Summary of Design/Analysis Procedure:

 

Reference(s):

Sopko, 2023

Keller, 2022

The steps generally involved for a ground freezing project are outlined below.

• Conducting geotechnical survey and investigation like Geotechnical Baseline Report (GBR), Geotechnical Data Report (GDR), and Supplemental Geotechnical Investigation (SGI).
• Collecting material properties from geotechnical survey and investigations.
• Structural Analysis
• Thermal Analysis
• Hydraulic Analysis
• Creep Analysis

In most cases, the Poetsch process is used in ground freezing projects. This process includes a primary refrigeration plant(s) to chill a secondary coolant that is continuously circulated through a distribution manifold at the ground surface and refrigeration pipes that are drilled vertically from the ground surface. The entire system is closed; no materials are injected into the ground; the entire process is non-toxic, non-flammable, and non-explosive. The refrigeration plants are powered by commercial or generated electricity with appropriate safety controls. The Poetsch process has been employed successfully on ground freezing projects for over one hundred years. It is a proven and reliable means of stabilizing the earth and controlling groundwater.

Material Properties

The design procedure requires the material properties, which are taken from the GBR and Supplemental Geotechnical Investigation Program (SGI). The purpose of the (SGI) is to confirm the information presented in the GBR and gain additional information and data. Specifically, the (SGI) will:

• Confirm soil stratification elevations and classifications.
• Install piezometers and monitoring wells to verify hydraulic gradient.
• Collect soil samples for index testing.
• Collect relatively undisturbed samples for frozen soil testing.
• Conduct on-site thermal property testing.

Structural Analysis

A structural analysis of the proposed frozen earth is required to determine the required dimensions of the frozen earth structure and the temperature regime within that structure.

The following are the most important factors to evaluate and determine the structural geometry and approximate state of stress that may be developed within the frozen earth structure.

• The approximate frozen wall thickness and related state of stress in the cylindrically shaped excavation.
• The allowable excavation time before the final lining is installed.

To evaluate these considerations a three-dimensional axisymmetric finite element analysis is conducted on several frozen structures using PLAXIS 3D or other FEM programs such as FLAC.

A preliminary design may be used to evaluated several frozen earth wall thicknesses to determine the following:

• The internal (hoop) stresses within the frozen earth structure to ensure that the structure can provide safe excavation support and groundwater control for shaft excavation.
• Initiation of time dependent creep based on these stresses.
• Initial elastic deformation.

Thermal Analysis

Based on the results of the structural analysis, conduct a thermal analysis based on the thickness of the frozen earth wall. This analysis can be done using the GeoSlope Temp/W program to evaluate the time required to form the frozen earth structure as well as the required refrigeration load.

Analyses should be performed on each individual soil strata. The required freezing time for each model should be based on the following factors:

• Initial ground temperature
• Thermal properties of the soil
• Refrigeration pipe spacing
• Circulating coolant temperature
• Circulating coolant flow rate

Assume an initial ground temperature and use it as a model boundary condition. An unfrozen water content curve should be developed.

To choose an efficient pipe spacing, evaluate the effect of refrigeration pipe space with different spacing.

A mesh is to be created to simulate the varied refrigeration pipe spacing for each stratum. However, deviation may occur during drilling making it necessary to evaluate the freezing time based on individual pipe spacing. Following the drilling and installation of refrigeration pipes, gyroscopic surveys will help to evaluate potential deviation. An “as-built” thermal model is to be created using these deviations, if directional drilling is not used, additional integrative pipes have to be considered based on the As-built model, in order to maintain pipe spacing in the design range.   

The temperature contours in the soil samples after X days will help understand and be consistent with the excavation schedule.

As time increases, the frozen earth will continue to grow. Develop the relationship between time and the thickness of the frozen wall. The thickness is defined as the distance from the excavation line to the extrados of the frozen zone.

The average temperature of a frozen wall is defined as the temperature at the midpoint between two adjacent refrigeration pipes and 0.0℃. For multiple rows of refrigeration pipes, consider the midpoint to be in the center of three adjacent pipes. The average temperature versus time is to be developed.

Hydraulic Analysis

Mechanical grain size analyses (ASTM D422) are should be conducted on the soil strata from samples retrieved at relevant location and depths.

To further evaluate the permeability conductivity of the aquifer, a slug test (ASTM D4044/D4044M-5) is to be conducted.

Evaluation of the lateral groundwater flow may be completed by using the highest derived coefficient of permeability from the grain size curves to establish the groundwater contour.

Creep Analysis

Creep deformation can occur in clay strata after excavation. The method described by Klein (Klein J., Non-linear Creep of Artificially Frozen Emschermarl (Silty Clay)], 1978) was used in the analysis.

Klein establishes time dependent strengths using the following equations:

The parameters used in these computations are derived primarily from the laboratory tests.

Applying the parameters, A, B, and C to equations for the compressive strength, evaluate the time-dependent reduction in unconfined compressive strength and elastic modulus.

An approach to defining a factor of safety is to compare the long-term strength of the soil with the long-term internal stresses computed in the PLAXIS analysis.

Table 1.  Typical Inputs and Outputs for Design and Analysis Procedures

Performance Criteria/Indicators	Hoop stress in cylindrical shaped excavation. Initial ground temperature Thermal properties of the soil Circulating coolant temperature Circulating coolant flow rate Elastic deformation
Subsurface Conditions	Hydraulic Conductivity Plasticity Organics Average Frozen Wall Temperature Ground water velocity Lateral Groundwater flow Moisture Content Friction Angle Cohesion
Loading Conditions	Shaft liner Dead Loads Construction Live Loads
Material Characteristics	Convective heat transfer coefficient Grain size Modulus of elasticity Pore water content Creep
Construction Techniques	Bore and Drilling
Geometry	Frozen wall thickness Depth