he,ei,havg,savg,df,m,1 ¤opt,gw)
DIMENSION fsxl0(ll),fsyl0(ll),fsx11(1l),fsyll(1l),1 fsyl4(1l),fsx20(l1),fsy20(ll),fsx30(ll),fsy30(ll),2fsxl0a(1l),fsy10a(ll),fsx1la(ll),fsy1la(1l),fsx14a(l1),3fsy14a(11),fsx20a(l1),fsy20a(1l),fsx30a(1l),fsy30a(1l),4adx(4),ady(4),abx(4),aby(4),asx(4),asy(4),asxa(4),5asya(4),fs(20),s(20),disp(20),fsx(1l),fsy(1l),asx1(4),6 fsxl4(ll),asyal(4)
COMMON de,hw,b,q,io,elnc
DATA £sx1o/so.0,56.0,70.0,62.0,100.0,1s0.o,2oo.o,soo.o,1 500.0,l000.0,3000.0/,2 fsyl0/3.0,2.5,2.0,l.75,1.55,l.3,l.2,l.l,l.0,0.9,3 0.825/,4 fsxll/20.0,30.0,50.0,70.0,80.0,l00.0,l50.0,200.0,5 300.0700.0,3000.0/,6 fsyll/2.85,2.2,1.6,l.3,l.25,1.l25,l.0,0.9,0.8,0.7,7 0.55/,8 fSxl4/15.0,20.0,30.0,50.0,70.0,l00.0,200.0,300.0,9 500.0,l000.0,3000.0/,1 fsyl4/1.525,l.3,l.l,0.9,0.8,0.7,0.6,0.525,0.45,2 0.375,0.3/,3 fsx20/15.0,20.0,30.0,50.0,70.0,l00.0,200.0,300.0,4 500.0,l000.0,3000.0/,5 fsy20/0.75,0.65,0.6,0.5,0.45,0.4,0.35,0.3,0.275,6 0.25,0.2/,7 fsx30/15.0,20.0,30.0,50.0,70.0,l00.0,200.0,300.0,8 500.0,l000.0,3000.0/,9 fsy30/0.35,0.325,0.3,0.25,0.25,0.225,0.225,0.2,l 0.2,0.l75,0.15/
DATA fsxl0a/0.825,0.9,1.0,1.1,1.2,1.3,l.55,1.75,2.0,2 2.5,3.0/,8 fsyl0a/3000.0,l000.0,500.0,300.0,200.0,l50.0,9 l00.0,82.0,70.0,58.0,50.0/,l fsxlla/0.55,0.7,0.8,0.9,l.0,l.l25,1.25,l.3,1.6,2 2.2,2.85/,3 fsylla/3000.0,700.0,300.0,200.0,l50.0,100.0,80.0,4 70.0,50.0,30.0,20.0/,5 fsxl4a/0.3,0.375,0.45,0.525,0.6,0.7,0.8,0.9,l.l,6 1.3,1.525/,7 fsyl4a/3000.0,1000.0,500.0,300.0,200.0,100.0,70.0,8 50.0,30.0,20.0,l5.0/,9 fsx20a/0.2,0.25,0.275,0.3,0.35,0.4,0.45,0.5,0.6,l 0.65,0.75/,2 fsy20a/3000.0,1000.0,500.0,300.0,200.0,100.0,70.0,3 50.0,30.0,20.0,l5.0/,4 fsx30a/0.l5,0.175,0.2,0.2,0.225,0.225,0.25,0.25,
ll3
5 O.3,0.325,0.35/,6 fsy30a/$000.0,1000.0,500.0,300.0,200.0,l00.0,70.0,7 50•0,30.0,20.0,15.0/
DATA adx/1.0,l.4,l.66,2.0/,8 ady/0.62,0.87,0.96,l.O/,9 abx/0.8,1.67,3.2,4.0/,1 aby/l.0,1.2,l•6,1.8/,2 asx/60.0,133.3,533.3,l666.7/,3 asy/1.17,1.0,0.785,0.75/,4 asxa/1666.7,533.3,133.3,60.0/,5 asya/0.75,0.785,l.0,l.17/
Cc.....alfa d (depth to firm layer) ........C
n=4ds=df/heIF(dS.LE„1.0) THEN
ad=0.62GOTO 3
ENDIFIF(ds.GE.2.0) THEN
ad=l.0GOTO 3
ENDIFCALL COEFS(n,adx,ady,ds,ad)
3 -CONTINUECc......alfa b (excavation width) ..........C
n=4bs=b/heIF(bs.LE.0.5) THEN
ab=0.9GOTO 6
ENDIFIF(bS.GE.3.5) THEN
ab=1.7GOTO 6
ENDIFCALL COEFS(n,abx,aby,bs,ab)
6 CONTINUEc
IF(nopt.EQ.3) GOTO 200C
114
c......alfa s (strut stiffness) ............C
n=4DO 60 i=l,n
asxl(i)=ALOGl0(asx(i))60 CONTINUE
stf=ALOGl0(savg/(gw*he))IF(stf.GE.3.22) THEN
aS=0.75GOTO 62
ENDIFCALL COEFS(n,asxl,asy,stf,as)
C62 IF(nopt.EQ.0) GOTO 200
IF(nopt.EQ.1) GOTO 210IF(nopt.EQ.2) GOTO 210
Cc..........NOPT = 0 (find maximum displacement) .........C
200 n=1lsystf=ALOGl0(ei/((havg**4.0)*gw))IF(SyStf•GE.3•5) THEN
WRITE(io,203)203 FORMAT(Tl5,’Limits of FS/movement/stiffness curves
1 have been exceeded. No calculations2 made.’)
