1. Introduction
On the surface of an underground mine, a collar is required for a shaft or raise entry, while a portal refers to the entrance for an adit, decline, or ramp.
Collar
Besides providing a mine entrance, a shaft collar for a production shaft performs the following functions.
• Keeps the shaft watertight.
• Provides a top anchor for the shaft sets and the plumb lines required for shaft surveying.
• Provides space for the shaft sinker to install equipment before the main excavation process begins.
• May support a portion of the headframe.
Collars are also required for ventilation shafts, service shafts, and for all raises that reach surface. Constructing collars in a rock outcrop or in shallow overburden is relatively straightforward; however, if the soil overburden is deep and especially if it is water bearing, collar construction can become a major project. The same is true of a portal, but in this case, if the overburden is deep and water bearing, the construction may be more difficult or even impractical. Shaft and raise collars are normally lined with concrete. The design of a concrete lining for shafts and shaft collars is discussed in Chapter 9, Shaft Sinking.
Portals
Portals may be left open to the elements in tropical zones; however, the entrance is often enclosed with a weather-tight structure in temperate or arctic climates. This structure was once often built with timber or reinforced concrete, but now miners usually employ corrugated metal archways similar to those used for large highway culverts. For a ramp entry in overburden, this structure can become significantly long. In the case where the portal carries a conveyor, the archway is designed with enough strength to accommodate hangers that suspend the conveyor support frames.
Portals for ramps and declines usually incorporate a reverse slope at the start to prevent surface water from running into the mine.
2. Rules of Thumb
Collars
• The elevation of a shaft collar should be 2 feet above finished grade. Source: Heinz Schober
• The typical thickness of a concrete lining for a production shaft collar is 24 inches in overburden and 18 inches in weathered bedrock. For a ventilation shaft collar, it is 18 inches in overburden and 12 inches in weathered bedrock. Source: Jack de la Vergne
• The finished grade around a shaft collar should be sloped away from it at a gradient of 2%. Source: Dennis Sundborg
• A shaft collar in overburden, completed by any means other than ground freezing (which may take longer), will be completed at an overall rate of 1 foot per calendar day. Source: Jim Redpath
• For a shaft collar in deep overburden, the minimum depth of socket into bedrock is 3m (10 feet) in good ground, more if the rock is badly weathered or oxidized. Source: Jack de la Vergne
• The minimum depth for a timber shaft collar is 48 feet (15m). Source: Jack de la Vergne
• The minimum depth for a concrete shaft collar is 92 feet (28m). If a long round jumbo is to be employed for sinking, it is 120 feet. Source: Jack de la Vergne
• For a ground-freezing project, the lateral flow of subsurface ground water in the formation to be frozen should not exceed 1m per day. Source: Khakinkov and Sliepcevich
• To determine the diameter of a proposed circle of freeze pipes around a shaft collar, 60% should be added to the diameter of the proposed excavation. Source: Sanger and Sayles
• When ground freezing is employed for a shaft collar, the area of the proposed collar excavation (plan view) should not be greater than the area to remain inside the circle of pipes (area that is not to be excavated). Source: B. Hornemann
• The minimum practical thickness for a freeze wall is 4 feet (1.2m). Source: Derek Maishman
• The maximum practical thickness for a freeze wall with a single freeze circle is 16 feet (5m).
Concentric circles of freeze pipes should be employed when a thicker freeze wall is required. Source: Derek Maishman
• The radiation (heat transfer) capacity of a freeze pipe containing brine may be assumed to be 165-kilocalories/square meter of pipe surface. However, if the brine velocity is too slow (laminar flow), this capacity will be reduced by 40%. Source: Jack de la Vergne
• The capacity of the freeze plant selected for a ground freezing project should be 2-2½ times the capacity calculated from the radiation capacity of the total length of freeze pipes installed in the ground. Source: Berndt Braun
• Groundwater movements over 3 to 4 feet per day are significant in a ground freezing operation. Source: U.S. National Research Council
• If the drill casing is left in the ground after installing the freeze pipes, it will cost more but the freeze pipes will be protected from blast damage or ground movement and the heat transfer will be increased due to the greater surface area of the steel casing. Source: Jim Tucker
• The heat gain from circulating brine is equal to the sum of the friction losses in the pipes plus the heat generated due to the mechanical efficiency of the brine pump. The value calculated for the heat gain should not exceed 10% of the refrigeration plant capacity. Source: Jack de la Vergne
• The amount of liquid nitrogen (LN) required to freeze overburden at a shaft collar is 1,000 Lbs. of LN/cubic yard of material to be frozen. Source: Weng Jiaje
• Due to the heat of hydration, the long-term strength of concrete poured against frozen ground will not be affected if the thickness exceeds 0.45m (18 inches). Below this thickness, designers will sometimes allow a skin of about 70-mm (2¾ inches). Source: Derek Maishman
Portals
• The minimum brow for a portal in good ground (sound rock) is normally equal to the width of the decline or ramp entry. It may be reduced in steeply sloped terrain or leaving “shoulders” (instead of a vertical face) and/or by proper ground support with resin grouted rebar bolts.
