Shaft Design

1. Introduction
Chapter 9 is mainly devoted to the design of vertical shafts; in particular, circular concrete-lined shafts because they are most commonly considered for new mines. For a production shaft, design starts with determining the cross section or plan view of the shaft. The production shaft is designed to the minimum dimensions required to contain and guide the shaft conveyances, as well as provide space to place and access the utility lines. The design may include provision for a man-way compartment and ventilation duct(s). The conveyances may ride on rope guides suspended in the shaft or fixed guides supported with structural steel members (the shaft sets).

For deep shafts, the minimum diameter of a production shaft may have to be increased, either to handle the volume of permanent ventilation air required or to accommodate the shaft sinking equipment. In the case of an open ventilation shaft, these two considerations (quantity of ventilation air and facility for shaft sinking) are the only design considerations to determine the shaft diameter.

For most hard rock mines, the circular concrete lining is now designed to the minimum practical thickness and is poured in place without reinforcing steel. The design of the lining is engineered in cases where the stiffness of the wall rock is less than the concrete, lining is required to be watertight (hydrostatic), temperature in the shaft will fall below the freezing point, or there is danger of ground movement.

If the shaft is to be equipped with rope guides, the required size and tension of the half-lock coil guide ropes and rubbing ropes (if required), as well as clearance between conveyances are determined as later detailed in Chapter 15 – Wire Ropes, Sheaves, and Conveyances. If rigid guides and steel sets are to be employed in a production shaft, they are designed to take into account vertical and lateral components of loads from conveyance travel, guide friction, cage dogging (if applicable), and resistance to ventilation air flow. It is normal practice to provide extra thickness in steel members and to specify a minimum thickness to account for corrosion. Today, rectangular structural tubing is usually employed for sets and guides, and the steel is often hot dip galvanized after fabrication. The structural analysis required to design the shaft steel is relatively simple where the proposed hoisting speeds are 2,000 feet per minute (fpm) (10m/s) or less. At higher speeds of hoisting, the steel design should be performed by a qualified engineering firm At one time, the shaft was equipped by inserting the horizontal members (buntons and dividers) into recesses left in the concrete lining. 

Today, the most common practice in North America is to support the horizontal members with saddle brackets bolted to inserts left in the lining. Utility hangers once bolted to curved angle irons are now more simply inserted into key-holes cut in a curved channel section that is bolted to inserts left in the lining. The inserts required for the shaft equipping are held in place with dummy bolts passed through the concrete forms through holes that have been drilled to precisely measured locations. In some cases, the shaft sinker elects to eliminate the inserts and uses anchored bolts in drilled holes, instead.

The well-engineered design of a circular concrete shaft must take “constructability” (facility of shaft sinking) into account. In addition, the employment of the shaft for pre-production development may require space for a larger ventilation duct than required for sinking. The shaft compartments and station design should be reviewed for the purpose of slinging large and heavy pieces of equipment as well as bundles of supplies underground.

It is unfortunate that there are few, if any “standard designs” for circular concrete shafts. Typically, each new shaft is designed “from scratch” to accommodate the particular requirements envisioned by the mine planners.

2. Rules of Thumb
Shaft Location
• The normal location of the shaft hoisting ore (production shaft) is near the center of gravity of the shape of the ore body (in plan view), but offset by 200 feet or more. Source: Alan O’Hara
• For a deep ore body, the production and ventilation shafts are sunk simultaneously and positioned within 100m or so of each other. Source: D.F.H. Graves

Depth of Shaft
• The depth of shaft should be such as is able to develop 1,800 days mining of ore reserves. Source: Alan O’Hara
• The first lift for a near vertical ore body should be approximately 2,000 feet. If the ore body outcrops, the shaft will then be approximately 2,500 feet deep to allow for gravity feed and crown pillar. If the outcrop has been or is planned to be open cut, the measurement should be made from the top of the crown pillar. If the ore body is blind, the measurement is taken from its apex. Source: Ron Haflidson
• In the Canadian Shield, a rectangular timber shaft is satisfactory to a depth of 2,000 feet. From 2,000 to 4,000 feet, it’s “iffy.” At greater depths, rectangular timber shafts should not be employed at all. Source: Bob Brown