GOTO 300
ENDIFC
IF(fS(m)„GE.3.0) THENIF(systf.LE.l.0) THEN
' WRITE(io,203)GOTO 300
ENDIFDO 10 i=l,l1
fsx(i)=fsx30(i)fsy(i)=fsy30(i)
10 CONTINUE
115
ENDIFIF(fS(m)•GE.2.0) THEN
IF(fs(m).LT.3.0) THENIF(systf.LE.l.0) THEN
WRITE(io,203)GOTO 300
ENDIFDO 11 i=1,11
fsx(i)=fsx20(i)fsy(i)=fsy20(i)
11 CONTINUEENDIF
ENDIFIF(fS(m).GE.l.4) THEN
IF(fS(m).LT.2.0) THENIF(systf.LE.1.l8) THEN
WRITE(io,203)GOTO 300
ENDIFDO 12 i=l,1l
fsx(i)=fsxl4(i)fsy(i)=fsyl4(i)
12 CONTINUEENDIF
ENDIFIF(fS(m).GE.1.l) THEN
IF(fs(m).LT.1.4) THENIF(systf.LE.l.3) THEN
WRITE(io,203)GOTO 300
ENDIFDO 13 i=l,l1
fsx(i)=fsxll(i)fsy(i)=fsyl1(i)
13 CONTINUEENDIF
ENDIF _IF(fS(m).LT.1.1) THEN
IF(systf.LE.l.7) THENWRITE(io,203)GOTO 300
ENDIFDO 14 i=1,11
fsx(i)=fsxl0(i)fsy(i)=fsyl0(i)
14 CONTINUE
116
ENDIFENDIFIF(fS(m).LT.l.0) GOTO 300DO l i=l,ll
fSx(i)=ALOGl0(fSx(i))1 CONTINUE
CALL COEFS(n,fsx,fsy,systf,dh)205 IF(nopt.EQ.3) GOTO 230
disp(m)=dh*ad*ab*as*he*0.01WRITE(io,l06) diSp(m)
106 FORMAT(T15,'Max. lateral wall movement = ',F10.3)GOTO 300
Cc........nopt=1 and nopt=2 curves .......C
210 n=11dh=d1m/(ad*ab*as)IF(fs(m).GE.3.0) THEN
IF(dh•GE.0.35) THEN .