Various Sources
• When slurry walls, freeze walls, or sheet piling are employed for portal entries in deep, saturated overburden, they should be placed to a depth 50% greater than the depth of the excavation to avoid uplift on the bottom. Source: Jacobs Engineering
• The maximum practical depth for sheet piling in cohesive soils approximately 60 feet (18m). In granular soils, it is usually little more than 40 feet (12m). Source: Jack de la Vergne
• Standard well point systems are based on suction (vacuum) lift and the practical limit for lowering the groundwater is normally about 5m (16 feet). It is typical to provide a second stage of well points to lower it further. Source: Stang Dewatering Systems
• Well point systems employing jet eductor pumps are capable of lowering the ground water by 12 to 15m (40 to 50 feet) in one lift. Source: Golder
3. Tricks of the Trade
• Excavating a shaft collar in rock may be expedited by pre-drilling blast and cut holes to the full depth. The drill holes are filled with an inert material a portion of which is blown from the holes for each successive blast cycle. Coarse sand has been used as the agent, but it tends to pack. Better results are obtained by employing pea gravel or the “micro-balloons” used as a bulking agent in explosives. Source: Bill Shaver and others
• No deep excavation in overburden should be executed without first obtaining a comprehensive soils report that will include recommendations for excavation methods to be employed. Source: Steve Boyd
• Shaft collars in soil overburden should be excavated with a circular cross section even if the shaft is to be rectangular or square. Source: Proctor and White
• For the design of the liner shaft collar in deep overburden, it is expedient to assume the ground water table at surface elevation and/or (to account for soil arching) that at least 70% of the maximum theoretical active soil pressure is applied throughout the total height of the collar. Source: Karl Terzaghi
• Shaft collars and ramp portals in overburden less than 20 feet (6m) deep are almost always most economically excavated by open cut. If the existing ground water table is beneath the depth of excavation, they may be economically excavated to depths of 50 feet (15m) by open cut; however, it is a rare event that the ground water table at a mine site is found deep. In most circumstances, the water table is near surface and the following guidelines will apply.
− If the soils are granular (coarse grained sand or gravel) and “clean” (no fines), they can be economically excavated up to 40 feet (12m) deep by open cut. In this case, dewatering can take place from within the excavation and side slopes may be laid out as steep as 1½:1.
