The following invention relates to a method of blasting rock whereby the result of the blasting operation, for example, the blasting in a borehole is quantitively calculated and projected, based on a special , objective plotting and quanti- tive description of the relevant rock mass structure, especially with regard to the actual or potential joints and planes of weakness.

Rock materials and rock masses generally have a more or less substantial anisotropic strength and are often intersected by actual or potential joints and bedding along which the ^' material usually slides (divides) at a sufficiently high loading. This rock structure has a strong influence on all rock fracturing operations, like rock blasting, mechanical rock drilling on a large and small scale and crushing. This has up until now somewhat impedded quantitive calculation and prediction of the results of rock blasting.

Earlier methods of calculation fall into one or the other of two main groups. In the first one has attempted to quantitively calculate tensions and stresses in the loaded rock material by the extremely simplified hypothesis that the rock material is isotropic and homogeneous. With such calcula¬ tions it has been possible with a certain amount of success, to ascertain the direction and length of the joints which radiate from a borehole when blasting homogeneous material or from the drill bit's cutting surface when drilling.

In the second, experience has been gathered on, for example, the- .di stri buti on of individual sizes of fragments during different blasting operations and attempts to establish

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empirical relationships between ingoing parameters such as borehole distance, charge size etc. and the final result, the average size of the largest fragments for example.

With such calculations as these it has been difficult to consider the influence of rock structure on the outcome of the rock blasting, especially in those cases where, for example, when blasting scale rock, the orientation of the rock structure has a significant effect on the results. Invention, general The invention is based on a method that predetermines and calculates the results of rock blasting, such as the individual fragmen.t size distribution of the fractured rock or the extent and type of effect on the remaining rock, which does not have the limitations of the methods mentioned above. This method permits consideration to the combined effect of the ongoing blasting and the relevant rock mass structure when cal culating.

The method is characterised by the stresses caused by the applied blasting forces being balanced with regard to the effects that the ongoing blasting has on the stresses. It is also characterised by the joints and planes of weakness in the rock structure as well as the elementry matter being described with special values which represent the strength and rupture properties of the structure element with regard to the relevant blasting mechanism. A further characteristic of the method is that different structure elements in the calculation as in reality can be influenced within different stress zones with differing large degrees in space.

There are three special subprocesses included in the method, namely: a) to calculate and plot the rock's actual stress at different points in connection with the blasting b) to plot and define the structure of the different rock structures with special attention to the strength and fracture properties, and c) to predetermine how and to what extent the rock is effected partly with regard to the size and strength of the material blasted and partly with regard to the strength and stability

of the remaining rock. Example of application

The invention shall be described below by means of an example which relates to the calculation of rock damage when contour blasting. The general application of the invention to other blasting processes, drilling and crushing for example, will then become apparent to the specialist in the field.

The size of the fractured zone in the remaining rock which occurs when blasting is obviously dependent on the size of the charge and the strength of the rock.

A. The dynamic loads that the rock is subjected to during the initial blast result in a wave motion through the rock. This arises when the explosive gases expand and fracture the encircling rock. The dynamic loading is proportional in rela- tion to the wave motion's particle velocity and its propoga- tion velocity; this diminishes at an unknown distance from the charge.

B. If the dynamic loading shall result in remaining damage to the rock, the occurrence of new fractures or movement of existing types, depends on the local strength of the rock. The rock structure is therefor an important parameter - the weakest planes in rock are often the facing surfaces between different geological zones, as for example different bedding pi anes . C. Whether the resultant damage remaining will have any bearing on the existance of the fractured rock's contour or not depends conclusively on the character of the damage and, by no means least, the orientation of the damaged plane in relation to the contour and the static loading. A practical and useful model of rock damage for contour blasting must include the following three elements:

- A relationship between the dynamic loading, the size of the charge and the reciprocal distance between the bore- hol es . - A definition and presentation of the rock structure's static loading and orientation.

- A definition of the fractured contour's static loading and orientation in relation to the rock structure.

A general and serviceable model must be three dimensional As a first step, however, a two dimensional model can be arranged, where the relationships are dealt with in a plane which includes borehole axis and is at right angles to the exposed rock surfaces. RELATIONSHIP BETWEEN DYNAMIC LOADING, CHARGE AND DISTANCE

The description will be continued in connection with enclosed drawings. Fig. 1 thereby shows a circular function, figs. 2 to 4 curve charts and figs. 5 and 6 rock structure models. Figs. 7A - C show broken rock profiles.