WRITE(io,203)GOTO 300
ENDIFIF(dh.LE.0.l5) THEN
WRITE(io,203)GOTO 300
ENDIFDO 15 i=1,1l
fsx(i)=fsx30a(i)fsy(i)=fsy30a(i)
15 CONTINUEENDIFIF(fS(m)„GE.2.0) THEN
IF(fs(m).LT.3.0) THENIF(dh.GE.0.75) THEN
WRITE(io,203)GOTO 300
ENDIFIF(dh.LE.0.2) THEN
WRITE(io,203)GOTO 300
ENDIFDO 16 i=l,ll
fsx(i)=fsx20a(i)fsy(i)=fsy20a(i)
16 CONTINUE
ll7
ENDIFENDIFIF(fS(m).GE.1.4) THEN
IF(fS(m).LT„2.0) THENIF(dh.GE.2.0) THEN
WRITE(io,203)GOTO 300
ENDIFIF(dh•LE.0.3) THEN
WRITE(io,203)GOTO 300
ENDIFDO 17 i=1,1l
fsx(i)=fsxl4a(i)fsy(i)=fsy14a(i)
17 CONTINUEENDIF
ENDIFIF(fs(m)•GE.l.l) THEN
IF(fS(m).LT.1.4) THENIF(dh•GE.2.85) THEN
WRITE(io,203)GOTO 300
ENDIFIF(dh.LE.0.55) THEN
WRITE(io,203)GOTO 300
ENDIFDO 18 i=l,1l
fsx(i)=fsxlla(i)fsy(i)=fsyl1a(i)
18 CONTINUEENDIF
ENDIF
IF(fs(m).LT.1.1) THENIF(dh.GE.3.0) THEN
WRITE(io,203)GOTO 300
ENDIFIF(dh.LE.0.825) THEN
WRITE(io,203)GOTO 300
ENDIF
118DO 19 i=1,1l
fsx(i)=fsxl0a(i)fsy(i)=fsy10a(i)
19 CONTINUEENDIF
DO 5 i=l,llfsy(i)=ALOG10(fsy(i))
5 CONTINUEIF(nopt.EQ.2) GOTO 220
cc.........nopt=1 calculations (find wall stiffness) .....c
CALL COEFS(n,fsx,fsy,dh,systf)235 ei=(10.0**systf)*gw*(havg**4.0)
WRITE(io,108) ei108 FORMAT(1H0,T10,' Required wall stiffness = ',El0.3)
GOTO 300cc.........nopt=2 calculations (find strut spacing) ........c
220 CALL COEFS(n,fsx,fsy,dh,systf)225 havg=(ei/((l0.0**systf)*gw))**0.25
WRITE(io,l09) havg109 FORMAT(lH0,Tl0,'Required average strut spacing = ',
1 F10.3)GOTO 300
cc.........nopt=3 calculations (find strut stiffness) ......C
•
230 n=4DO 232 i=1,n
asya1(i)=ALOG10(asya(i))232 CONTINUE
as=d1m/((dh/l00)*he*ad*ab)IF(as.LE.0.75) THEN
sstf=l666.7‘GOTO 234
ENDIFCALL COEFS(n,asxa,asya1,as,sstf)
234 savg=(10.0**sstf)*gw*heWRITE(io,236) savg
236 FORMAT(1H0,Tl0,'Required average strut stiffness = ',1 E13.4)
c300 RETURN ·
END
119
cc........................SUBROUTINE COEFS ..................c
SUBROUTINE COEFS(n,x,y,a,b)DIMENSION x(n),y(n),c(4,4),d(4),work(4),ipvt(4)
cIF(a.GT.x(2)) GOTO 1
xl=x(1)x2=x(2)x3=x(3)x4=x(4)Y1=y<l)y2=y<2)y3=y(3)y4=y(4>
GOTO 2c
1 nl=n—lIF(a.LT.x(nl)) GOTO 5
xl=x(n—3)x2=x(n-2)x3=x(n—l)x4=x(n)Yl=y(n—3)Y2=y(¤—2)y3=y(n—l) -Y4=y(¤>
GOTO 2c
5 n2=n—2DO 3 i=2,n2
IF(a.LT.x(i).OR.a.GT.x(i+1)) GOTO 3xl=x(i-l)x2=x(i)x3=x(i+1)x4=x(i+2)yl=y<1—1>y2=y(i>Y3=Y(i+l)Y4=Y(i+2)
GOTO 23 CONTINUE2 CONTINUE
120
CDO 4 i=l,4
IF(i.EQ.l) xc=xlIF(i.EQ.2) xc=x2IF(i.EQ.3) xc=x3IF(i.EQ.4) xc=x4
c(i,l)=xc*xc*xcc(i,2)=xc*xcc(i,3)=xcC(i,4)=l.0
4 CONTINUEc
CALL DECOMP(4,4,c,cond,ipvt,work)c
d(l)=yld(2)=y2d(3)=y3d(4)=y4
cCALL SOLVE(4,4,c,d,ipvt)
cb=d(l)*a*a*a+d(2)*a*a+d(3)*a+d(4)
cRETURNEND
cc........................SUBROUTINE DECOMP .................c
SUBROUTINE DECOMP(ndim,n,a,cond,ipvt,work)c
INTEGER ndim,nINTEGER ipvt(n)REAL a(ndim,n),cond,work(n)
cipvt(n)=1IF(n.EQ.l) GOTO 80nml=n-1anorm=0
cDO j=lyn
t=0.0DO 5 i=l,n
t=t+ABS(a(i,j))5 CONTINUE
IF(t.GT.anorm) anorm=t10 CONTINUE
l2l
cDO 35 k=l,nml
kpl=k+lm=kDO 15 i=kp1,n