− In typical glacial till with minimal water flow, they may also be economically excavated up to 40 feet (12m) deep by open cut. In this case, it is normally required that the water table be lowered with the use of well points (in stages, if necessary) on the perimeter of the excavation to minimize the flow of water into the excavation. In this case, the side slopes of the excavation can usually be laid out at approximately 2:1. Various Sources
• When well points or deep wells are employed for dewatering it is important to provide a standby generator and spare pumps at the job site. Source: Joe Evans
• Well point headers should not be placed at the surface of the excavation. They will be more effective if they are placed just above the existing water table because this will reduce the suction lift to a minimum. Source: Edward Johnson
• If the soils to be excavated contain distinct horizontal layers of coarse sand or gravel (with relatively high permeability), deep wells with in-the-hole pumps are very effective and should be considered as an alternative to well points. Source: Harry Cedergen
• Shaft collars in granular soils may normally be dewatered as deep as 65 feet (20m) with the use of deep wells. Deeper collars are normally frozen to keep the excavation watertight and support the walls of the excavation until the permanent lining is placed. Source: Jack de la Vergne
• Dewatering is not normally a practical method for fine-grained soils such as clays and silts, unless they occur in thin horizontal beds within a granular matrix. Either ground freezing or big-hole drilling is normally an economical and practical choice for this circumstance. Source: Terry McCusker
• The ground water in silt, silty sand, or very fine-grained sand that does not respond to normal gravity draw down, may be lowered using electro-osmosis. This method employs an existing line of metal well points as cathodes and a line of steel rods placed on the excavation side of the well points used as anodes. When an electrical current is introduced, water flows toward the cathodes where it is pumped to surface. Source: Leo Casagrande
• Sinking caissons are rarely employed today for shaft collars because they are no longer considered economical or practical when compared with other methods. In the past, significant problems have occurred with this method, the main one being obtaining a seal at the bedrock elevation. Source: Jim Redpath
• Shaft collars in deep overburden should be advanced with an excavation radius at least 5 feet larger than the proposed excavation radius of the shaft. This is to account for overbreak at the rock entry and to permit an integral concrete bearing ring to be poured at the interface instead of down deeper into bedrock. Source: Steve Boyd and others
• Shaft collars in deep overburden can be excavated at less expense if the excavation is first advanced by open cut down to the elevation of the water table (to a maximum of 40 feet of depth) by open cut. It is important to provide a level working area and space for a collection ditch and sump of at least 10 feet (3m) around the perimeter of the planned excavation at the bottom of the cut. The open cut should include an access roadway to the bottom of the excavation at a gradient of approximately 10%. Source: Redpath and Dengler
• Most shaft collars in deep overburden are most economically excavated by using liner plate segments to support the walls. If the excavation is of large diameter, the liner plates are reinforced with ring beams. Source: Joe Evans
• If provided with a soils report and the required dimensions, suppliers of liner plates and ring beams will often provide useful advice and perform the necessary engineering calculations to ensure a safe design (at no cost) in support of their quotation to supply the materials. Source: George Martin
• Liner plate collars can be prevented from shifting off vertical during excavation by drilling and installing a pipe casing at the four quadrants of the excavation circle. Source: George Martin
• When the stand-up time is too short to install the next ring in a liner plate collar, the excavation may proceed under cover of spiling. If the spiles to be driven are made by tapering the end of pipe or square structural tubing (HSS), they may be later used for nitrogen freezing, if you get into real trouble. Source: George Martin
• When using sheet piling to excavate a shaft collar in overburden, it is advantageous to build a scaffold inside the ring to guide the piles. Source: Jim Redpath
• When using sheet piling to excavate a shaft collar beneath the water table, it is advisable to chemical grout around the outside perimeter of the piling, especially at the soil/rock interface. Source: Burt Eastman
• Soldier piles (H-beams) and lagging are rarely employed for shaft collars in deep overburden, mainly because this method is not considered suitable for working beneath the water table in close confinement. It is virtually impossible to lower the water table right to bedrock horizon due to the draw-down cone between well screens or points. For portal entries in saturated overburden, they may be employed (with cross bracing or tiebacks) when there is no room for an open cut excavation. In this case, they typically require well points to lower the ground water to well beneath the depth of the excavation. Source: Jack de la Vergne
• Slurry walls are rarely employed for shaft collars in deep overburden, mainly because this method is too expensive. The high cost is partly due to the fact that a second concrete lining is normally found to be required inside the slurry wall. For portal entries in saturated overburden, slurry walls may be employed (with cross bracing or tiebacks) when there is no room for an open cut excavation. They have an advantage over soldier piles and lagging for this procedure because they are supposed to be watertight. Most contractors will construct a water-tight slurry wall in cohesive soils. In glacial till or other soils containing cobbles and boulders, the contractor (that submitted the low bid) for a slurry wall is often not successful in providing a 100% watertight diaphragm. In one extreme case, there were holes later found in a slurry wall large enough to drive a truck through. Source: Moretrench American Corporation