Shaft Orientation
• The long axis of a rectangular shaft should be oriented perpendicular (normal) to the strike of the ore body. Source: Ron Haflidson
• The long axis of a vertical rectangular shaft should be oriented perpendicular (normal) to the bedding planes or pronounced schistocity, if they are near vertical. Source: RKG Morrison
• The long axis of a rectangular shaft should be oriented normal to regional tectonic stress and/or rock foliation. Source: Jack Morris

Shaft Inclination
• In hard rock mines, shafts sunk today are nearly always vertical. Inclined shafts are still employed in some developing countries when the ore body dips or plunges at less than 60 degrees. Source: Jack de la Vergne

Shaft Lining
• The concrete lining in a circular shaft may be put into tension and shear by external forces where the horizontal ground stress in one direction is more than twice the horizontal stress in the other. But only if the lining is “stiffer” than the wall rock and/or is subjected to high pressure grouting that may subject the lining to non-uniform compression. Source: Jack de la

Vergne
• The stiffness of concrete (Young’s Modulus of Elasticity, E) in a shaft lining is approximately 1,000 times the compressive strength of the concrete (i.e. for 3,600 psi concrete, E is approximately 3,600,000 psi, and for 25 MPa concrete, E is approximately 25 GPa). Source: Troxell and Davis
• The concrete lining in a circular shaft develops greater strength than is indicted by standard concrete cylinder tests, because it is laterally constrained. Tri-axial tests indicate this increase to be in the order of 20%. Source: Witold Ostrowski
• The pressure at which grouting takes place through a concrete lining should not exceed 50 psi (345 kPa) in the shaft collar near surface and at depth should not increase beyond the hydrostatic head by more than 25%. Source: Peter Grant
• Non-reinforced (no reinforcing steel) concrete linings in a circular shaft may be subjected to sufficient tension to result in crack propagation if the temperature environment is varied widely. This is especially relevant to design life if the temperature change routinely falls below the freezing point and moisture is present. It is known that concrete subjected to a tensile stress greater than 30 kg/cm2 (425 psi) will crack. The lining of a circular concrete shaft will crack if it is subject to a fluctuation in temperature greater than 200C (36 0F). This is because the coefficient of linear expansion of concrete is 1 x 10-5/0C (0.56 x 10-5/0F) and the maximum allowable elongation of concrete is 2 x 10-4. This explains why shafts in temperate climates will eventually sustain damage to the concrete walls if the ventilation air inside it is not heated during the winter months. Source: Prof. Yu Gonchum, China Institute of Mining and Technology
• A concrete lining may not be satisfactory in the long run for external pressures exceeding 500 psi (3.5 MPa). Concrete is not absolutely impermeable. When subjected to very high hydrostatic pressure, minute particles of water will eventually traverse the lining and as they approach the interior face (under high differential pressure) they will initiate spalling of small particles of the concrete wall. Eventually, over a period of years, repetitive spalling will destroy the integrity of the lining. Grouting through the lining may temporarily arrest this action, but it will eventually resume. Source: Fred Edwards
• A University of Texas study found that substituting 25 to 35% fly ash for Portland cement in high strength concrete could cut permeability by more than half, extending the life of the concrete. Source: Engineering-News Record, Jan/98 

Ventilation Capacity
• The maximum practical velocity for ventilation air in a circular concrete production shaft equipped with fixed (rigid) guides is 2,500 fpm (12.7m/s). Source: Richard Masuda
• The economic velocity for ventilation air in a circular concrete production shaft equipped with fixed (rigid) guides is 2,400 fpm (12m/s). If the shaft incorporates a man-way compartment (ladder way), the economic velocity is reduced to about 1,400 fpm (7m/s). Source: A.W.T. Barenbrug
• The maximum velocity that should be contemplated for ventilation air in a circular concrete production shaft equipped with rope guides is 2,000 fpm and the recommended maximum relative velocity between skips and airflow is 6,000 fpm. Source: Malcom McPherson
• The “not-to-exceed” velocity for ventilation air in a bald circular concrete ventilation shaft is 4,000 fpm. Source: Malcom McPherson
• The typical velocity for ventilation air in a bald circular concrete ventilation shaft is in the order of 3,000 fpm to be economical. Source: Jack de la Vergne

