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CHAPTER 2
TECHNICAL BACKGROUND
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2.1 BEHAVIOR OF STIFF EXCAVATION SUPPORT SYSTEMS
IN SOFT TO MEDIUM CLAY
Deformations of an excavation support system
and the adjacent ground are influenced by a number of factors
including support
system stiffness, method of support system installation,
and soil conditions. When average to good workmanship is
employed and the clays are relatively soft, the resulting
deformations are most influenced by the support system stiffness,
and thus, is the key design parameter used to control ground
movements. The ability to explicitly consider the support
system stiffness is important to producing predicted behavior
consistent with
the observed ground and wall response.
A stiff braced support system is typically
used when the deformations of ground adjacent to the excavation
must be
limited, particularly when excavating through soft clays.
The stiffness of an excavation support system is a function
of the flexural rigidity of the wall element, the structural
stiffness of the support elements, and the type of connections
between the wall and supports, and the vertical and horizontal
spacing of the supports.
The overall stiffness of the support
system is typically expressed in terms of an effective
stiffness of the system.
Mana and Clough (1981) gave the effective wall stiffness,
S, as:
where EI is the wall flexural stiffness per
horizontal unit of length (E is the modulus of elasticity
of the wall element and I is the moment of inertia
per length of wall), H is the average vertical spacing between supports,
and γ is
the total unit weight of the soil behind the wall. Koutsoftas et al. (2000)
and Clough at el. (1989) defined effective system stiffness similar to the
definition in (2.1), except the unit weight of soil is replaced with the
unit weight of water, γw.
The unit weight is introduced to non-dimensionalize the equation.
Walls that
are considered stiff on the basis of the rigidity of the wall element include
secant and tangent pile walls
and structural slurry walls (often referred to as diaphragm
walls in the literature). Walls that are considered flexible
on the basis of the rigidity of the wall element include
steel sheet pile walls and soldier pile and lagging walls.
2.1.1 General Deflection Behavior of Excavation
Support System
The behavior of excavation support systems
can be expressed in terms of the ground surface settlements
and lateral wall
deformations. These movements are a function the flexural
rigidity of the wall component, the stiffness of the supports,
the earth pressures and water loads, the general soil and
groundwater conditions, and the construction procedures.
Lateral ground deformations associated with excavation support
systems are a response to the wall deflection. For relatively
small deformations, the profile of lateral ground movements
behind the support system tend to match the deflected shape
of the wall near the wall.
Braced excavations are typically
performed in three stages:
(i) Wall installation
(ii) Cycles of excavation and lateral support installation
(iii) Removal of the supports and backfill.
General ground movements profiles, not considering the
effects of wall installation, as observed for a typical excavation
are illustrated in Figure
2-1. These profiles would most likely be obtained from
inclinometer and settlement measurements. The figure shows
that during the initial excavation, before the installation
of the first level of lateral support, the wall deforms as
a cantilever. Settlement of the adjacent soil tends to decrease
with distance from the edge of the excavation. Settlements
during this stage may be represented by a triangular distribution
of displacements. When the excavation advances to deeper
elevations, upper wall movements are restrained by the installation
of new supports. Deep inward movements of the wall occur.
The deflected shape of the wall shows a bulge in the deeper
portion of the excavation.
If deep inward movements are the
predominant form of wall deformation, as in the case with
deep excavations in soft
to medium clay, then the settlements tend to be bounded
by a trapezoidal displacement profile. If cantilever movements
predominate, as can occur for excavations in sands and
stiff
to very hard clay, then settlements tend to follow a triangular
pattern. Further inward bulging of the wall occur as the
bottom supports are removed. The combination of cantilever
and deep inward components results in the cumulative wall
and ground surface displacements shown in Figure 2-1. Additional
cantilever-type deformation at the top of the wall results
when the upper supports are removed. In soft to medium
clays, small amounts of deformation may be observed until
backfill
is complete. There are typically no additional movements
in stiff clays during the backfill operations.
The patterns
of movements shown in Figure 2-1 have been justified by theory
and from observed behavior. Theoretical
and experimental studies by Milligan (1985) have shown that
incremental deformations of the wall will generate deformations
consistent with those for the cantilever and deep inward
movements delineated in Figure 2-1. O'Rourke et al.
(1976), O'Rourke (1981), and Finno et al. (1989) have
presented cases of observed behavior supporting the patterns
of movements shown in Figure 2-1. However, this figure only
describes the general deflection behavior of the wall in
response to the excavation. The soil conditions, wall installation
methods, and the effective stiffness of the excavation support
system are specific factors that influence the magnitude
of movements of the support system.
2.1.2 Influence of Soil Conditions
The behavior of an excavation support system in clay is
greatly influenced by the undrained shear strength of the
clay. Clough and O'Rourke (1990) concluded that the
average horizontal and vertical movements of support systems
in stiff clays were roughly 0.2 percent and 0.15 percent
of the total excavated depth, respectively. Their findings
agree with guidance established in Canadian Foundation Engineering
Manual (1985), which states that lateral movements of temporary
support systems in stiff clay are less than 0.2 percent of
the excavation depth. This compares to guidance established
in NAVFAC DM-7.2 (1982) that suggests in stiff fissured clays
lateral movements may reach 0.5 percent of the total excavated
depth or higher depending on quality of construction.