• Big-hole drilling is not normally employed for shaft collars in deep overburden due to the expense of mobilization and the high cost of the lining; however, they are competitive for small shaft collars (finished inside diameter 4m, or less) in very deep overburden (over 50m) that is water bearing. Source: Louis Donolo
• Using blankets of filter cloth or selected granular (filter) material on portal excavation side slopes where seepage is emerging will often aid in holding the soil in place and prevent sloughing. Source: Harry Cedergen
• When necessary, the bottom slopes of an open cut portal excavation may be kept stable even when they penetrate the water table by employing a rip-rap support constructed of boulders or oversize shot rock. Source: John Seychuck
• When necessary, the bottom slopes of an open cut portal excavation may be kept stable when they penetrate the water table by installing horizontal drains consisting of 1½-inch diameter PVC plastic pipes machined with fine slots that are as narrow as 0.010-inch (¼ mm). Source: U.S. Patent No. 3,391,543
• Ground freezing with liquid nitrogen should only be considered for temporary or emergency conditions (1-2 weeks). For the longer term, conventional freezing with brine is less expensive. Source: George Martin
• The freezing method may be simply applied to a small problem by laying bags of solid carbon dioxide (“dry ice”) against the problem area and covering it with insulation. In this manner, ground may be frozen to a depth of up to 1.5m (5 feet). Source: C.L. Ritter
• When making the calculations required for ground freezing, it is necessary to have a value for the natural temperature of the ground. If this temperature is not available, the average or mean annual surface temperature at the project may be used for this value without sacrificing accuracy. Source: Jack de la Vergne
• The brine circuit employed for a ground-freezing operation requires a surge chamber. The best one consists of an elevated tank (open to the atmosphere) in a short tower. It provides simple visual observance of the pumping head and, if equipped with a sight gage, gives precise changes in the volume of brine in the system and early notice if a leak should occur. Slight losses in brine volume will occur as it becomes colder (coefficient of volumetric thermal expansion is 0.00280 per degree Fahrenheit). Source: Leo Rutten
• When freezing a shaft collar with a conventional brine system, you can tell when the freeze wall cylinder has built up to the point of closure by noting a sudden rise of the water level in the pressure relief hole drilled in the center. Excavation may normally commence soon afterwards, since the ground pressure against the freeze wall is smallest near surface. Source: Derek Maishman
• When freezing a shaft collar with a conventional brine system, the freeze pipe headers must be bled of any air accumulation, once a day. Source: Leo Rutten
• When freezing a shaft collar with a conventional brine system, thermometer instruments should be re-calibrated once a week by inserting a thermocouple into a container filled with water and ice (temperature exactly equal to the freeze point of water). Source: John Shuster
• If the freeze wall does not close when calculated, the problem may be due to a flow of ground water. If the return temperature of the brine from holes on opposite sides of the freeze circle is slightly higher than the average, there is very likely a significant lateral flow of ground water. The elevation of this flow in the ground strata may be determined by stopping the brine flow to one or more of the “problem” freeze holes, waiting two hours and then measuring the standing brine temperature at vertical intervals (usually 2 feet). The water is flowing where the brine temperature is slightly higher than the rest of the measurements. If the return temperature of the brine from only one hole is higher than average, it can mean that ground water is flowing from the bedrock where it is penetrated by the freeze pipe. In either case, the default remedy is to grout from holes drilled to the vicinity of the problem area(s). If the return temperature from one hole is lower than average, it usually means there is a short circuit in that hole. (The inner freeze pipe, usually plastic, was not installed to the bottom of the hole or it has come apart at a splice.) The proof is to pull the inner freeze pipe from the hole so it can be measured and examined. Source: Jack de la Vergne
• When a liability rider is incorporated in the contract documents for a ground-freezing project, the contractor will often extend the ground freezing cycle. For a shaft collar, this often means that the excavation will be frozen solid inside the freeze circle before releasing it for excavation. While this procedure provides added safety, it increases the costs and delays the project because excavation is much more difficult in frozen ground than it is in a soft core. Source: Derek Maishman
• An acoustic instrument has been developed to measure the thickness of a freeze wall under construction. (The speed of sound is different in frozen and unfrozen ground.) This instrument is not reliable (and its use may lead to great confusion) unless it is employed by a single experienced operator and is properly calibrated before the freezing process begins on a particular project. Source: Jack de la Vergne
• If a brine freeze plant does not cool to the expected final temperature [at least -250C (-130 F)], the most likely causes in order of greatest frequency are as follows.