Shaft Guides
• The single most important requirement of a guide string is to have near-perfect joints. Straightness is the second most important, and verticality probably the third. Source: Jim Redpath
• The force exerted on a fixed guide from a moving conveyance due to imperfections in the guide string varies (1) in direct proportion to the mass of the conveyance, (2) in direct proportion to the square of the speed of the conveyance, and (3) in inverse proportion to the square of the distance over which the deflection takes place. Source: Lawrence O. Cooper
• For purposes of design, the equivalent static lateral force from a shaft conveyance to the guide string may be taken as 10% of the rope end load (conveyance + payload), provided the hoisting speed does not exceed 2,000 fpm (10m/s). Source: Steve Boyd
• For purposes of design, the calculated deflection of wood guides should not exceed 1/400 and that of steel guides 1/700 of the span between the sets supporting them. Source: German Technical Standards (TAS) 1977
• Acceleration values of 8% -10% obtained from a decelerometer test are reasonable rates to expect from a new shaft in good alignment. Source: Keith Jones
• In an inclined shaft, guides are required for the conveyance cars (to prevent derailing) when the inclination exceeds 700 from the horizontal. Source: Unknown

Shaft Sets
• Tests initiated at McGill University indicate that a rectangular hollow structural section (HSS) shaft bunton will have 52% of the resistance (to ventilation air) of a standard structural member (I-beam). Source: Bart Thompson

Shaft Stations
• At the mining horizon, the nominal interval for shaft stations is between 150 and 200 feet; however, with full ramp access to the ore body this interval can be higher, as much as 400 feet. Source: Jack de la Vergne
• Above the mining horizons, shaft stations are not required for access, but stub stations should be cut at intervals of ±1,000 feet, because this is a good distance for safely supporting steel wire armored or riser teck power cables. Source: Jim Bernas
• Above the mining horizons, full shaft stations are not required for access, but intermediate pumping stations are required at intervals not exceeding 2,500 feet (typically 2,000 feet) when shaft dewatering is carried out with centrifugal pumps. They may still be required for shaft sinking and initial development, even though the mine plans for using piston diaphragm pumps for permanent mine dewatering. Source: Andy Pitz
• The minimum station depth at a development level to be cut during shaft sinking is at least 50 feet (15m). Source: Tom Goodell

Shaft Clearances
• For a fixed guide system employing steel guides, the minimum clearance between a conveyance and a fixed obstruction (i.e. shaft dividers or shaft walling) is 1½ inches for small, square compartments; otherwise it is 2 inches. Source: Jack de la Vergne
• For a fixed guide system employing wood guides, the minimum clearance between a conveyance and a fixed obstruction (i.e. shaft dividers or shaft walling) is 2½ inches for small, square compartments; otherwise, it is 3 inches. Source: Jack de la Vergne
• For a rope guide system in a production shaft, the minimum clearance between a conveyance and a fixed obstruction is 12 inches and to another conveyance is 20 inches. These clearances may be reduced with the use of rub ropes. Source: George Delorme
• The side-to-side clearance between the skip shoes and guides should be designed ¼ inch and should not exceed 3/8 inch in operation. The total clearance face to face of guides should be ½ to 5/8 inches and not exceed ¾ inch. Source: Largo Albert

Shaft Spill
• For a well-designed skip hoist installation, the amount of shaft spill will equal approximately ½% of the tonnage hoisted. (This rule of thumb is based on interpretation of field measurements carried out at eight separate mines, where the spill typically measured between ¼% and 1% of the tonnage hoisted.) Source: Jack de la Vergne