Clough
and O'Rourke (1990) also conducted a finite
element parametric study on stiff clays. Their analyses showed
that parameters such as wall stiffness and support spacing
have only a small influence on the predicted movements in
these soils because in most circumstances these soils are
stiff enough to minimize the need for stiff support elements.
They found soil modulus and coefficient of lateral earth
pressure have a more significant impact on the ground movements.
Their results suggested that in a stiff soil, variations
in soil stiffness have a more profound effect on wall behavior
than system stiffness.
Clough and O'Rourke (1990) noted
that basal stability is typically not an issue in stiff clays.
In soft clays however,
a major portion of movement occurs below excavation bottom
as a result of basal instability. Lateral movement may be
in the range of 0.5 percent to 2 percent of excavation depth,
depending on the factor of safety against bottom instability
and the stiffness of the support system. Higher movements
are associated with smaller factors of safety against basal
heave. Peck (1969) and, Clough and Reed (1984) showed that
the movements of an excavation support system become large
when the magnitude of the stability number, N, exceeds the
bearing capacity factor for failure of the base of the excavation.
The stability number is defined as:
where γ is
the unit weight of the soil above the excavation bottom, H is the depth of
the excavation, and Su is the undrained shear strength of the clay
beneath the excavation. Clough and Reed (1984) concluded that the increase
of movements were a result of plastic yielding of the soft clay at and beneath
the bottom of the excavation.
Clough et al. (1989) presented the design curves
in Figure
2-2. The figure allows the user to estimate lateral movements in clay
in terms of effective systems stiffness and the factor of safety against
basal
heave. The factor of safety against basal heave used in the figure is that
given by Terzaghi (1943). For wide excavations (H/B<1), the factor of
safety against basal heave is given as:
For wide excavations where there is a strong stratum near
the base of the excavation, the factor of safety is given
as:
where Sub and Suu is the undrained
shear strength below and above the bottom of the excavation,
respectively, Nc is the bearing capacity factor at the bottom
of the excavation, H is the height of the excavation, B is
the width of the excavation, γ is
the unit weight of the soil, and D is the distance from the
bottom of the excavation to a relatively hard stratum.
Figure
2-2 was created from parametric studies performed using
results of finite element analyses. For the analysis,
sheetpile and slurry walls with varying effective stiffness
were modeled. The figure illustrates the influence of basal
stability on movements. In particular, the figure shows
that for a given wall stiffness, a lower factor of safety
against
basal heave results in higher movements caused by the excavation.
Clough et al. (1989) suggested that the figure could be
used to estimate maximum lateral wall movement in circumstances
where movements are primarily due to the excavation process.
2.1.3 Influence of System Stiffness and Installation
Techniques
Figure 2-2 also shows that in soft clays, where
the factor of safety against basal heave is low, increasing
the stiffness
of the support system helps to reduce movements. A stiffer
support system can be obtained by reducing the vertical spacing
between the supports. This assertion agrees with observations
made by Goldberg et al. (1976), which showed that both vertical
and horizontal support spacings are an important factor in
increasing the support stiffness. They concluded that closely-spaced
horizontal supports provided as significant contribution
to the effective stiffness of the support system as closely-spaced
vertical supports.
The overall stiffness of a support system
is also influence by the stiffness of the supports themselves.
The support
components include either cross-lot braces or tiebacks, and
walers, which are structural members that distribute the
load from the wall to the brace. The theoretical stiffness
of the supports can be defined in terms of its axial stiffness,
KA:
where A is the cross sectional area of support, E is the
elastic modulus of the support, and L is the unsupported
length of the support. Cross-lot braces are compression members,
which are subjected to axial loading and elastic bending.
Movement of the wall or preloading of the member is required
before the stiffness of these members is engaged. O'Rourke
(1981) concluded that their actual stiffness is significantly
affected by the nature of the connections to the wall, the
use of preloading, and the elastic deformation of the brace.
Conversely, tiebacks are preloaded in tension. The stiffness
of these members is engaged when the tiebacks are stressed
higher than the design load and then unloaded to a lock-off
load, typically 70 percent to 80 percent of the design load.
Their theoretical stiffness is close to their actual stiffness.
It is noted that although the stiffness of the support components
contribute to the overall support system stiffness, support
stiffness is not as important a factor to the system stiffness
as either the stiffness of the wall component or the spacing
of the supports. Clough and O'Rourke (1990) used finite
element analyses to show that within the normal range of
system parameters, variations in the stiffness of the cross-lot
braces and tiebacks accounted for about 20 percent of the
overall combined wall and support stiffness.
The effective
stiffness of the support system can be improved by preloading
the supports. Preloading reduces the slack
in the support system that otherwise would have to be taken
up by movements of the wall. For a compression member like
a brace, this increases the effective stiffness of the
brace. Also, preloading reduces the shear stress levels in
the soil
that are induced by the excavation process. The reduction
of shear stresses allows the soil to follow an unloading-reloading
response instead of the softer primary loading response.