There is now a good experimental basis for measuring vibration velocity (particle velocity) with different charges and distances (Holmberg 1977). To systemize the measured results, especially concerning the vicinity around the layed out charges, we depart from the general relationship between the ground vibration velocity v, the charge weight Q and the distance R in the formula

KQ I W (1)

where tx-- , _/ 4 _ and K are constants (e. g .& = 0.7, ? = 1.5 and

K = 700 if Q is measured in kg, R in meters and v in mm/sec).

The relationship (1) applies to relatively concentrated charges at distances which are long with regard to the charges greatest dimension.

For a layed out charge we now view every part of the charge as a concentrated part-charge. The contributing factors to the oscillatory intensity w caused by the part- i lot charges defined as w = v ' are added and the resultant oscillatory velocity is calculated in (2).

In the equation (2) / is the charge weight per borehole longitudinal unit and r the perpendicular distance between the longitudinal axis of the borehole and the measuring point (see enclosed fig. 1 ). Further, dO = y . άx. . Equation (2) is numerically integrated. Enclosed figs. 2 and 3 show in diagram form the results of two such calcula¬ tions, one for a broad hole of 15 m depth and one for a narrow hole of 3..m depth. In figs. 2 and 3 the distance of the abscissa R is given in meters from the borehole and the ordinates the maximum vibration velocity v in mm/sec. This is assumed to reach a critical value within an area between approx. v = 700 to 1000 mm/sec, i .e. the area for initial damage which in figs. 2 - 4 is indicated by the horizontal lines, must be considered, should the blast effect be limited to a given area and the remaining rock shall stay undamaged. Inversely, one should weigh , the charges so that the value v falls above 1000 mm/sec where the entire blast effect is in¬ tended. The curves in the diagram refer to each effect of one and the same charge, that is 75 and 34 kg per meter charged hole. The charge in fig. 2 is 15 m and in fig. 3 3 m; with a charge of, for example 12 kg/ , the borehole according to fig. 2 should not lay closer than approx. 8 meters from the rock mass that is to remain intact. On the other hand it is possible with the charge 1.0 kg per hole meter according to fig. 3 to go within approx. 1 meter of the unfractured rock face and so on. With for example, contour blasting, the size of the charge is varied in the holes at different distances from the remaining rock face, so that the strength of the charge decreases the nearer the boreholes are to this face. Under normal stress zero, the shear strength of granite Y is between 0.3 and 0.6 kbar. £ diminishes with reduced normal stress. Homogeneous granite can, however, "hold" under the stresses that occur at oscillatory velocities in the region of 1000 mm/sec. For cracked granite or weaker, especially strateous rock types of- ow strength one can expect breaks or movement in joint planes at significantly lower oscillation velocities. It is therefor apparent that if the rock adjacent to

the zone that is to be blasted shows itself to have weakened sections that will not withstand more than e.g. v = 200 mm/sec, one should not go nearer to this section with boreholes than approx. 30 m if the strength of the charge is 12 kg/m accor¬ ding to fig. 2.

In fig. 4, experimental measurements have also been entered in the diagram. These come within surprisingly accurate proximity of the calculated values, which confirms that the method of calculation used takes sufficient con¬ sideration to the influence of the ongoing blasting.

The dynamic loa.ding on the rock during blasting can be approximately defined

,_ _ _ _ ____ _

* ^■ =- ^" E ^" E ^" C

where <5 is the 1 oading , _τ"the strain or compression stress, £ corresponds to the shear stress, E the elasticity modul and c the wave motion's propagation velocity, which for the majority of oscillation modes can be expressed as a fraction of the speed of sound (acoustic velocity) c .

Let us especially consider homogeneous crack free granite, where E = 0.8 x 10 ¹¹ N/m ² (80 GPa or 800 kbar), C _r = 3800 m/sec (Rayleigh distribution). The oscillation velocity v = 1000 mm/sec. then gives a shear stress of τ :

T __H 800 1 = 0.11 kbar 2c 3800

ROCK STRUCTURE MODELS

To substantiate our handling of the rock structure's influence on the rock damage, two rock structure mode ^' ls are selected, the first according to fig. 5 enclosed is charac¬ terised by having one or several systems of relatively parallel jointing planes, the second according to fig. 6 being characterised by one or more overlapping systems of randomly distributed jointing planes. Jointing planes in the sense mentioned here refer to both potential columnar planes, for example, foliation of the sediment or bedding type, flaws in granite, slatiness and planes with actual

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separation, for example, joints with or without previous parallel movement between the faces.