Timber Shaft
• The classic three-compartment timber shaft employing one hoist for skip and cage service is normally satisfactory for production up to 1,000 tpd, although there are a few case histories with up to twice this rate of production. Source: Jack de la Vergne
• For a timber shaft, the minimum dimension of the space between the shaft timber and the wall rock should be 6 inches. Source: Alan Provost
• For a timber shaft, set spacing should not exceed 8 feet. Source: J.C. McIsaac
• For a timber shaft, catch pits are typically installed every six sets (intervals of approximately 50 feet). Source: Jim Redpath

3. Tricks of the Trade
• A part of the design for a shaft equipped with conveyances is the orientation of the shaft, which should consider both surface and underground layouts. Normally, a circular shaft has its sets oriented to best suit the desired underground station and loading pocket layouts and the surface structures subsequently oriented to fit. Source: Jack de la Vergne
• The old rule that says a vertical shaft should be located 200 feet from the crest of an open pit has been proven invalid by sorry experience. The set back distance should be determined by rock mechanics (and soil mechanics where applicable). Source: Jack de la Vergne
• In the case of a deep ore body, it has already been well proven that a twin shaft layout can be used to bring a new mine into a high rate of production at an early stage, which must be the aim of every new mining venture. Sinking two shafts simultaneously also provides desirable insurance against the possibility of one shaft encountering serious sinking difficulties. Source: L.D. Browne
• A twin shaft layout for a deep mine that is significantly offset from a single mining horizon will require twin cross cuts to the ore body to complete the ventilation loop. It may be better to set the shafts far apart to provide an efficient ventilation circuit. Source: Jozef Stachulak
• Hot dip galvanizing of shaft steel has so far demonstrated to provide the best practical protection from corrosion, when compared with epoxy, coal tar, or polymer based paints. Galvanized steel is not scratch resistant, but this is not required since zinc in the immediate vicinity of the scratch will prevail against the propagation of rust. Source: Jack de la Vergne
• The process of hot dip galvanizing involves temperatures almost identical to the standard procedure for stress relieving. This means that a significant cost saving can be had by purchasing Grade C HSS tubing instead of the more expensive Grade H (stress-relieved). Source: Ron Elliot
• Equipped circular concrete shafts have often been designed with a divider beam between the cage and counterweight. In most cases, this member is not required and represents an unnecessary expense. Source: Jack de la Vergne
• A frequently overlooked item is the large diameter of flanges that may be required for a highhead pump column to fit into a shaft. The flange diameter should be determined at the design stage to avoid later problems. Source: Gord Stewart.
• In the elastic (stiff) rocks found in hard rock mines, horizontal loads on concrete shaft linings are relatively small and never attain the values that occur as lateral loads on lined tunnels. The rock loads themselves (against the concrete shaft lining) may be zero in the case of strong elastic rock formations. Source: Peter Grant
• The concrete lining in a circular shaft is normally subjected only to compressive forces and is alleviated from the effects of shrinkage because of its bond to the wall rock. Hence, in a stable temperature environment, the concrete lining should require no reinforcing steel and normally none is employed. Source: Jack de la Vergne
• The influence of light reinforcing is not taken into account in the stiffness calculation for a concrete lining. Reinforcement, such as mesh in shotcrete or light reinforcing steel in concrete, may play an important role in controlling and distributing stresses and cracks, but it does not significantly increase the stiffness. Source: Hoek and Brown
• The compressive strength of a circular concrete lining may be increased by the addition of reinforcing steel, but this procedure is inefficient. It is normally easier and less expensive to simply employ a higher strength concrete. Source: Witold Ostrowski
• It is convenient to assume that the increase in concrete lining strength due to confinement of the lining is equal to that required for resisting grouting pressures. Therefore, both can normally be ignored in design calculations. Source: Jack de la Vergne
• For a timber shaft, bearing sets are usually placed beneath each station and loading pocket. Source: Jim Redpath
• For a timber shaft, the function of the hanging rods is to assist in hanging and aligning the sets. They do not contribute to the integrity of the permanent installation. Integrity is accomplished with the blocking and bearing sets. Source: Del Anderson

4. Function of Concrete Lining in a Circular Shaft
Curb Rings
The first shafts sunk in hard rock mines had no lining. When some were sunk deep, problems developed during the sinking and subsequent operations. These problems were principally related to ground control. The way to overcome this problem was to do what others had already done in mines that had to traverse soft ground formations – sink them circular and line them with masonry. Because it is difficult to lay masonry upside down, the procedure was to pour concrete curb rings at intervals so that the masonry could be laid up between them as the shaft sinking advanced.

