The pressure arch theory

Before an excavation is done in an underground mine rocks in situ are subjected to vertical and lateral pressures which are in equilibrium. In Fig. 9.1 the vertical compressive force is pi. The effect of pi is to compress the rocks in a vertical direction and as the strata are not able to expand sideways, there is induced a lateral compressive force along the beds denoted by P₂. When an underground roadway is made in the mine, the equilibrium of the pre-mining forces is disturbed and there is a redistribution of the vertical and lateral pressures. New kinds of forces also come into play. This redistribution of pressure is explained by the "Pressure Arch Theory" and is illustrated in fig. 9.2. In this figure,

B = Bending forces whose magnitude increases with width of excavation.

P₂ = Lateral forces, intensity of which increases with depth.

S = Shearing forces; intensity is highest when coal and floor beds are strong and lowest when they are weak and excavation is narrow.

P₁ = Vertical compressive forces., proportional to the depth

C — Increased pressure: roadway abutment pressure. 

Fig. 9.1. Forces acting on a cube of rock in-situ.

In a narrow roadway, as is driven in the bord and pillar method of working, the vertical compressive forces which were acting in the area of roadway before it was formed are deflected to the pillars of coal after the formation of the road. The redistribution of pressures takes place as shown by arrows. The rocks in the immediate roof bend downwards under their own weight and tend to separate from one another. This phenomenon is known as bed separation. The weight of higher strata is transferred to the coal sides as shown by the curved arrows CC. At the same time the side pressures P₂,  P₂ tend to push the rocks into the roadway. The sides of the coal pillars formed are subjected to shearing forces S S. The immediate roof beds AB, LL, MM and NN act as beams which tend to bend downwards due to their own weight. The lower layers of these beds are, as in the case of any beam, under tension and therefore, liable to fracture. To prevent the lower layers from excessive sagging and ultimate fracture, supports have to be erected in the roadway.

Redistribution of pressures on formation of a gallery in an underground coal mine, resulting in five "zones of influence"

Zone I — Bed separation in immediate roof strata due to differential sag of beds.

Zone 2 — No bed separation though the strata sag slightly due to gravity.

Zone 3 — Horizontal and vertical pressures build up to their "p re -excavation" value.

Zone 4— Floor heaves up but there is no bed separation in the floor.

Zone 5 — Pillar bulges towards the gallery due to release of horizontal stress at pillar sides.

The dotted line represents the "Pressure arch" or "pressure dome" with its supports (or abutments) situated at the sides of the coal pillar. The weight of the strata outside this arch is carried by the solid coal and the abutment pressure concentrated at these points is much more than the static pressure, i.e. the pressure merely due to depth.

The pressure on the coal pillars is also transmitted to the floor of the coal seam and in the excavated gallery the floor, if not strong enough, may lift upwards, and reduce the height of the gallery.

At greater depths the coal abutments are not able to withstand the increased pressure if it is more than the crushing strength of the coal and this causes the coal pillars to .crush. The crushing commences at the edges of the coal pillars. The weight of the beds within the arch is carried or controlled by the roof supports.

With wide excavations the magnitude of the bending forces B increases and if these bending forces are not kept in check by artificial supports for the roof, the rocks in the immediate roof bend downwards, develops cracks and in course of time the cracks become long and wide resulting in breakage of the roof rocks

fig. : Schematic of fast-response, closed-loop, servo-controlled testing system (Adapted from MTS manual 1970)

As the width of excavation increases, the span of the pressure arch also increases. Beyond some maximum width, which will vary with the nature of rocks and the depth from the surface, sagging of the immediate roof can no longer be prevented by artificial supports and the rocks in the excavation collapse, sometimes right upto the surface. This maximum width of roadway is known as "width of maximum pressure arch."

It will be obvious that a larger pillar will carry a greater load than a number of smaller pillars of the same size.

A number of headings in solid coal relatively close together, as in the bord and pillar method of working, release the pressure inside the arch but the abutments formed by the extreme sides of the outer headings are under great pressure. In the bord and pillar method of development, as there are galleries along the strike and along the dip-rise, there is a pressure dome spanning the galleries instead of the pressure arch.