Cause Remedy
− Low level of refrigerant Top up
− Clogged water spray holes Remove and clean piping over condenser
− Oil build-up in refrigerant Bleed off at bottom
− Air in refrigerant Bleed off at top
− Vacuum feed to compressor Adjust to positive feed
− Faulty valves in brine line Replace
− Faulty expansion valve Replace
− Undersize brine mains Replace
− Oversize brine pump Replace
Source: Jack de la Vergne
• If the freeze wall ruptures during excavation of a shaft collar, it will occur near the bottom of the excavation. Normal practice is to immediately clear personnel and equipment from the bottom and dump a truck load(s) of fine gravel or coarse sand in the excavation to prevent further inflow of soil through the freeze wall. It is then typical practice to drill from surface and chemical grout in the vicinity of the breach. Then, drill and install another freeze hole in the vicinity of the breach to accelerate and reinforce its closure, after which the excavation may resume. The new freeze hole may be frozen with liquid nitrogen to minimize the delay. Source: Leo Rutten
• If a freeze wall rupture occurs in a section of the excavation that is in very compact granular soil, undisturbed glacial till, or in the bedrock, normally only water will flow into the excavation. In this case, it is typical procedure to allow the excavation to flood. When the level of the water in the shaft collar has peaked, ready-mix concrete is tremied or pumped down through the water to form a concrete pad on the bottom. Once the concrete has set and sufficiently cured, the shaft collar is pumped dry and grout is injected through the pad. When the grouting is completed and the freeze wall restored, the pad is broken up and the excavation can safely resume. Source: Jack de la Vergne
4. Well Points and Well Pump Dewatering
The primary function of a well points or deep well is to lower the level of the ground water within the working area of a proposed excavation in soil (overburden). The ground water is lowered by collecting and pumping it to surface in wells adjacent to the excavation perimeter. The procedure is generally referred to as “dewatering.” The procedure works very well in coarse-grained sands. It can be much less efficient with fine-grained sands and is usually not practical for cohesive soils (silts and clays) unless they occur in horizontal layers underlain by permeable coarse-grained soils.
Some dewatering contractors may engage in “creative engineering” to sell a contract for dewatering a particular project, when in fact, the procedure is not practical for the application. When it is effective, dewatering benefits the excavation procedure in a number of ways.
• It greatly reduces or eliminates the requirement to pump ground water from within the advancing excavation.
• It prevents the bottom of the excavation from becoming “quick” or heaving.
• In open cut excavation, it raises the angle to which the side slopes can be safely cut without danger of sloughing or slope failures significantly reducing the amount of material to be excavated.
• In vertical excavations, it removes the hydrostatic pressure against temporary ground supports or sheet piles.
• In vertical collar excavations (that are sunk), it normally provides sufficient stand-up time on the exposed walls for temporary supports to be installed.
Well point systems are usually defined as groups of closely spaced wells connected to a header pipe (manifold) and pumped by suction lift. The riser casing in the well usually consists of a 1½ -inch diameter steel pipe. A screen section is incorporated at the bottom of the casing (usually 2-inch diameter) referred to as the “point.” The point is specially designed for water jetting the well casing in place (without drilling). The jetting consists of forcing water under pressure down through the riser pipe and out through orifices in the tip of the point. After a well point has been advanced to the full depth, a ball valve automatically provides a seal at the orifices and restricts the flow of ground water to the slotted section.
Once the well points are in place they are connected on surface to a manifold line leading to a centrifugal pump(s). An air separation chamber ensures that the pump is kept full of water at all times. In some soil conditions, point jetting does not work and in this case either a separate jet pipe is first employed or the wells are drilled. Once the excavation and construction work is completed, the well casings (and points) are extracted for re-use on the next project.
Deep wells are the same as ordinary drilled water wells that incorporate conventional in-the-hole pumps. While there are few contractors experienced with well points, there are hundreds of well drilling contractors well experienced in drilling and installing deep wells. It is usually the case that a local drilling firm is employed for providing deep wells because his experience in drilling similar terrain in the area of the project can be of great value. Unfortunately, a typical well drilling contractor is normally concerned only with the yield of a drilled well and not with its capacity for dewatering a proposed excavation. He may have to be “educated” in advance about the special requirements for successful deep wells on a dewatering project.