However, quantifying the effects of preloading is difficult
using only observed data. Mana and Clough (1981) performed
additional finite element analyses to determine the influence
of preloading. They found that the use of preloads in the
struts reduced movements, although there is a diminishing
returns effect at higher preloads. Very high preloads may,
in fact, be counter productive since local inward movements
at support levels can damage adjacent utilities by inducing
horizontal strains.
2.1.4 Wall Installation Effects
Often when estimating movements for a wall it is common
to envision the wall in place, and consider only what occurs
after that point. However, ground movements are caused by
factors other than excavation-induced stress relief. One
principal source of movements is related to the construction
of the wall itself. D'Appolonia (1971) showed that
poor construction techniques could also account for large
movements of the ground adjacent to insitu walls. He defined
insitu walls as secant piles walls, tangent piles walls,
structural slurry walls, and soldier pile walls that are
augured into place. The quality of construction for an insitu
wall project depends upon many factors, including the contractor's
experience with the subsurface conditions at the site and
with the insitu wall system being used. O'Rourke (1981)
also found that significant surface settlement can occur
as a result of installing insitu walls. He noted that settlement
in soft clays and sands occurred as a result of ground loss
when excavating the trench for a diaphragm wall or when drilling
shafts for secant and tangent pile walls. In soft clays, "soil
squeeze" appeared to contribute to the surface settlement,
depending on the amount of time the trench or shaft remains
open before placing the concrete.
O'Rourke (1981) presented
case histories where between 50 percent and 70 percent of
the total settlements observed
were associated with the construction of the insitu wall.
Koutsoftas et al. (2000) presented a case history that involved
installation of both a soldier pile and tremie concrete (SPTC)
wall and a conventional diaphragm wall. The SPTC wall was
constructed by first installing wide-flange steel sections
in pre-drilled shafts spaced at 3.7 m intervals. The spaced
between the steel sections was then excavated using techniques
similar to those used to install the conventional diaphragm
wall. They initially estimated that in soft clays, settlement
caused by the wall installation could extend to a distance
equaled to approximately 1.0 to 2.0 times the depth of the
wall. They also estimated that the maximum settlement would
occur directly behind the wall with a maximum value equaled
to about 0.12 percent of the depth of the wall. Similar to
the findings of O'Rourke (1981), Koutsoftas et al.
(2000) found that the actual observed surface settlement
associated with the wall installation was a function of the
length of time the drilled shafts and trenches remained unsupported.
They observed surface settlements equaled to approximately
0.2 percent of the wall depth at locations where drilled
shafts were augured through fill without casing. However,
lateral wall deflections and the consequent surface settlements
were relatively small during the diaphragm wall installation
because a positive (net outward) differential slurry pressure
was maintained prior to placing the concrete.
The pore water
pressures are also significantly impacted by the installation
of the support wall. Support walls consisting
of driven or pre-augured H-piles typically experience a
significant increase in pore water pressure during the driving
and auguring
process. However, the pore pressures tend to dissipate
to near hydrostatic levels shortly after installations are
complete
(Koutsoftas et al., 2000 and Poh and Wong, 1998). Insitu
walls that remain open for sometime prior to placing the
concrete tend to act as sinks. Groundwater levels often
decrease and do not return to pre-construction levels. These
drops
in the groundwater level increase the insitu effective
stress of the soil, leading to increased ground surface settlements.
2.1.5 Settlement Behind Excavation Support Walls
2.1.5.1 Peck (1969)
The first rational basis for estimating ground
movements adjacent to excavations was presented by Peck (1969).
He
compiled ground surface settlement data measured adjacent
to temporary braced sheetpile and soldier pile walls, and
summarized the data in a chart. Figure
2-3 presents Peck's (1969) chart. The chart presents
normalized values of ground settlement versus the distance
from the excavation. Both axes are normalized using the final
depth of the excavation. Peck (1969) grouped the data on
the chart into three categories. The categories were developed
on the basis of the soil conditions and the level of workmanship
employed when constructing the wall. Peck (1969) also recognized
that portions of the ground surface deformation patterns
might be due to basal instability in the soft and medium
clays. Category I includes excavations in sands, stiff clays,
and soft clays of small thickness. Category II includes excavations
in very soft to soft clays extending a small distance below
the bottom of the excavation or with a stability number,
Nb, less than 6 or 7. Category III includes excavations in
very soft to soft clays that extend to a significant depth
below the bottom of the excavation, and with stability numbers
greater than the critical stability number for basal heave.
In the figure, γ is
the unit weight of the soil above the excavation, H is the
final depth of the excavation, and Cb is the undrained
shear strength of the soil beneath the excavation. The remaining
variables are defined in the figure.
It can be seen from Figure 2-3, that for Category
I soils the maximum surface settlement is limited to 1 percent
of
the final excavation depth. The maximum surface settlement
of Category II soils is 2 percent of the final excavation
depth. However, the extent of the influence extends 2 to
4 times the depth of the excavation.