IF(ABS(a(i,k)).GT.ABS(a(m,k))) m=i15 CONTINUEipvt(k)=m
IF(m.NE.k) ipvt(n)=-ipvt(n)t=a(m,k)a(m,k)=a(k,k)a(k,k)=t
IF(t.EQ.0.0) GOTO 351 DO 20 i=kpl,na(i,k)=-a(i,k)/t
20 CONTINUEDO 30 j=kpl,n
t=a(m,j)a(mrj)=a(krj)a(k,j)=tIF(t.EQ.0.0) GOTO 30DO 25 i=kpl,n
a(i,j>=a(i,j)+a(i„k)*t25 CONTINUE30 CONTINUE35 CONTINUE
cDO k=lyn
t=0.0IF(k.EQ.1) GOTO 45kml=k-1DO 40 i=l,km1
t=t+a(i,k)*work(i)40 CONTINUE45 ek=1.0
IF(t.LT.0.0) ek=-1.0IF(a(k,k).EQ.0.0) GOTO 90work(k)=-(ek+t)/a(k,k)
50 CONTINUEc
DO 60 kb=1,nmlk=n-kbt=0.0kpl=k+lDO 55 i=kp1,n
t=t+a(i,k)*work(k)55 CONTINUE
122
work(k)=tm=ipvt(k)IF(m•EQ•k) GOTO 60t=work(m)work(m)=work(k)work(k)=t
60 CONTINUEC
ynorm=0.0DO i=lyn
ynorm=ynorm+abs(work(i))65 CONTINUE
C
CALL SOLVE(ndim,n,a,work,ipvt)znorm=0.0DO 70 i=l,n
znorm=znorm+ABS(work(i))70 CONTINUE
C0¤d=a¤0rm*znOtm/yuorm
IF(cond.LT.l.0) cond=l.0RETURN
80 cond=1.0IF(a(1,l)„NE.0.0) RETURN
90 cond=1.0E+32C
RETURNEND
C
c..........................SUBROUTINE SOLVE„..•„„„...„„„„.„C
SUBROUTINE SOLVE(ndim,n,a,b,ipVt)C
INTEGER ndim,n,ipvt(n)REAL a(ndim,n),b(n)
CIF(n.EQ.l) GOTO 50nml=n—lDO 20 k=l,nm1
kpl=k+lm=ipvt(k)t=b(m)b(m)=b(k)b(k)=tDO 10 i=kpl,n
b(i)=b(i)+a(i,k)*t10 CONTINUE20 CONTINUE
123
CDO 40 kb=l,nml
kml=n—kbk=kml+lb(k)=b(k)/a(k,k)t=-b(k)DO 30 i=1,km1
b(i)=b(i)+a(i,k)*tR 30 CONTINUE
40 CONTINUE50 b(l)=b(l)/a(l,l)
CRETURNEND
Cc.....................SUBROUTINE DSTRB....„..„..„•.„......•
—
SUBROUTINE DSTRB(m,fs,he,disp,d,dv,dl)DIMENSION fS(20),d(8,20),dV(8,20),dl(8,20),x(9,20),
1 V y(8,20),z(8,20),fl0x(8),fl0y(8),fl3x(8),fl3y(8),2 fl7x(8),fl7y(8),f22x(8),f22y(8),f24x(8),f24y(8),3 gl0x(8):Ql0y(8):gl5x(8)«ql5y(8),disp(20)
COMMON de,hw,b,q,io,elnCc .........distrib. of vert. movement ...........C
DATA g10x/0.0,0.5,1.0,1•5,2.0,2.5,3.0,3.5/,1 glOy/1.0,1.0,1.0,0.575,0.25,0.125,0.1,0.09/,2 gl5x/0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5/,3 g15y/1.0,1.0,0.95,0.75,0.6,0.45,0.3,0.25/n=8
i=lx(i,m)=0.0fs1=fs(m)
14 dl=x(i,m)IF(fS1„LE.1.25) CALL COEFS(n,g10x,gl0y,d1,d2)IF(fs1.GT.1.25) CALL COEFS(n,gl5x,g15y,d1,d2)y(i,m)=d2d(i,m)=x(i,m)*hedv(i,m)=y(i,m)*disp(m)j=i+lx(j,m)=x(i,m)+0.5i=i+1IF(i.EQ„9) GOTO 15GOTO 14
15 CONTINUEC
124
c ........distrib. of lateral movement .......c
DATA f10x/0.0,0.5,1.0,l.5,2.0,2.5,3.0,3.5/,1 fl0y/0.05,0.14,0.35,0.26,0.l7,0.1,0.06,0.02/,2 fl3x/0.0,0;5,l.0,l.5,2.0,2.5,3.0,3.5/,3 f13y/0.06,0.18,0.4,0.38,0.26,0.l7,0.1,0.06/,4 fl7x/0.0,0.5,1.0,l.5,2.0,2.5,3.0,3.5/,5 f17y/0.15,0.34,0.5,0.43,0.32,0.22,0.14,0.08/,6 f22x/0.0,0.5,l.0,l.5,2.0,2.5,3.0,3.5/,7 f22y/0.2,0.45,0.71,0.78,0.6,0.44,0.35,0.26/,8 f24x/0.0,0.5,l.0,l.5,2.0,2.5,3.0,3.5/,9 f24y/0.36,0.72,0.92,0.98,0.94,0.82,0.65,0.5/
ci=lx(i]m)=o•0
16 d1=x(i,m)IF(fsl.LE.l.17) CALL COEFS(n,f10x,f10y,dl,d2)IF(fs1.GT.l.l7) THEN
IF(fs1.LT.1.5) CALL COEFS(n,fl3x,f13y,dl,d2)ENDIFIF(fsl.GE.l.5) THEN
IF(fs1.LT.l.95) CALL COEFS(n,fl7x,f17y,d1,d2)ENDIFIF(fs1.GE.1.95) THEN