5. Big Hole Drilling
A large number of big-hole drilling contractors are equipped and experienced for drilling in overburden on civil projects. These firms may believe and propose that a shaft collar need only to be drilled to the rock horizon. When such a proposal is executed, it often leads to difficulties because the rock horizon is where acute problems are most likely to occur. These include obtaining an adequate seal at the soil/bedrock interface and unavoidable overbreak when sinking into the rock from the bottom of the drilled shaft.
To drill a shaft collar successfully, a contractor should be selected whose rig and procedure is readily capable of drilling and lining the excavation at least 5m (16 feet) into the bedrock. The contractor’s procedure should ensure that the installation of the permanent lining (casing) extends to the bottom of the hole in the bedrock and includes provision a good seal between it and the walls of the socket into the bedrock.
6. Ground Freezing
Ground freezing is considered the most reliable means to support a collar excavation in deep overburden. The method may be used for ramp entries; however, ground freezing is unusual for deep entries due to the large number of pipes required and because of the difficulty in arranging the piping to obtain a freeze in the overburden above and beneath the proposed excavation.
Ground Freezing Procedure
Shaft collars have been sunk employing ground freezing for over a century and so today the procedure is well understood and straightforward. Normal practice is to engage a contractor that specializes in ground freezing. A number of vertical freeze holes will be drilled around the perimeter of the proposed excavation to form the “freeze circle.” The spacing between the freeze holes varies from 2½ feet (0.8m) for shallow excavations with small freeze pipes and to 6½ feet (2m) for very deep excavations with larger freeze pipes. Each freeze column extends into the bedrock. Two pipes are installed in each freeze hole, one inside the other.
The larger pipe is sealed at the bottom so that chilled brine directed in a continuous flow down the inner pipe will return to surface in the annular space between the pipes. Having taken up heat in the ground, it is then re-cooled in a refrigeration plant. Traditionally, the brine velocity in the annular space was designed high enough to obtain turbulent flow and assure good heat transfer. More recently, it has been determined that the transfer will not be affected if the velocity is lowered into the “mixed- flow” region; however, it should not be so slow that the flow is laminar. The brine selected is almost always calcium chloride (road salt), which in theory is capable of lowering the freeze point of the brine to a minimum of -510C (-600F) at a concentration of 29.6 % calcium chloride (SG =1.290).
Ground Freezing for a Frozen Shaft Collar
Following is a procedure and an example for designing the ground freezing for a frozen shaft collar. To design the required thickness of the freeze wall, it is first necessary to determine the strength of the soil once it is frozen. Normally, the soil is saturated. In the rare case that a portion of the freezing is in dry soil, it is wetted when the freezing takes place. The strength of wet soil when it is frozen depends on the temperature (the colder, the harder) and the type of soil to be frozen (frozen sand is stronger than frozen clay).
The actual temperature of the freeze wall varies from the temperature of the brine near the freeze pipes to the freezing point of water (which is zero on the Celsius scale and 32 degrees on the Fahrenheit scale) at the perimeters. To simplify the calculations, one temperature is assumed for the whole cross-section of the freeze wall. For normal brine freezing, this temperature is +140 F (-100 C). At this temperature, the strengths may be assumed for the freeze wall from Table 12-1.
Table 12-1 Approximate Unconfined Compressive Strengths of Frozen Ground
(Interpreted from the results of tests taken at various laboratories)
The ground pressure against the freeze wall to be designed is best obtained from the soils report, or a soil mechanics specialist. For relatively shallow collar excavations, a minimum practical thickness of freeze wall (roughly equal to the distance between the freeze pipes) is usually thicker than required for strength. For preliminary calculations on deeper excavations, the ground pressure beneath the water table may be assumed as follows.
• Cohesive soils (clays and silts) 2.0 times the hydrostatic pressure
• Granular soils (sands and gravel) 1.5 times the hydrostatic pressure
• Bedrock 1.0 times the hydrostatic pressure
Note
The hydrostatic pressure is the pressure at the bottom of a column of water at the depth considered. It is equal to 0.4335 psi multiplied by the depth in feet (9.807 kPa multiplied by the depth in meters). With the strength of the freeze wall and the ground pressure against it determined, the required thickness of the freeze wall is most often calculated by the Domkë formula, which contains an appropriate factor of safety and provides the dimension (S) equal to half the total thickness required.