2.1.5.2 Clough and O'Rourke (1990)
Clough and O'Rourke (1990) observed that a relatively
well-defined grouping of excavation-induced settlement data
was evident when the settlements were plotted as fractions
of maximum settlement. They presented dimensionless settlement
profiles in Figure
2-4 as a basis for estimating vertical movement patterns
adjacent to excavations. Separate profiles were developed
for sand, stiff to very hard clays, and soft to medium clays.
With knowledge of the maximum settlement, the dimensionless
diagrams in Figure 2-4 can be used to obtain an estimate
of the actual surface settlement. The figure shows that the
settlement influence zone is 3H for excavations in stiff
to very hard clays and 2H for excavations in sands and soft
to medium clays.
Figure 2-4 shows that a trapezoidal envelope
bounds the settlement distribution in soft clays. Inside
the envelope
two zones of movement could be identified. The zone in which
the maximum settlement occurred was at 0 = d/H = 0.75 (d
is the distance from the excavation, H is the final height
of the excavation). At 0.75 < d/H = 2.0, there was a transition
zone in which settlements decreased from maximum to negligible
values.
In using the diagrams presented by Clough and
O'Rourke (1990), it should be recognized that they pertain
to settlements
caused during the excavation and bracing stages of construction.
Movements associated with other activities, such as dewatering,
deep foundation removal or construction, and wall installation,
must be estimated separately. Excavations in stiff to very
hard clays show variable behavior, with heave possible
for some conditions.
For stiff to very hard clays, the dimensionless
diagram in Figure 2-4 should be used as a conservative
estimate, provided that the wall is stable and not affected
by poor
construction techniques
2.1.5.3 Hsieh and Ou (1998)
Hsieh and Ou (1998) suggested that there were
two types of settlement profiles caused by excavations: (i)
spandrel
type, in which maximum settlement occurs very close to the
wall; and (ii) concave type, in which maximum settlement
occurs at a distance away from the support wall. The spandrel
type of settlement profile occurs if a large amount of wall
deflection occurs at the first stage of excavation when cantilever
conditions exist and the wall deflection is relatively small
due to subsequent excavation. After the initial stages of
excavation, additional cantilever wall deflection is restrained
by installation of support as the excavation proceeds to
deeper elevations. The concave settlement profile reflects
the ground settlement profile that develops when the movements
are more deep-seated.
Hsieh and Ou (1998) presented the relationship
shown in Figure
2-5 for a spandrel-type condition. The data are presented
as normalized settlement, δv/ δ vm,
where δvm is
the maximum ground surface settlement, versus the square
root of the distance-from-the-edge-of-the-excavation divided
by the-excavation-depth (d/He). This relationship
was based on 10 case histories from Taipei, Taiwan. The "mean" estimate
curve shown in the figure was derived based on the results
of regression analysis.
Hsieh and Ou (1998) developed the
curve in Figure
2-6 for the concaved settlement profile from case
histories compiled by Clough and O'Rourke (1990) and
obtained from
additional sites in Taipei. Hsieh and Ou (1998) concluded
that the distance from the wall to the point where the
maximum ground surface settlement occurred was approximately
equal to half the excavated depth. Assuming the maximum
lateral wall deflection occurs near the excavation bottom,
the distance where the maximum ground surface settlement
occurs can be taken as half the final excavation depth
(He/2). Using case histories, the settlement
at the wall was established as 0.5 δvm.
The point marked by d/He=2 corresponds to
the extent of the primary influence zone, which was defined
by Hsieh and Ou (1998) as being equaled to approximately
two excavation depths (2He). The case histories
also showed that settlement was practically negligible
at a distance from the wall equaled to four excavation
depths (4He) and was thus used as the farthest
most point on the curve. For simplicity, a linear relationship
was assumed between each turning point.
2.2 BUILDING RESPONSE DUE TO EXCAVATION-RELATED
DEFORMATIONS
The response of buildings adjacent to deep
excavations refers to the translation and rotation of individual
structural
members and to the translation and rotation of the structure
itself as a rigid body in reaction to lateral ground movements
and surface settlement. These translations and rotations
result in direct tensile strains, bending strains, and diagonal
tensile strains in the structural and non-structural members
of the buildings. For buildings adjacent to deep excavations,
the severity of the responses are dependent upon the stiffness
of the excavation support system, the installation procedures
of the system, the soil conditions, the excavation procedures,
the type of building, the distance of the building from the
excavation, the orientation of the building with respect
to the excavation, and the size of the building with respect
to the excavation. A purely theoretical approach to estimating
building response to excavation-related deformations is not
possible due to the variability of the many factors that
contribute to the response. Consequently, building response
is estimated and evaluated on the basis of empirical observations
and simplified structural approximations. The goal of estimating
and evaluating building response is to provide limiting criteria
that will safeguard the structure against unacceptable damage.