Potential bedding is characterised by a shear stress £ p for the shear rupture parallel with the bedding and a rupture tensile stress crp for tensile movement at right angles to the joint. The actual jointing plane is characterised by the tensile strength zero at right angles to the plane and a shear strength which is proportional to the normal pressure <rή over the plane (7^ = V _* ⁰ ^ ) •

The material lying between is characterised by a tensile r>> stress of c _m and a shear stress _m where £ _m = σ'„l2 . m m

In fig. 5 the two dimensional rock structure has two systems of relatively parallel jointing planes. In fig. 6 are shown with broad lines suggested jointing planes of such a nature that the size of v according to the above should fall below 200 mm/sec when blasting adjoining rock zones to prevent permanent influence at the jointing plane. The narrower lines represent other jointing planes which are not effected before, e.g. , v = 500 mm/sec. In between the jointing planes existing homogeneous rock starts to fracture at v = 1000 mm/ sec or more.

Before the blasting operation, descriptions or drawings as with figs. 4 or 5 for example, should be made of the relevant rock, base, which shows, among other things, any possible jointing planes, their character and position in the rock zones which shall be left unfractured and blasted respectively. On the basis of these descriptions and drawings the boreholes for applying the charge are then considered, at an amount per hole depth unit of the borehole and the total length of the individual boreholes according to the diagrams in figs. 2 and 3. At the same time the holes' relative distance and the strength of their charges are estimated so that the remaining rock mass can be in a pre¬ determined position and remain free from deformation. On the other hand the emphasis of the blasting operation should be that the size _^ of the blasted rock mass is balanced against the charges so ^' that the value v according to figs. 2 and 3 attains a sufficiently high value even in the rock that i

free from jointing planes.

The descriptions or drawings previously mentioned of the rock jointing planes can be confirmed experi encewi se after observation of the visible rock surface and/or test drillings or seismic analysis. Presentations can be continuously drawn up as the blasting of the rock takes place in several stages. INFLUENCE OF THE ROCK STRUCTURE ON THE ROCK DAMAGE

Wi th..knowl edge of the charge concentration ji and the charge or charges' length and relative geometrical arrange- ment, equations 2 and 3 give a value of the maximum transient tensile and shear stress respectively generated by the blast in ery part of the rock at an arbitrary distance and in an arbitrary direction from the charge or charges. The maximal stresses thus calculated are at every moment carefully reckoned vector magnitudes, especially in the area near to the charge. The directions of the main stress, however, run almost completely round during the course of the vibration wave through one point. We therefor presume that a jointing plane situated at a certain distance from the charge is influenced in the same way regardless of the orientation in Relation to the charge. The calculated transient maximum stress is considered consequently in the future as a scalar, which simplifies the treatment considerably.

The remaining effect of the transient stress in a jointing plane exceeding the characteristic rupture strain is assumed to be loss of cohesion in potential jointing planes and loss of shear strength at the normal load zero for actual jointing planes. Subsequently the jointing plane can only transfer positive normal loads and thereby pro- portional friction stresses.

CHARACTERIZATION OF THE CONTOUR AND ITS LOADING

For continued handling a description is required of how the blast effected rock is loaded at the blasted contours. We choose three simple types of blasted contours: a slope, a column and an arch; in every case it is assumed the static loads -s,tated or caused only by the weight of the rock itself. These three contours appear in figs. 7A, B, and C enclosed where the rock masses' jointing planes are

also indicated.

The slope is characterised by, as shown in fig. 7A, a step height k and an inclination angle'tf ^' as well as the rock ^' density. The column according to fig. 7B, is characterised by its thickness b, its height h, and the overlying load F of the rock density. The arch according to fig. 7C is characterised by its span S, which is presumed to be double the radius, of curvature at the roof, the depth of the base below ground level h^ as well as the rock density. THE STRENGTH AND STABILITY OF THE BLASTED ROCK

With knowledge of the orientation of the rock structure in relation to the blasted contour and its loading, the changes in the jointing plane's strength caused by the blasting can be evaluated. In the simplest evaluation we assume that the fractured fragments which are not subjected to other forces than those related to their own gravitation and do not rest stabily in their positions fall away.

At a later stage more refined, existing rock stability programmes in modified form could be used to evaluate the stability of the structure.