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GROUNDFREEZING TECHNICAL PAPERS
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Frozen Earth Cofferdam Design
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Printable Version 
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Joseph A. Sopko, Ph.D., P.E.
Orlando B. Andersland
Abstract
Structures designed to transfer storm runoff water from surface collector systems to deep large diameter
tunnels pass through a variety of subsurface soils in the Milwaukee, Wisconsin area. During construction,
problems developed relative to the use of conventional earth support systems. Ground freezing was selected
for temporary ground support and ground water control during excavation and construction. Irregular wail
geometry required the use of reinforcement members to avoid excessive tensile stresses in the frozen soil at
critical wall locations. Design and evaluation of the frozen earth structure required specialized
computational methods to account for the time-, stress-, and temperature-dependent material behavior and adfreeze
bond between frozen soil and reinforcement members. The analysis clearly showed where modifications in
cofferdam design were required. Small displacements predicted for sides of an excavated wall opening were
in agreement with no observed movement during the construction period.
Introduction
Structures designed to transfer storm runoff water from surface collector systems to deep large diameter tunnels
pass through a variety of subsurface soils in the Milwaukee, Wisconsin area. During shaft construction,
problems developed relative to the use of conventional earth support methods. Earlier failures with slurry
diaphragm walls made ground freezing an attractive alternative method. Required excavation limits for a
transition structure imposed an irregular wall geometry on the proposed frozen earth cofferdam. Preliminary
design of this cofferdam, using simplified numerical methods, showed the potential for large tensile stresses in
certain areas within the wall.
The frozen earth wall system selected included a deep shaft and three adjacent cells, two elliptical and one
circular in cross-section. Required excavation involved cutting an opening through the frozen wall between
cells. Excessive tensile stresses within the wall and adjacent to the wall openings were avoided by the use
of steel-concrete reinforcement members placed so as to transfer loads to less critical areas. Stresses and
deformation within the frozen earth cofferdam and reinforced frozen wall sections were evaluated for the excavation
and construction phase using both an elastic and a time dependent nonlinear finite element analysis with soil
stiffness and soil creep parameters. Field measurements during construction showed agreement with predicted
wall movements.
The dropshaft and approach structures (Figure 1) were intended for transfer of storm runoff water from surface
collector systems to a deep large diameter tunnel. The dropshaft, with an inside diameter of 5.64m, extended
down through 50+m of water bearing soils and another 35m of rock. Each dropshaft included a vortex type
entrance, an approach box structure, and a trash rack structure located near the ground surface (Figure 1).
Excavation for construction of the dropshaft and approach structures involved two phases, each with different earth
support methods. A circular excavation with diameter of about 6.1 m and extending down to bedrock was required
for the dropshaft. Construction schedules included the dropshaft as part of the first phase. The second
phase included the trash rack and transition structure. The trash rack, with a 6.1 m square cross-section,
required excavation to a depth of I 9.8m. The transition structure with width of 3.66m and varying depth extended
from the trash rack to the dropshaft (Figure 1). These dimensions represented the minimum excavation limits
required to build the dropshaft and approach structure.
Construction was located on a 4.8 ha site on the south bank of the Menomonee River in proximity to the Menomonee
and Milwaukee River junction. Glacial till was the most abundant soil on all boring logs. There was no
consistent soil stratification and the till was composed of a clay matrix with varying quantities of silt, sand,
gravel and boulders. A generalized boring profile for the site is given in table 1.
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Strata
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Depth (m)
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Description
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I
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0.0 - 4.0
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Fill soils, sands and clayey silts
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II
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4.0 - 18.3
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Post glacial estuarine silts
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III
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18.3 - 21.3
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Glacial silty sand-clay mixtures
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IV
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21.3 - 33.5
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Glacial lacustrine sands
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V
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33.5 - 38.1
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Lacustrine sands and silts
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VI
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38.1 - 50.6
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Top of rock
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50.6 |
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table 1. Generalized soil profile.