Continuous Lining
Following World War II, a procedure was developed in South Africa where the curb ring pour was simply continued up to the next ring. This procedure was used in achieving extraordinary rates of advance and was soon copied elsewhere. In North America, this procedure and the circular shaft section were quickly adopted in hard rock mines to replace the concrete lined rectangular shaft and, in many cases, to replace the traditional rectangular timber shaft.

Role of Lining
For a circular shaft in a hard rock mine, the wall rock is stiffer than the concrete so ground stresses are not transmitted to the concrete from the country rock. The only structural role of the concrete is a passive one. The concrete has little effect on the stress distribution in the surrounding strata; however, the concrete can have a considerable effect on the strength of the wall rocks, even if it only stops the development of loose and prevents the wall rock from unravelling or sloughing. This allows the wall rock to continue to support even though fractured. The advance of the concrete lining of a shaft sunk in a hard rock mine is normally kept 2-3 diameters above the advancing shaft bottom to permit relaxation of the wall rock; however, when a hard rock mineshaft encounters bad ground, the lining may be expected to provide active structural support. To maximize this support (by taking advantage of the slight wall closure), the concrete should normally be placed as close to the bottom of the excavation as practical (there are exceptions). Even for purposes of this support, the concrete rarely needs be very thick at all, especially when unavoidable over-break is taken into account.

Concrete Lining Advantages
The concrete lining has other advantages. Perhaps the most important is to provide an anchor for the shaft steel and utility hangers. The regular dimensions of the shaft means that the shaft steel and hardware can be shop-fit to the shaft on an ‘assembly line’ basis as opposed to field-fitting on a oneof-a-kind basis. Inserts placed in the concrete (using dummy bolts in the shaft forms) eliminate the requirement for drilling anchors to support the hangers for sets and utilities.

Another advantage is that the concrete lining provides a smooth surface for ventilation air. The resistance of a concrete lined ventilation shaft is about ¼ that of a raw raise of the same diameter. In wet shafts, the concrete lining is of assistance in controlling and collecting the flow of groundwater and provides benefit to dry wall grouting.

5. Stiffness of Concrete
The stiffness of concrete (Young’s modulus of elasticity, E) to compare with the stiffness of the rock to be sunk through and can be calculated from the following formula.
E = 57,000 (f’c)½
(American Concrete Institute, 1977)
Example
Find the modulus of elasticity for 3,600 psi (25 MPa) concrete.
Solution: 
E = 57, 000 (3,600)½ = 3.4 million psi (23.5 GPa)
Check calculations Lloyd Rangan formula, E = 3,320 (f’c)1/2 + 6900, .... [values in MPa]
Solution: E = 16,600 + 6,900 = 23,500 MPa = 23.5 GPa

6. Stiffness of Rock
Minimum and typical values for the stiffness of rocks typically encountered in shaft sinking are tabulated in metric units in the following tabulation (Table 9-1). Hard rocks are normally stiffer than a concrete lining. It should be noted that the values given are for sound rock and do not consider decomposition (degenerative alteration) that may sometimes occur.
Table 9-1 Stiffness of Common Rocks in GPa
(1 GPa = 145,000 psi)


7. Concrete Liner Design
Concrete liners are not usually “designed” for hard rock applications. As previously explained, the stiffness of the concrete is normally less than the wall rock; therefore, the concrete will not be subjected to ground stress. Conditions do exist where the concrete lining for a hard rock mineshaft must be “engineered.” One common example is the collar of a circular concrete shaft that is sunk in a deep soil overburden. In this case, the concrete liner of the shaft section in over burden is designed to resist the soil pressure and the ground water pressure.