Burland
and Wroth (1974) presented definitions that describe types
of ground movements and building responses that result
from ground settlement. These definitions are presented
in Figure
2-7a to Figure 2-7c. Boscardin and Cording (1989) added
definitions describing the ground movement and building
response associated with excavations. These definitions
are present
in Figure 2-7d
Descriptions of the terms given in Figure
2-7 are as follows:
1. Settlement, Relative Settlement, and
Rotation—The
symbol ρ in
Figure 2-7a denotes downward displacement. The symbol ρh implies
upward displacement, which is termed heave. Relative settlement
is given by the symbol δρ and
is used to denote differential settlement or differential
heave. As can be seen in the figure, the differential settlement
is the difference between two settlement points of interest.
The symbol θ denotes
rotation and is angle formed from the differential settlement, δ between
two points divided by the distance, l, between them. Rotation
is typically used to describe the slope of the settlement
trough.
2. Relative Deflection and Deflection Ratio—The
term Δ shown
in Figure 2-7b is the maximum displacement relative to
the straight line connecting two reference points a distance
L apart. Relative deflection that produces an upward concavity
is termed relative sag. Relative deflection that produces
a downward concavity is termed relative hog. The term Δ/L
is the deflection ratio and is an approximate measure of
curvature of the settlement curve. The deflection ratio
is often correlated with bending related distortions in
a structure.
3. Tilt and Angular Distortion—The rigid body rotation
of the entire superstructure is termed tilt and is denoted
as ω in
Figure 2-7c. Angular distortion is denoted as β.
It is often referred to as relative rotation in the earlier
literature. Angular distortion is the rotation given in
Figure 2-7a minus the rigid body tilt. Angular distortion
is a measure of the shearing distortion of a structure.
Of note, Burland et al. (1977) suggested that accounting
for tilt in frame buildings on separate footings might
be quite inappropriate. This also agreed with Leonards
(1975) who observed that, for frame structures on isolated
footings, it was unlikely that each individual footing
would rotate through the same angle as the overall structure.
Therefore, tilting would contribute to the stresses and
strains in the frame and should be included in the distortion
calculations for these types of structures.
4. Horizontal Displacement and Horizontal
Strain—Figure
2-7d gives horizontal displacement and strain as ρh,
and εh,
respectively. These two parameters are typically associated
with excavation-related movements and thus describe the
direct lateral movement component of the building.
Building response to excavation-related ground movements
differs from the building response to ground movements caused
by application of the weight of the building, i.e., self-weight
settlement. Excavations generate horizontal and vertical
ground movements. Thus, excavation-related deformations will
induce some direct tensile strains in structures. This is
not to say that the horizontal strains in a building adjacent
to an excavation equal the associated horizontal ground strains.
Horizontal buildings strains do not equal the associated
horizontal ground strains in structures where there is significant
horizontal stiffness. The stiffness is a result of tensile
reinforcement in the foundation system and walls, and "rigid" floor
systems. The substructures of most modern buildings consist
of reinforced concrete bearing walls or reinforced strip
footings and grade beams. In addition, the floors of most
modern buildings are laterally stiff relative to the other
structural members.
2.3 PREVIOUS STUDIES TO DEFINE LIMITING CRITERIA
2.3.1 Limiting Criteria Based on Self-Weight Settlement
Only
In the initial studies of building response
to ground movements, researchers studied damage caused by
differential settlement
due to the self-weight of the building only. Table 2-1 summarizes
the results of empirical studies that relate building damage
to these ground movements.
Skempton and MacDonald (1956) reviewed
case histories of 98 buildings and observed the onset of
damage at various
magnitudes of total and differential settlement. The buildings
included both steel and reinforced concrete frame structures
and structures with load bearing walls. They observed that
most of the damage appeared to be in response to distortional
deformations. Thus, they selected angular distortion, β,
as the critical index for building response and established
the limiting angular distortion as the distortion at the
initiation of visible cracking in a structure.
They concluded the following:
(i) Cracking of panels in frame buildings
or walls in load bearing wall structures was likely to
occur if β exceeded
1/300, and,
(ii) Structural damage to columns and beams was likely if β exceeded
1/150.