IF(fs1.LT.2.3) CALL COEFS(n,f22x,f22y,d1,d2)ENDIFIF(fSl.GE.2.3) CALL COEFS(n,f24x,f24y,d1,d2)z(i,m)=d2dl(i,m)=z(i,m)*disp(m)j=i+lx(j,m)=x(i,m)+0.5i=i+lIF(i.EQ.9) GOTO 17GOTO 16
17 CONTINUEc
WRITE(io,20)20 FORMAT(lH0,Tl5' Distribution of Ground Surface
l Movement',)WRITE(io,2l)
21 FORMAT(lH0,T23,'dist. fr. wall',4X,'vert. disp.',1 5X,'1at. disp.'/)
DO 25 i=1,8WRITE(io,22) d(i,m),dv(i,m),d1(i,m)
25 CONTINUE22 FORMAT(T20,F10.2,T40,Fl0.4,T55,Fl0.4)
cRETURNEND
125
Cc...................SUBROUTINE CHNG•••••...„.„••.„...•.„.••
CSUBROUTINE CHNG(mopt,nopt,ei,nstrt,hs,s,title,n1ay,df,
1 -gw,wt,dc,gt,h,j,c0,1,dlm,savg)DIMENSION hS(20),1(20),dc(20),gt(20),h(20),j(20),
1 c0(20),S(20)CHARACTER tit1e*72COMMON de,hw,b,q,i0,e1n
chstrt=0IF(nopt.EQ.l) GOTO 107
c100 WRITE(*,101)101 FORMAT(//20X,'Change wall stiffness? (yes=l, no=2)'/
1 20X,' Please specify -—> '\)READ(*,102) iyn
102 FORMAT(I2)IF(iyn.LT.1) GOTO 100IF(iyn„GT.2) GOTO 100IF(iyn.EQ.2) GOTO 107WRITE(*,103)
103 FORMAT(//20x,'New wall stiffness ——> '\)READ(*,*) ei
cIF(nopt.EQ.3) GOTO 107IF(nopt.EQ.2) THEN
120 WRITE(*,121)121 FORMAT(//20X,'Change average strut stiffness?
1 (yes=1, no=2)'/ 20X,' Please specify —-> '\)READ(*,102) iynIF(iyn.LT.1) GOTO 100IF(iyn.GT.2) GOTO 100IF(iyn.EQ.2) GOTO 107WRITE(*,123)
123 FORMAT(//20X,'New average strut stiffness ——> '\)READ(*,*) savgGOTO 500
ENDIFc
107 WRITE(*,l08)108 FORMAT(//20X,'Change number of struts? (yes=1, no=2)'/
1 20X,' Please specify —-> '\)READ(*,102) iynIF(iyn.LT.l) GOTO 107IF(iyn.GT.2) GOTO 107
”
IF(iyn„EQ•2) GOTO 105WRITE(*,109)
109 FORMAT(//20X,'New number of struts -—> '\)READ(*,110) nstrt
110 FORMAT(I2)
126
ms=nstrtGOTO 113
C105 WRITE(*,l06)106 FORMAT(//20X,'Change strut spacing? (yes=1, no=2)'/
1 20X,' Please specify -—> '\)READ(*,102) iynIF(iyn.LT„1) GOTO 105IF(iyn.GT.2) GOTO 105IF(iyn.EQ.2) GOTO 114
113 DO 112 i=1,nstrtWRITE(*,111) i
111 FORMAT(/20X,'New spacing for strut ',I2,' -—> '\)READ(*,*) hs(i)hstrt=hstrt+hs(i)
112 CONTINUEIF(hStrt.GE.hW) GOTO 114ms=ms+1 -hs(ms)=hw-hstrt
CIF(n0pt.EQ.3) GOTO 500
C114 WRITE(*,115)115 FORMAT(//20X,'Change strut stiffness? (yes=1, no=2)'/
1 20X,' Please specify --> '\)READ(*,102) iynIF(iyn„LT.1) GOTO 114IF(iyn.GT.2) GOTO 114IF(iyn.EQ•2) GOTO 500
118 DO 116 i=1,nstrtWRITE(*,l19) i
119 FORMAT(/20X,'New stiffness for strut ',I2,' ——> '\)READ(*,*) S(i)
116 CONTINUECc........write data into file......C
500 REWIND 5WRITE(5,*) titleWRITE(5,*) mopt,noptWRITE(5,*) n1ay,nstrtDO 501 i=1,n1ay
wR1TE(5,*) 1,h(i),qt(i),c0(1),dc(1)501 CONTINUE
WRITE(5,*) df ·WRITE(5,*) gw,wtWRITE(5,*) b,e1n,hw,q
C
127
IF(n0pt.EQ.0) GOTO 1000IF(n0pt•EQ.l) GOTO 2000IF(n0pt.EQ.2) GOTO 3000IF(nopt.EQ.3) GOTO 4000
C1000 WRITE(5,*) ei1001 DO 1002 i=1,nstrt
WRITE(5,*) i,hs(i),s(i)1002 CONTINUE
GOTO 5000C
2000 WRITE(5,*) dlmGOTO 1001
C3000 WRITE(5,*) dlm
WRITE(5,*) eiWRITE(5,*) savg
C4000 WRITE(5,*) dlm
WRITE(5,*) eiDO 4002 i=l,nstrt
WRITE(5,*) i,hS(i),S(i)4002 CONTINUE
C5000 CLOSE (5)
RETURNEND