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Frozen Wall Geometry
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The trash rack, transition structure, and dropshaft (Figure 1) form a single structure in what would appear to be best
suited for a rectangular excavation. Lateral earth support using straight frozen walls would include high tensile
stresses and bending moments which are not acceptable for frozen soils. More
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conventional frozen walls are typically
circular or elliptical in cross-section so as to create a structure with only compressive stress. Use of a single
elliptical cofferdam would require a large number of freeze pipes making the single elliptical cofferdam economically
unfeasible.
In order to minimize the frozen wall length, reduce the required refrigeration capacity, and limit the excavation volume,
a series of four separate but interconnected frozen soil structures were selected (Figure 2). Each unit would be a
curved compressive structure and could be frozen independently. The dropshaft was constructed to a depth of about
55m as part of Phase 1, hence the shaft wall was in place prior to freezing cells 1, 2 and 3. Cell 1 was of elliptical
cross-section with a major axis of 12.2m, minor axis of 1 1.9m and extended to a depth of 42.7m. Cell 2 was also of
elliptical cross-section with a major and minor axis of 12.8m and I 2.2m, respectively, and a depth of
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Figure 1. Proposed underground structures (from Contact Documents, 1983).
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30.5m. Cell 2 provided lateral earth support during excavation and construction of the entrance to the transition structure. Cell
3 was a circular frozen cofferdam with diameter of 10.7m and depth of 30.5m placed tangent to cell 2. The trash rack was
constructed within cell 3.
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Figure 2. Three dimensional illustration of the proposed frozen earth structures. Frozen walls formed by installing 76
mm diameter steel freeze pipes on approximately 0.9m centers.
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After freezing and excavation of these separate cofferdams (Figure 2), subsequent construction would involve cutting
an opening through adjacent cell walls for construction of the transition structure. Of major concern was the
development of tensile stresses within the frozen soil adjacent to the wall opening. To avoid this problem,
vertical reinforcement members were placed, prior to ground freezing, to the buttress sections near the wall openings.
A steel beam, embedded in concrete, served to transfer lateral loads to less critical areas above and below the wall
opening. Stresses and displacements within the frozen wall cofferdam were evaluated using methods outlined in
subsequent sections.
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Material Properties
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Soil properties required for evaluation of stresses and displacements within the frozen earth cofferdam are listed in
table 2. Since weaker fine-grained soils control design limits, all samples were obtained from stratum II (estuarine
silts in table 1) at elevations corresponding to proposed wall openings required for construction of the transition
structure. Detailed information on sample preparation, uniaxial compression and tensile tests on frozen samples,
and data analysis, is given by Sopko (1990). An upper limiting test temperature of - 109oC was selected
for this project. This temperature would be easily attainable for most refrigeration plants and selection of wall
thickness recognized that temperatures would be colder near the freeze pipes and warmer near the outer wall surface.
Soil parameters and bond link element values for the nonlinear analysis were obtained from work reported by Soo (1983).
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*Frozen soil (Soo, 1983; Sopko, 1990)
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Property
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Compression
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Tension
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Parameter n
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1.61
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5.00
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Parameter b
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0.26
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0.55
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Proof stress (MPa)
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95.45
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9.38
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Elastic modulus (MPa)
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54.92
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--
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Poison's ratio
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0.33
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--
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Uniaxial compressive strength (MPa)
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3.11
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--
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Composite steel / concrete (Merrit, 1983)
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Elastic modulus (MPa)
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54.92
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54.92
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Poison's ratio
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0.45
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0.45
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Bond link elements (Soo, 1983)
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KY
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9500
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KZ
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3000
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PMX
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100
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PMY
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100
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Parameter n
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1.6
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Parameter b
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0.2
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*Temperature = -10 oC
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Structural Analysis and Duscussion
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Conventional methods of analysis (Sanger and Sayles, 1979) provide very conservative approximations for design of
frozen earth cofferdams with complex wall geometry. More accurate methods of analysis were needed.