TABLE 2-1. SUMMARY OF EMPIRICAL LIMITING CRITERIA
| Damage Description |
Limiting
Distortion, β |
Source |
| Safe limit against cracking |
1/500 |
Skempton and MacDonald (1956) |
| Cracking of panels in frame buildings or walls in
load bearing wall structures |
1/300 |
Skempton and MacDonald (1956) |
| Structural damage in columns and beams |
1/150 |
Skempton and MacDonald (1956) |
| Cracking in load bearing walls or continuous brick
cladding |
1/1000 |
Meyerhof (1956) |
| Cracking of infilled frames |
1/500 |
Meyerhof (1956) |
| Cracking in beams and columns of frame structures |
1/250 |
Meyerhof (1956) |
| For steel and reinforced concrete frame structures
(cracking of infill) |
1/500 |
Polshin and Tokar (1957) |
| For end rows of columns with brick cladding |
1/1000 |
Polshin and Tokar (1957) |
| For structures where auxiliary strain does not arise
during non-uniform settlement of foundations |
1/200 |
Polshin and Tokar (1957) |
| Tilt of rigid structures (smokestacks, towers, silos,
etc.) |
1/250 |
Polshin and Tokar (1957) |
| Slope of crane way, as well as tracks for bridge
crane truck |
1/300 |
Polshin and Tokar (1957) |
| Danger to machinery sensitive to settlement |
1/750 |
Bjerrum (1963) |
| Danger for frames with diagonals |
1/600 |
Bjerrum (1963) |
| Safe limit for buildings where cracking is not permissible |
1/500 |
Bjerrum (1963 |
| First cracking in panel walls is to be expected |
1/300 |
Bjerrum (1963) |
| Difficulties with overhead cranes are to be expected |
1/300 |
Bjerrum (1963) |
| Tilting of high, rigid buildings becomes visible |
1/250 |
Bjerrum (1963) |
| Considerable cracking in panel walls and brick walls |
1/150 |
Bjerrum (1963) |
| Safe limit for flexible walls, L/H > 4 |
1/150 |
Bjerrum (1963) |
| Structural damage of general buildings is to be feared |
1/150 |
Bjerrum (1963) |
| Safe limit for hogging of unreinforced load-bearing
walls |
1/2000 |
Meyerhof (1982) |
| Safe limit for sagging of unreinforced load-bearing
walls |
1/1000 |
Meyerhof (1982) |
Limiting β to
less than 1/500 would provide a factor of safety against
cracking. In a discussion of the Skempton and MacDonald (1956)
paper, Meyerhof (1956) suggested more stringent criteria
and made a distinction between load bearing wall structures
and frame structures. Meyerhof's (1956) recommendations
to preclude damage were to limit angular distortion to 1/1000
for load bearing walls, 1/500 for panel walls of brick and
similar unit masonry (infill frames), and 1/250 for beams
and columns of frames.
Meyerhof (1953) performed laboratory
experiments on full-size brick bearing walls and infill
frame walls and reported observations
of tensile stress, deflection ratio, and angular distortion
at the onset of cracking. Although he suggested some permissible
values, Polshin and Tokar (1957) are credited for introducing
deflection ratio, Δ/L,
as an index to establish limiting criteria. Polshin and
Tokar (1957) correlated the deflection ratio to the onset
of damage
in structures with varying length to height (L/H) ratios.
They observed that cracks in masonry bearing walls typically
occurred after the tensile capacity of the material had
been exceeded and concluded that the maximum allowable
deflection
ratio was a function of the development of a critical value
of tensile strain in the wall. For brick walls, the critical
tensile strain was observed to be 0.05 percent. Polshin
and Tokar (1957) also used the slope of the settlement
trough
(rotation) as an index to relate damage due to settlement
in frame structures. Later, Bjerrum (1963) presented data
relating angular distortion to building performance based
on additional data and the Skempton and MacDonald (1956)
data. These data provided the framework wherein damage
severity could be categorized as a function of angular
distortions.
Angular distortion and relative deflection
have been used to define limiting conditions in these empirical
studies.
It is noted that the table includes later recommendations
from Meyerhof (1982), which provide safe limits for both
the sagging and hogging modes of deflection for the load
bearing wall structures. The termed "hogging" refers
to concave downward deflection profiles and "sagging" refers
to concave upward deflection profiles. Burland and Wroth
(1974) established limiting criteria by applying the Polshin
and Tokar (1957) concept that visible cracking begins once
a critical value of tensile strain is reached. Burland and
Wroth (1974) assumed that a building could be represented
approximately as an elastic deep beam. Figure
2-8 shows the deep beam approximation applied to a building.
Using beam-bending theory and assuming a centrally loaded
beam, Burland and Wroth (1974) developed limiting deflection
ratios of masonry and brick walls of varying L/H ratios and
building stiffness. The limiting deflection ratios corresponded
to critical tensile strains resulting from bending and shearing
deformations. Burland and Wroth (1974) considered the effects
of a sagging deflection profile on a building by assuming
the neutral axis of the deep beam model was located at the
center of the building. The effects of a hogging deflection
profile were considered by assuming the neutral axis was
located at the bottom of the building.
For load bearing walls
with little to no tensile reinforcement undergoing a sagging
deflection profile, Burland and Wroth
(1974) presented the following equation that relates deflection
ratio, Δ/L,
to the maximum bending strain, εb(max):
For load bearing walls with little to no tensile
reinforcement undergoing a hogging deflection profile, Burland
and Wroth(1974) presented the following relation
For framed buildings and reinforced load bearing walls, Burland and Wroth (1974)
presented the following equation that relates deflection ratio to the maximum
diagonal strain, εD(max):
Equation 2.8 assumes the neutral
axis of the deep beam model is located at the bottom of the
building.
This assumption was made in an effort to approximate real
structures where the foundation and soil would offer considerable
restraint. They concluded that structures with relatively
low stiffness in shear or a significant degree of tensile
restraint, cracking due to diagonal tensile strain occurring
at the neutral axis would be the limiting factor.
Burland
and Wroth (1974) found that the critical tensile strains
ranged from 0.5 percent to 0.1 percent for
brick walls and masonry. They used 0.075 percent, the average
of that range, as input for the strain terms in Equation
2.2 to 2.8. From these equations, they established limiting
criteria for cracking in brick walls and brick infill frames
for various L/H ratios.