S/R =0.95 P/K + 7.54 (P/K)2….. Domkë (metric or Imperial units)
In which R = Radius of the collar excavation (select any unit of length)
S = Freeze wall thickness inside the ring (same unit of measure as R)
P = the ground pressure (select any unit of pressure)
K = compressive strength of frozen ground (same unit of pressure as P)
Example
Find the required freeze wall thickness (t).
Facts:
1. R = 3.75m (includes an allowance for overbreak)
2. P = 1.38 MPa (Maximum Ground Pressure)
3. K = 6.9 MPa (Silty Sand)
Solution: 1. P/K = 1.38/6.9 = 0.20
2. S = 3.75[(0.95 x 0.2) + (7.54 x 0.2 x 0.2)]
3. S = 3.75[0.19 + 0.30] = 1.84m (6 feet)
4. Freeze wall thickness, t = 2S = 3.68m (12 feet)
A concrete lining is designed to be poured in place against the frozen ground as the excavation proceeds (or in some cases, afterwards). The lateral design pressure against the concrete lining is the same as was determined for the freeze wall. The thickness of this concrete lining is determined by the method detailed for shaft linings in Chapter 9 Shaft Design. In most cases, the calculated result will be less than the standard minimum thickness of 18 inches (450 mm), so this dimension may be assumed correct unless the shaft collar is extremely deep.
The size of the freeze wall circle is then calculated by determining its radius, which is the sum of the excavation radius (R =3.75m) plus the thickness (S =1.84m), calculated for the thickness of the freeze wall inside the ring plus a small allowance for contingency. In this case, these dimensions will add up to 5.6m. Therefore, the diameter of the freeze circle is calculated at 11.2m. This diameter can be enlarged to provide the contingency. In this case, the diameter, D, of the freeze circle may be determined at D = 12m (40 feet).
With all of the dimensions of the required freeze wall determined; the distance between the freeze holes and the size of the freeze plant required may be calculated. Since these values are interdependent, it is convenient to tabulate a series of results from different pipe spacings. The tabulation will include the time required to freeze the wall for each case. With these results, the most economical spacing may be estimated.
To complete these calculations, the diameter of the outer freeze pipe must first be determined. For shallow excavations, it can be assumed that a 3-inch diameter pipe will be used because it is the largest diameter that will fit inside a standard 5-inch diameter drill casing. (By convention, the casing dimension often refers to the outside diameter while the pipe dimension always refers to the inside diameter.) For deeper shaft collar excavations, it may be assumed that the outside freeze pipe will be 5 to 6 inches in diameter. For the purposes of the following calculations, it is assumed to be 5.5 inches in diameter, since this is the outside diameter of a standard sized well pipe commonly used as the freeze pipe for deeper shaft collar projects. For very deep ground freezing projects where the shaft as well as the collar is to be frozen, great attention is paid to the specifications for the selection of the freeze pipe and its couplings. The reason for this is mainly due to the fact that the coefficient of thermal contraction of the pipe is less than the ground to which it adheres. For this purpose, D.I.N. (German) and American Petroleum Institute (API) specifications are relied upon. In one case where freeze pipes ruptured, it was necessary to replace the calcium chloride with lithium chloride (freeze point of -830F) to freeze the contaminated ground.
The most difficult part of the calculations can be determining the heat transfer from the ground to the cold brine through the freeze pipe wall. It is convenient (and common practice for shaft collars) to simply use a rule of thumb for this figure. Another rule of thumb provides the capacity of the refrigeration plant required. The time required to complete the freeze wall is calculated by the following formula.
T = (Vγ/q dLN) [Cg(t1-t2) + w (80 + t2 -0.5t1)]….. Fritz Mohr (metric units)
In which T= Time to complete freeze wall hours
V = volume of ground to be frozen (dm)3
γ = Dry bulk density of soil kg/(dm)3
q = radiation capacity of freeze pipes k cal/m3
Cg =Specific heat of soil material dimensionless
d = outside diameter of freeze pipe m
L = length of each freeze pipe m
N = number of freeze holes dimensionless
To facilitate calculations, they can be simplified by substituting known values and given criteria.
Following are the known values (constants).