Application of the finite elements method (FEM) to be frozen earth structures has been described by Klein and
Jessberger (1979), Klein (1981), Jessberger (1982), Soo (1983), and Soo, et al (1985). Its use for analyzing
frozen earth structures has been slow due to limited commercial availability of FEM programs that can handle the
time-dependent behavior and material properties which vary with temperature and stress, typical of frozen soil
materials. Use of the FEM with a three-dimensional model will be described.
5.1 ELASTIC ANALYSIS
Individual Cells. The linearly elastic SAP IV program using a three dimensional grid model (Figure 3) with
steel/plate elements was used to determine both internal stresses for individual cofferdams and forces transferred
to buttress sections (Figure 2). Dimensions were scaled to proposed field values for each cell. A four
node shell element was selected
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Figure 3. Three dimensional grid used for the elastic analysis.
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for this phase of the analysis because it could model the three-dimensional geometry
of the cofferdam while limiting the total number of nodes and required computer time. Nodal coordinates in the
z-direction were selected to best correspond with major soil strata changes. Horizontal nodal coordinates were
selected to best define the plan cross-section of each cell with spacing set so as not to exceed a 2-to- I aspect
ratio for each three dimensional element. A thicker soil strata required more rows of elements. The
element (wall) thickness initially selected for the dropshaft was 1.37m and 0.91 m for individual cells. These
thicknesses could be readily attained in the field using a single row to freeze pipes. Note that these wall
thicknesses are significantly less that those indicated by conventional analysis methods (Sanger and Sayles, 1979).
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Figure 4. Boundary conditions imposed on the grid shown in Figure 3.
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Boundary conditions were essentially the same for all four models. Each node at the bottom of the grid was
restrained in the x y and z directions, and permitted to rotate about the x and y axis. Nodal points along the
outer vertical edge were restrained as shown in Figure 4. To determine reactive forces imposed on buttress sections,
it was necessary to replace the restrained nodal joints with boundary elements, one parallel to the x and y axis,
respectively. The resultant forces and moments are computed later in the analysis. Nodal points
representing portions of the frozen cofferdam embedded in unexcavated earth were restrained with springs directed
radially toward the center of the shaft.
Since it was uncertain whether passive earth pressures would
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develop, some analyses were run without spring restraints
for comparison. Normal pressures applied to the external surface of all elements were extrapolated from the
pressure diagram available in project specifications (Contract Documents, 1 983). Internal stresses computed
in this first analysis identified the location and magnitude of maximum stresses.
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Comparison with available compressive strengths showed that the design would be adequate except that the time-dependent
behavior and a decrease in frozen soil strength with time had not been accounted for. Using results from
compression creep tests conducted on the organic silt, Sopko (1 990) developed a relation between time and reciprocal
of stress. Based on these relationships and the maximum computed compressive stresses, the service life or time
to failure was determined for each cell. High compressive stresses at the cell 1 wall/dropshaft intersection
indicated a potential problem area. To compensate for these high stresses an additional row of freeze pipes was
installed so as to double the wall thickness at the critical areas.
Buttress Sections. The next concern
was buttress sections and the potential for high tensile stresses when openings were excavated through the wall between
two cells. Before proceeding with this phase of the analysis, reaction forces and moments, determined by boundary
elements, were computed and summarized. Again a three-dimensional elastic model (Figure 5) was used to determine
(1) nodal deflections in the y-direction, (2) magnitude and location of maximum compressive
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Figure 5. Three-dimensional grid for the buttress section showing location of excessive tensile stresses (shaded) for
the elastic analysis.
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stresses, (3) location and
magnitude of any tensile stresses, and (4) reactions in the y-direction for use in a subsequent analysis. The
buttress section between cells 1 and 2, with the higher stresses, was selected for analysis. Elements illustrated
in the FEM grid (Figure 5) are the eight-node brick (type 5) available in the SAP IV program. Loads, imposed at the
various nodes, included forces and moments determined from the elastic analysis for cells I and 2, Nodes along the base of
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Figure 6. Two-dimensional FEM grid for a buttress section between cells 1
and 2.