Note that self-weight movements
of buildings generally result in sagging profiles, whereas
excavation-induced
movements can result in sagging, hogging, or both, of an
adjacent building. Consideration of the type of settlement
profile typically leads to more restrictive limits in a
structure, especially for a building that hogs.
2.3.2 Limiting Criteria Based on Excavation-Induced
Distortions
Boscardin and Cording (1989) extended the concepts
of Burland and Wroth (1974) to develop limiting deformation
criteria for buildings adjacent to excavations by explicitly
considering the effects of horizontal strains associated
with excavation-induced movements. Figure
2-9 presents a summary of these efforts. The figure presents
a plot of horizontal strain versus angular distortion. The
plot is divided into categories of potential damage to buildings.
The categories are established by theoretical considerations
of structural response to deformation, field observations
of building damage, and measurements of horizontal and vertical
differential displacements associated with the damage. Also
included in Figure 2-9 are a limited number of case histories
involving damage. The cases were used to verify the validity
of using the figure as a basis for limiting criteria. The
categories of damage in the figure are based on the damage
classification criteria presented by Burland et al. (1977),
as given in Table 2-2.
In Figure 2-9, each curve represents
a given value of critical tensile strain. Polshin and Tokar
(1957)
initially defined critical tensile strain as the strain
at the onset of visible cracking, which is considered the
start
of observable damage. Burland and Wroth (1974) modified
that definition by expressing critical tensile strain as
either
maximum bending strain or maximum diagonal tensile strain.
Boscardin and Cording (1989) extended the Burland and Wroth
(1974) definition by defining the critical tensile strain
as the sum of the maximum extreme fiber strain
TABLE 2-2. CLASSIFICATION OF VISIBLE
DAMAGE (AFTER BURLAND ET AL., 1977)
| Damage Category |
Description
of Damage |
Approximate
Crack Width |
| Negligible |
Hairline Crack |
< 0.1 mm |
| Very Slight |
Fine cracks which can easily be treated during normal
decoration. Perhaps isolated slight fracture in building.
Cracks in exterior brickwork visible on close inspection |
1 mm |
| Slight |
Cracks that can be easily filled. Redecoration probably
required. Several slight fractures showing inside building.
Cracks are visible externally. Some repointing may be
required for watertightness. Doors and windows may stick
slightly. |
5 mm |
| Moderate |
Cracks may require cutting out and patching. Suitable
linings can mask recurrent cracks. Repointing of external
brickwork and possibly a small amount of brickwork to
be replaced. Doors and windows sticking. Service pipes
may be fracture. Weathertightness often impaired. |
5 mm to 15 mm or several cracks > 3
mm |
| Severe |
Extensive repair involving removal and replacement
of sections of wall, especially over doors and windows.
Windows and door frames distorted, floor slopes noticeably.
Walls lean or bulge noticeably, some loss of bearing
in beams. Utility service disrupted. |
15 mm to 25 mm, depends on number
of cracks |
| Very Severe |
Major repair required involving partial or complete
reconstruction. Beams lose bearing; walls lean badly
and require shoring. Windows broken by distortion. Danger
of instability. |
Usually > 25 mm, depends on
number of cracks |
and the horizontal strain. From Figure 2-9,
it is noted that when angular distortions are equaled to
zero, the horizontal
strains equal the tensile strains. When the horizontal strain
equals zero, the tensile strain equals the diagonal tension
strains.
The critical tensile strains corresponding
to the boundaries of the zone labeled very slight were taken
as
0.0005 and
0.00075. This is the threshold for cracking to first become
noticeable. The upper bound of the zone in which damage
is considered slight was established at a critical tensile
strain
of 0.0015. This corresponds to an angular distortion of
1/300 for a horizontal strain of zero. This value of angular
distortion
is the threshold for first cracking in panel wall and load-bearing
walls for structures settling under their own weight as
reported by Skempton and MacDonald (1956). The upper bound
of the
zone in which the damage is considered moderate to severe
was established at a critical tensile strain of 0.0030,
which corresponds to an angular distortion of 1/150 for a
horizontal
strain of zero. An angular distortion of 1/150 corresponds
to the threshold angular distortion for severe cracking
and structural damage in structures settling under their
own
weight, also given by Skempton and MacDonald (1956).
Boscardin
and Cording (1989) concluded:
1. Buildings sited adjacent to excavations
are generally less tolerant to excavation-induced differential
settlements
than similar structures settling under their own weight.
They attributed this to the lateral strains that develop
in response to most excavations. These strains add to the
strains imposed by the vertical movements associated with
the excavation.
2. Angular distortion is an appropriate
parameter to correlate with observed response.
3. If
reasonable estimates of critical tensile strain and L/H
can be made for a structure adjacent to the proposed
excavation, then the limiting deflection
ratio and angular distortion for that structure can be estimated and
compared to the estimated ground movement. This will allow
the engineer to assess
the potential for damage and suitability of possible remedial measures.
4.