The pressure from ground water (hydrostatic pressure) is readily determined if the maximum height of the ground water table is known. The soil pressure is simple to calculate for granular soils (sand and gravel), but for overburden containing cohesive soils (silts and clays) or a mixture of granular and cohesive soils, determining the design pressure is better left to a soil mechanics expert.

A concrete cylinder subjected to a uniform pressure (radial) around its outer circumference will develop an internal compressive stress tangential to its circumference. If the pressure is applied suddenly, the concrete will react elastically and the stress near the interior wall of the lining will be greatest and gradually reduce towards the outer wall. The formula to be employed for this case is the Lamé or “thick wall” formula.

If the pressure is great and applied slowly, the concrete may react plastically and the stresses will tend to redistribute themselves evenly across the thickness of the concrete wall. A number of formulas have been developed to account for this plastic or visco-elastic property of concrete, the best recognized of which is the Huber formula.

Hard rock miners are more comfortable with the elastic analysis (Lamé) because it is more conservative (safer) and miners find it difficult to imagine that concrete can deform to a plastic condition. Furthermore, miners are not satisfied with the factor of safety employed in concrete design codes for a “dead” load (which may be 1.4). For good reason, miners prefer to use a SF of approximately 2 to design a concrete lining. Miners will not allow a shaft collar lining less than 18 inches (450 mm) thick.

For the design of the liner shaft collar in deep overburden, it is wise to assume the ground water table is at surface elevation and/or that (to account for arching) at least 70% of the maximum theoretical active soil pressure is applied throughout the total height of the collar.


Example (Imperial Units)
Determine the required concrete thickness for the lining of a circular concrete shaft subjected to external pressure using the Lamé formula.
Facts: 
1. The circular concrete shaft has a 20-foot inside diameter
2. The circular concrete shaft is subjected to an external pressure of 200 psi
3. The concrete is to have a 28-day strength of 3,500 psi
Solution: 
1. f’c = 3,500 psi = unconfined compressive strength of the concrete
2. F = 2.0 = SF with respect to compressive strength of concrete.
3. P = 200 psi = external pressure
4. r = 120 inches = inside radius of the circular shaft
5. t = ? = thickness required measured in inches


Example (Metric Units) (same problem with comparable values):
Determine the required concrete thickness for the lining of a circular concrete shaft subjected to external pressure using the Lamé formula.
Facts: 
1. The circular concrete shaft has a 6.1m inside diameter
2. The circular concrete shaft is subjected to an external pressure of 1,400 kPa
3. The concrete is to have a 28-day strength of 25 MPa
Solution:
1. f’c = 25 Mpa= unconfined compressive strength of the concrete
2. F = 2.0 = SF with respect to compressive strength of concrete.
3. P = 1400 kPa = external pressure
4. r = 3050 mm = inside radius of the circular shaft
5. t = ? = thickness required measured in millimeters



Example (Check Calculations)
Determining the ultimate strength (implosion pressure), Pult of the thickness designed and comparing it to the design pressure provides a SF based on the ratio of these values. Checking the design calculation may be worthwhile by employing the Haynes formula (empirical) in the following form.
Pult = f’c (2.17t/Do - 0.04), in which Do = outside diameter of the lining
Pult = 25 (0.14 –0.04) = 2.5 MPa = 2,500 kPa
Safety factor with respect to ultimate strength = 2,500/1,400 =1.8

8. Shaft Design Tolerances
Following are typical tolerances permitted for shaft sinking contracts.
Timber Shafts
Set to set distance ± ½ inch
Sets ± 1/8 inch
Face to face of guides ± 1/8 inch
Clearance to wall rock 6-inch to 24-inch
Overbreak Blocks exceeding 24 inches in length to be pinned to the wall rock

Concrete Shafts (with steel sets)
Concrete forms (circumference) - ¼/+0 inch
Concrete lining (out of plumb) ± ½ inch
Set to set distance ± ¼ inch (but not allowed to be cumulative)
Sets ± 1/8 inch
Face to face of guides ± 1/16 inch
Minimum concrete thickness 6 - 9 inches (typical overbreak is 9 – 12 inches)