APPENDIX D
List of Variables
128
129
A = cross—sectional area of struta = vertical dimension of tributary areaB = width of excavationD' = distance between base of excavation and firm layerE = modulus of elasticityFS = factor of safety against basal heaveH = total height of excavation wallh = thickness of individual soil layershavg = average strut spacing
I = moment of inertiaka = coefficient of active earth pressure
Ke = effective strut stiffness
Ki = ideal strut stiffness
KS = ratio of Sugo to Suo n
L = longest vertical span between struts (equation 2.6)L = length of failure surface below excavation
(equation 2.7)L = length of excavation (equation 2.10)L = unsupported strut length (equation 3.1)M = bending moment of the wallN } stability numbersNbNC = bearing capacity factor
N; = anisotropic bearing capacity factorP = average strut preloadPa = horizontal force on wall from earth pressure
q = surcharge adjacent to excavations = horizontal dimension of tributary areasu = average undrained shear strength adjacent to the
excavationsub = average undrained shear strength below the excavation
suo = average undrained shear strength for vertical majorprincipal stress
su45 = average undrained shear strength for major principalstress at 45°
sugo = average undrained shear strength for horizontal majorprincipal stress
w = uniformly distributed load
130
GB = correction factor for excavation width
GD = correction factor for depth to firm layer
GS = correction factor for strut stiffnessOW = correction factor for wall stiffness
SH;ax = corrected maximum lateral wall movement
Sümax = uncorrected maximum lateral wall movementX = total unit weight of soil
K' = effective unit weight of soil
Kw = unit weight of water
¢ = angle of internal frictionU‘é = horizontal effective stress
131
ab = alfa bad = alfa db = excavation widthbcf = bearing capacity factorbs = excavation width/height of excavtionb7 = 0.7 ° excavation widthcm = avarage cohesion below excavationcml = cohesion times length of failure surfacec0(i) = undrained shear strength of layer 'i'cl = average cohesion below excavationc2 = cohesion at either bottom of layer or bottom of
failure mechanismd = distance between bottom of excavation and firm layerde = depth of excavationdf = depth to firm layerdh = nondimensionalized wall movementdlm = maximum allowable displacementds = depth to firm layer/height of excavationd(i,j) = ratio of distance from wall to wall height at
distance 'i', stage 'j'dc(i) = change in shear strength with depth of layer 'i'disp(i) = wall movement at stage 'i'dl(i,j) = distribution of lateral ground movementdv(i,j) = distribution of vertical ground movementei = wall stiffnesseln = excavation lengthfdb = depth of failure mechanismfin = name of input file -fout = name of output filefsk = factor of safety at previous stagefs(i) = factor of safety for stage 'i'gm = average total weight adjacent to excavationgw = unit weight of watergt(i) = total unit weight of soil layer 'i'hb = distance form ground surface to bottom of failure