The magnitude of angular distortion associated with critical
tensile strains and the effect of the horizontal strains
is a function of the
building type
and the lateral stiffness of a structure. Frame-type structures, depending
on geometry and number of stories, can often resist some ground movements
better than masonry bearing-wall buildings. Conversely, a frame structure
would be affected more by horizontal ground strains than a structure
with reinforced concrete walls supported by continuous footings or
with stiff
floor systems.
Boone (1996) proposed an approach, summarized in Figure
2-10, to assess damage that considers flexural and
shear stiffness of building sections, the nature of the
ground movement profile, location of the building within
this profile, degree of slip between the ground and the
foundations, and building configuration. He used cumulative
crack width as an indicator of damage severity, and defined
severity in terms of tensile strains from bending, elongation
of the ground and direct lateral extension. The basis of
the equations in Figure 2-10 is the assumption that the
building wall deforms as a simply supported, uniformly
loaded, deep beam. On that basis, component tensile strains
and shear strains can be derived for a wall, using the
relative rotations at the ends. These component strains
are then used to obtain principal strains. Crack widths
are estimated from the principle strains and compared to
damage severity levels Boone (1996) developed from 20 case
histories.
The following procedures are employed for Boone's
(1996) approach:
1. Calculate settlement and horizontal movement of an infill
wall at the end of the wall closest to the excavation (S1 and
h1, respectively) and at the end of the wall furthest
from the excavation (S1 and h1, respectively).
Also, calculate the slope (g) of the settlement trough beneath
the infill wall. In the absence of measured data, these values
can be obtained from the maximum settlement at the excavation
edge (Smax), the distance to the point where settlement/lateral
movement is zero (Dmax), the maximum horizontal
movement (hmax), and the distance each end is
from the excavation (D1 and D2).
2.
Measure or calculate the rigid body tilt (t) of the infill
wall and obtain the rotation slope (v'), which is equivalent
to angular distortion
3. Determine the proportion of deformation
due to moment (v'(M) and the proportion of deformation
due to shear (v'V). Note, substitute (v'Max(m))
and (v'Max(v)) for an infill
wall that is relatively flexible in shear (i.e. the presence
of openings).
4. Calculate the radius of bending (Rm),
the bending strain at the top of the wall (εM),
the lateral extension strain εle ),
and the shear strain (γ).
5. Calculate the cumulative
maximum tensile strain along the top of the infill wall (εt)
and the principal tensile strain (εp)
using the previously calculated strain components.
6. Cumulative
tension crack width (Ct) and Cumulative
diagonal crack width (Cp) are calculated and
plotted in the graph given in Figure 2-10. From this information,
potential damage severity is estimated for the infill walls.
As
a point of clarification, critical tensile strains represent
the tensile strain at which cracking becomes evident. The
critical tensile strains often given in the literature
(Boscardin and Cording, 1989; Burland and Wroth, 1974; and
Polshin and
Tokar, 1957) are given in terms of bending and diagonal
strains for buildings settling due to self-weight only (Burland
and
Wroth, 1974) and given in terms of either bending strains
plus direct horizontal strain or diagonal strain plus direct
horizontal strain for buildings adjacent to open excavations
(Boscardin and Cording, 1989). Critical cracking strain
has also been given in terms of shear strain (Bozozuk, 1962,
Mainstone and Weeks, 1970; and Mainstone, 1971) and in
terms
of principal tensile strains (Boone et al., 1999 and Mainstone,
1974). Principal tensile strain only equals the maximum
bending strain at the edge of the tensile fiber and only
equals diagonal
strain at the neutral axis or for shear only conditions.
Burland and Wroth (1974) concluded that the critical tensile
strain for brickwork and other masonry infill frames using
the maximum bending and direct tension strains ranged from
0.0005 to 0.001 with the recommended value being 0.00075.
Bozozuk (1962) reported that critical shear strains for
concrete and masonry structures ranged from 0.001 to 0.002.
Mainstone
(1974) gave the range of critical principle tensile strains
for full-scale frames with brick infills as 0.00015 to
0.0003. Thus, a range of critical tensile strain criteria
has been
reported in the literature.
2.3.3 Summary
The implication from the previous work related to excavation-induced
damage to buildings is that limiting criteria based on self-weight
settlement are inadequate for precluding damage resulting
from excavation-related movements. One possible explanation
for this inadequacy is that tensile strains develop in structural
members as a result of self-weight settlement. These tensile
strains become "locked in" and become the pre-existing
strain condition at the beginning of excavation. Excavation-related
movements result in additional tensile strains. The excavation-related
tensile strains add to the pre-existing tensile strains to
cause damage in adjacent buildings at much lower distortions
than may be found in literature (i.e. Skempton and MacDonald,
1956; Meyerhof, 1956; Polshin and Tokar, 1957; Bjerrum, 1963;
and Burland and Wroth, 1974). Boscardin and Cording (1989)
and Boone (1996) have both recognized that excavation-related
limiting criteria is a function of building type and orientation
with respect to the excavation, type of support system, excavation
techniques, and soil conditions.
|
(2.1)
(2.2)
(2.3)
(2.4)
(2.5) 
(2.6)
(2.7)
(2.8)