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the model were restrained to represent hinges with three degrees of freedom. Boundary nodes along the internal
side of the buttress section were restrained with boundary elements representing rollers with five degrees of freedom.
Boundary elements were used to determine the y-component of loads imposed on the buttress section from the cells.
These load components were used in a later two-dimensional analysis.
Results of the analysis indicated that (1 ) excessive tensile stresses near the face of the opening through the buttress
sections would likely result in structural failure (Figure 5), (2) compressive stresses within the buttress section were
well within the acceptable range as compared with laboratory test results, and (3) deflections along the x-axis due to stress
imbalance from adjacent cells were negligible. High tensile stresses showed that modifications in the cofferdam design
were required. A review of several options indicated that use of reinforcement members designed and placed so as to
transfer loads to less critical areas was the most practical. Preliminary considerations involved drilling a 0.9m hole
prior to ground freezing, placement of a steel member, and backfilling with concrete. Questions remained concerning size
of the composite
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steel/concrete reinforcement and whether adfreeze bonds would be sufficient for load transfer from frozen soil
to the reinforcement members.
5.2 REINFORCED SECTIONS
Linear Analysis. The FEM grid shown in Figure 6 represents a vertical section through the
buttress area between cells 1 and 2. A two-dimensional plane strain linear elastic model was used for initial evaluation of
nodal displacements adjacent to the proposed wall opening and the magnitude of shear stresses developed between the frozen soil
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and the steel/concrete beam. Boundary conditions consisted of simulated hinges along the horizontal base of the grid with simulated
rollers along the vertical symmetric slice. loads applied at nodal points were those obtained from boundary element forces for
the FEM model shown in Figure 5. These loads would contribute to bending of the reinforcement member. Reinforcing elements
were the same as those described by Merritt (1983). Material properties are listed in table 2.
Results of this analysis indicated that tensile stresses along the opening between cells 1 and 2 would be transferred to the
steel/concrete reinforcing member. Computed displacements along the face of the opening where less that 1.6mm. Based on
the elastic analysis, shear stresses at the interface between frozen soil and reinforcing members were less than 287 KPa, below
the range which would cause adfreeze bond failure. A further analysis of the reinforced section considered the
time-dependent properties of the frozen soil.
Time Dependent Nonlinear Analysis. A computer program described by Soo (1 983) appeared to contain the features needed for
this analysis. A nonlinear plane stress element was capable of representing both linear and nonlinear material behavior in
both tension and compression, ideal for the frozen soil. The reinforcing element (steel/concrete) was modeled with linear
elastic elements using the same parameters in both tension and compression (Merritt, 1983). The adfreeze bond between
frozen soil and the reinforcement member was modeled by a bond link element. These three element types permitted simulation
of the time dependent creep deformation of the adfreeze bond up to some limiting deformation, at which time slip failure would
occur. The two-dimensional nonlinear FEM grid for the buttress section is shown in Figure 6. The shaded area represents the
reinforced section. Material properties required for the three element types are listed in table 2.
Time steps used to evaluate creep deformation were arbitrarily selected as one, seven and thirty-days. Compatible creep
proof stresses and proof strain rates (table 2), selected by Soo's (1 983) method, ensured proper execution of the program.
The analysis indicated that the reinforcement would transfer loads to less critical areas, thus avoiding high tensile stresses
in the wall adjacent to the opening. The analysis showed that most of the displacement at the sides of the opening between
cells occurred in the initial elastic phase. Very little deformation was predicted for times of one, seven and thirty-day
intervals. Deformation indicated on Figure 7 are extremely small and were not observed during construction, possibly due to
limitations of available measurement equipment.
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Figure 7. Computed nodal deformations at the side of the opening between cells 1 and 2.