Latent heat of freezing water = 80 cal/ gm = 144 BTU /LB (1 k cal = 3.968 BTU)
Specific heat of water = 1.00 Specific heat of ice = 0.50
Specific heat of soil = 0.23 Specific heat of rock = 0.23
Example
Calculate the time required to freeze the ice wall and refrigeration plant capacity required for several likely hole spaces (4, 5 and 6 feet). The calculations will be based on the previously described collar excavation, with the following additional facts.
Facts:
1. The depth of overburden is 240 feet
2. The holes are drilled 22 feet into bedrock (freeze pipe length, h= 262 feet or 80m)
3. The natural temperature of the ground is 410F (50C)
4. Water content, w = 20%
5. Bulk dry density, γ = 106 Lbs./cubic foot (1.7 kg/dm3)
Solution:
1. The Mohr formula may then be employed – the volume of the completed ice wall, V
as designed is first calculated:
a. Outside radius of freeze wall cylinder, Ro = 6 + 1.84 = 7.84m
b. Inside radius of freeze wall cylinder, Ri = 6 - 1.84 = 4.16m
2. V =πh(Ro2- Ri2) = 80π (7.842 - 4.162) = 11,100m3 = 11,100,000 dm3
3. T x N = (11,100, 000 x 1.7/165π x 80 x 0.14) x [0.23(5 +10) +0.20 (80 +5 +10/2)]
4. T x N = 3,250 [3.45 + 18] = 69,720 hours = 415 weeks
Table 12-2 Freeze Pipe Spacing (1)
This tabulation provides the freeze plant capacity and the time taken to complete the total freeze wall; however, excavation may begin shortly after the freeze wall is closed. The overall schedule for a ground freezing project (and hence the cost) is more dependent on the freezing time elapsed until the excavation may start than it is for completing the full thickness of the freeze wall. The time of ground freezing required until excavation can begin is provided by the following formula.
T = R2/4KVS {(L +C1V0+3C2V0) (2 lnR’-1) +C1VS} Sanger (Imperial units)
In which T= Time to complete freeze wall hours
R= ½ the maximum actual pipe spacing (z+2)/2 feet (1 foot deviation)
K = conductivity of frozen ground 1.4 BTU/hr/ft2/0F/foot
Vs =degrees below freezing (brine) 32 - (-4) = 360F
Vo =degrees above freezing (soil) 41 – 32 = 90 F
L = Latent heat of fusion of water in soil 144 x 0.2 x 106 = 3,053 BTU/ft3
C1 = Thermal capacity of frozen soil 0.5 x 0.2 x 106 +0.23 x106 = 35 BTU/ft3/0 F
C2 = Thermal capacity of thawed soil 1.0 x 0.2 x 106 +0.23 x106 =56 BTU/ft3/0 F
R’ = R/radius of freeze pipe 12 x2R/5.50 =4.36R
Table 12-3 Freeze Pipe Spacing (2)
Selecting a suitable brine pump completes the design exercise. Normally, a single stage centrifugal pump is employed; however, a sliding vane pump is better suited to the application. The ideal design has the flow of brine in the annulus just into the turbulent range while the flow of brine in the inner pipe is laminar. In practice, it is only necessary (and provides for lower heat loss due to friction) if the annular flow is just in the mixed flow range. Usually, it is not practical to provide an inner pipe of the diameter required to obtain laminar flow. The characteristics of the pump required are determined as it is for pumping water, considering Reynold’s Number; however, an adjustment is made to account for the different viscosity of brine that varies with the temperature, as follows (for the optimum concentration of 29.6 %).
Table 12-4 Viscosity Compared to Temperature
The maximum head loss calculated of the pump selected for the application above should be roughly 13 feet (4m). The heat loss can be converted to tons of refrigeration (TR) as shown in the following formula.
Q = F.Hf……...(Cooper)
In which Q = Heat loss (foot-Lb./second)
F = brine flow (Lb./second
Hf = head loss (feet)
Q is then converted to tons of refrigeration (TR) with the appropriate conversion factors:
1 BTU = 778.2 foot-Lbs.
1 TR = 12,000 BTU/hour
Q is then increased to account for the mechanical efficiency of the brine pump. The value thus obtained should normally be less than 10% of the capacity of the refrigeration plant selected.