mechanismhe = incremental height of excavation (per stage)hl = portion of soil layer adjacent to excavationhstrt = incremental strut height sumht = incremental layer thickness sumhw = final height of excavation wallh(i) = thickness of soil layer 'i'hs(i) = distance between strut 'i' and next higher strutio = output destination (screen, printer, or disk)iopt = ending control option (changes, new program, DOS)mopt = movement optionnlay = number of soil layers adjacent to and below
excavation
132
111.6; 9; 1aL.i9.b.1s.$ .1.9 LOL;. (con'1:)
nopt = design optionnstrt = number of strutspe = incremental total stress sumq = surcharge adjacent to excavationrc = resistance to sliding (from cohesion) on vertical
failure planesavg = average strut stiffnessshs = temporary strut spacing sumsss = temporary strut stiffness sumstf = nondimensionalized strut stiffness sumsystf = nondimensionalized strut stiffnesss(i) = stiffness of strut 'i'title = any identifying titlewt = depth to water tablex(i,j) = distance 'i' from the wall at stage 'j'y(i,j) = ratio of vertical ground movement to maximum“
movement at distance 'i' from wall at stage 'j'z(i,j) = ratio of lateral ground movement to maximum
movement at distance 'i' from wall at stage 'j'
giääg}-—coordinates of FS = 1.0 curve in Figure 3.3§;;§§}——coordinates of FS = 1.1 curve in Figure 3.3giääj}-—coordinates of FS = 1.4 curve in Figure 3.3§;;äg}——coordinates of FS = 2.0 curve in Figure 3.3§;;äg}——coordinates of FS = 3.0 curve in Figure 3.3giäägä}--inverted coordinates of FS = 1.0 in Figure 3.3ääääää}-—inverted coordinates of FS = 1.1 in Figure 3.3§;;ä:;}——inverted coordinates of FS = 1.4 in Figure 3.3giäägä}-—inverted coordinates of FS = 2.0 in Figure 3.3fSX30a}——inverted coordinates of FS = 3.0 in Figure 3.3fsy30a;;;}—-coordinates of alfa — S curve in Figure 3.4ääää}--inverted coordinates of alfa — S curve in Figure 3.4ggg}--coordinates of alfa — D curve in Figure 3.7;ä;}——coordinates of alfa - B curve in Figure 3.8
133
Lis; 9.; in LOELS; (con't)
gäg;}-—coordinates of FS = 1.0 in Figure 3.9
gig;}-—coordinates of FS = 1.5 in Figure 3.9
§äg;}—-coordinates of FS = 1.0 in Figure 3.10§§ä;}—-coordinates of FS = 1.3 in Figure 3.10§ä;;}—-coordinates of FS = 1.7 in Figure 3.10ggg;}--ccordinates of FS = 2.2 in Figure 3.10§ä:;}—-coordinates of FS = 2.4 in Figure 3.10
APPENDIX E
Appareut Pressure Program
134
135
The subroutine listed here, called APRES, was written to
calculate the apparent pressure, strut loads, and the bending
moment in thewall of a braced excavation. There are some
technical and conceptual difficulties with APRES as it now
stands, that should be addressed in the future. Since the
subroutine is compatible with MOVEX, with some changes it
could be included in the program.