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Nodal Displacement
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(mm)
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| Position |
Time(days) |
Vertical |
Horizontal |
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1 |
-0.30 |
1.34 |
| 7 |
-0.40 |
1.40 |
| 30 |
-0.30 |
1.43 |
| 2 |
1 |
-0.33 |
1.37 |
| 7 |
-0.37 |
1.43 |
| 30 |
-0.33 |
1.49 |
| 3 |
1 |
-0.30 |
1.37 |
| 7 |
-0.33 |
1.49 |
| 30 |
-0.30 |
1.52 |
| 4 |
1 |
-0.27 |
1.43 |
| 7 |
-0.30 |
1.52 |
| 30 |
-0.30 |
1.58 |
| 5 |
1 |
-0.24 |
1.46 |
| 7 |
-0.27 |
1.55 |
| 30 |
-0.27 |
1.62 |
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Conclusion
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- This project has demonstrated that the analysis techniques used are suitable for design of frozen earth
cofferdams having complex wall geometry, and that they are capable of evaluating the effect which reinforcement
members placed in the frozen wall have on stresses and wall deformation.
- The linearly elastic SAP IV program with a three-dimensional model and shell/plate elements computed both
internal wall stresses for each cell and the magnitude of forces transferred to the buttress sections.
Stress levels indicated adequacy of cell wall thickness and loads were used for subsequent analysis of buttress
sections.
- The time-dependent nonlinear analysis of reinforced buttress sections provided both stresses and displacements
at specified locations in the wall. The three element types available appeared to correctly represent the
reinforced wall behavior. Small displacements predicted for sides of the excavated wall opening were in
agreement with no observed movement during the construction period.
- Placement of reinforcement elements (before freezing) in the cofferdam buttress sections reduced tensile
stresses in the frozen soil adjacent to the wall opening to acceptable levels and permitted construction to
proceed using the most economical frozen wall geometry.
- It is important that complete information, relative to frozen soil moduli and creep parameters, be available
on future projects which include detailed structural analysis of complex wall geometry. Standardized
laboratory test procedures are needed for evaluation of these moduli and frozen soil parameters.
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Ackowledgments
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This research was encouraged and supported by the Geocentric Engineering Corporation. The authors wish to express
their appreciation to Professor R.K. Wen for this helpful advice on the analysis phase of this project.
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References
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Contract Documents. 1983. Crosstown interceptor and inline pump station, Milwaukee
Metropolitan Sewer District, Milwaukee, Wisconsin.
Jessbeirger, H.L. 1982. A state of the art report, ground freezing: mechanical properties, processes and design.
GROUND FREEZING 1980, Developments in Geotechnical Engineering Vol. 28, Elsevier Scientific Publishing Company, Amsterdam,
pp. 5-30.
Klein, J. 1981. Finite element method for time dependent problems of frozen soils. lnt. J. for Numerical and Analytical
Methods in Geomechanics, 5: 263-283.
Klein J., and Jessberger, N.L. 1979. Creep analysis of frozen soils under multiaxial states of stress.
Engineering Geology, 13: 353-365.
Merritt, F.S. 1983. STANDARD HANDBOOK FOR CIVIL ENGINEERS. McGraw-Hill Book Company, New York.
Sanger, F.J., and Sayles, F.N. 1979. Thermal and rheological computations for artificially frozen ground construction.
Engineering Geology, 13: 311-337.
Sopko, Joseph A. Jr. 1990. New design method for frozen earth structures with reinforcement. Ph.D. Dissertation,
Michigan State University, East Lansing, Michigan.
Soo, Swannum. 1983. Studies of plain and reinforced frozen soil structures. Ph.D. Dissertation, Michigan State
University, East Lansing, Michigan.
Soo, S., Wen, R.K., and Andersiond, O.B 1985. Finite element models for structural creep problems in frozen ground.
GROUND FREEZING 1985, Proc. 4th International Symposium, ed. by S. Kinosita and M. Fukuda, A.A. Balkema, Rotterdam, Netherlands,
2:28
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