IlIOIOOISUBRINE ESOOOIOIII
cSUBROUTINE APRES(hs,nstrt,wt,gw,h,n1ay,ms,c0,dc,gt,he,
l qstrt,wmom,df)DIMENSION hs(10),h(20),c0(20),dc(20),9t(20):Phi(20),
1 cavg(20),a(20),qStIt(20)COMMON de,hw,b,q,io
ctri=0ht=0ep=0sigz=0sigzw=Oacont=0tcont=0
cWRITE(io,l00)
100 FORMAT(lH0,T5,'STRUT LOADS')cc.....define tributary areas.......c
DO 18 j=l,nstrtk=j+lIF(j.EQ.l) a(j)=hs(j)+0.5*hs(k)IF(j.GT.1) a(j)=0.5*(hs(j)+hs(k))IF(j.EQ.nstrt) a(j)=0.5*hs(j)+hs(k)
18 CONTINUEc
DO 10 i=1,n1ayl=i-1hl=h(i)ht=ht+h(i)IF(ht.GT.df) GOTO 10IF(ht.GT.hw) h1=hw—(ht—h(i))
136
Cc.....calculate sand earth pressure.....C
3 IF(phi(i).EQ.0.0) GOTO 12ang=(3.14159/180.0)*(45—phi(i)/2)aep=(tan(ang))**2
CIF(wt.GE•ht) THEN
ep=ep+l.3*aep*(0.5*gt(i)*h1**2.0+sigz*h1)sigz=sigz+gt(i)*hlGOTO 10
ENDIFIF(wt.LT•ht) THEN
hp=ht-h(i)IF(wt.GT.hp) THEN
hup=wt-hphdn=h1-hupep=ep+l.3*aep*(0.5*gt(i)*hup**2.0+sigz*hup)sigz=sigz+(gt(i)*hup)sigw=sigw+(gw*hdn)ep=ep+1.3*aep*(0.5*(gt(i)—gw)*hdn**2.0+
1 · sigz*hdn)+0.5*sigzw*hdnGOTO 10
ELSEsigzw=sigzw+gw*hl€p=ep+l.3*aep*(0.5*(gt(i)—gw)*h1**2.0+
1 sigz*hl)+0.5*sigzw*hlsigz=sigz+(gt(i)—gw)*hlGOTO 10
ENDIFENDIF
Cc.....calculate clay earth pressure....C
12 cavg(i)=(c0(i)+(c0(i)+dc(i)*hl))/2sigz=sigz+gt(i)*h1é1=1.75*h1*(0.3*(Sigz+q))e2=l.75*hl*(sigz+q-2*cavg(i))ep=AMAXl(e1,e2)IF(i•EQ•l) THEN
tri=0.25*hwELSE
tri=0.0ENDIF
C10 CONTINUE
1374
Cc.......appareut pressure diagram........C
w=ep/hwIF(tri„GT.0.0) THEN
w=eP/(0.875*hw)ENDIFWRITE(io,50) w
50 FORMAT(lH0,Tl0,'Apparent pressure = ',El5.7,/)Cc......calculate strut loads........C
DO 25 j=l,nstrtacont=acont+a(j)IF(tri•EO•0.0) THEN
qstrt(j)=w*a(j)GOTO 20
ENDIFIF(tcont.EQ.0.0) THEN
IF(acont.LT.tri) qstrt(j)=(0.5*w*(a(j)**2.0))/triIF(acont.EQ.tri) qstrt(j)=O.5*w*triIF(acont.GT.tri) qstrt(j)=0.5*w*tri+w*(a(j)-tri)GOTO 20
ENDIFIF(tcont.LT.tri) THEN
IF(acont.LT.tri) THENbl=w*acont/trib2=w*tcont/triqstrt(j)=bl*a(j)+0.5*(b2—bl)*a(j)GOTO 20
ENDIFIF(acont.EQ.tri) THEN
bl=w*tcont/triqStrt(j)=0.5*(w—bl)*a(j)+bl*a(j)GOTO 20
ENDIFIF(acont.GT.tri) THEN
bl=w*tcont/triqstrt(j)=bl*a(j)+0.5*(w-bl)*a(j)+(acont-tri)*wGOTO 20
ENDIFENDIFIF(tco¤t.GE.tri) qstrt(j)=a(j)*w
20 tcont=tcont+a(j)WRITE(io,32) j,qStrt(j)
32 FORMAT(Tl5,'Strut ',I2,' load = ',El2.4)25 CONTINUE
138
Cc.....wall stiffness.........C
IF(hS(l).GT•0.0) THENl=3
ELSEl=2
ENDIFDO 40 j=l,nstrt
k=j—lIF(hs(j).GE.hs(k)) span=hs(j)
40 CONTINUEC
pww=0.6667*wWRITE(iO,44) pww
44 FORMAT(lH0,T10,'Pressu:e for wall and wale design = 'IF(hs(l).EQ„0.0) GOTO 96IF(tIi„GT•0„0) THEN
IF(hs(l).LT.tri) THENpwc=(0.6667*hs(l)**2.0*tri)/w
ENDIFIF(hS(l)•EQ•tIi) THEN
pwc=0.6667*tri*wENDIFIF(hs(l).GT.tri) THEN
pwc=0.6667*tri*w+((hs(l)-tri)*w)ENDIF
ELSEpWC=pWW
ENDIF96 IF(hs(l).GT.0.0) THEN
wmoml=0.5*pwc*(hs(1)**2.0)ELSE
wmoml=0.0ENDIF
g C98 IF(nstrt.LT.3) wmom2=0.l25*pww*span**2
IF(nstrt.EQ.3) wmom2=0.l0*pww*span**2IF(nstrt.GT.3) wmom2=0.083*pww*span**2
Cwmom=AMAXl(wmoml,wmom2)WRITE(io,62) wmom
62 FORMAT(Tl0,'Maximum bending moment in wall = ',E15.7,/)C
RETURNEND
E
