Gravimetric surveys for assessing rock mass condition around a mine shaft

Abstract

The fundamentals of use of vertical gravimetric surveying method in mine shafts are presented in the paper. The methods of gravimetric measurements and calculation of interval and complex density are discussed in detail. The density calculations are based on an original method accounting for the gravity influence of the mine shaft thus guaranteeing closeness of calculated and real values of density of rocks beyond the shaft lining. The results of many gravimetric surveys performed in shafts are presented and interpreted. As a result, information about the location of heterogeneous zones of work beyond the shaft lining is obtained. In many cases, these zones used to threaten the safe operation of machines and utilities in the shaft.

Introduction

Vertical gravimetric measurements performed in a borehole require specialist equipment, i.e., a borehole gravimeter. The results obtained with this tool are very useful for the interpretation of geophysical surveys associated with the results of other geophysical methods.

The gravimetric measurements can also be performed in mine shafts. First such works (Fajklewicz 1956; Fajklewicz and Zespolem 1984; Fajklewicz et al. 1986, 1988) were based on a field gravimeter for measuring relative gravity. Thanks to the use of a special measuring bridge (Fajklewicz et al. 1988), the gravimetric observations were realized in a mining cage. Thanks to the bridge, the gravimeter could be disposed in a system completely independent of the cage, its vibrations and movements. In such conditions, when the vibrations of the skips and shaft equipment were not transmitted on the bridge, the gravimetric observations could be safely realized. For this reason, the gravimetric surveys in a shaft may play an important role in recognizing geotechnical conditions of the rock mass beyond the shaft lining (Łój 2012).

Basic methods

Gravimetric profilings in a shaft lie in measuring the vertical distribution of gravity. This distribution creates bases for calculating the Bouguer anomaly, i.e., a difference determined with the following formula (Fajklewicz 1980; Snyder 1976):

$$ {\Delta g_{\text{B}} = \Delta g^{\prime}_{\text{p}} - \Delta g_{\text{N}} }, $$

(1)

where $\Delta g^{\prime}_{\text{p}}$ measured gravity with corrections and Δg _N average change of gravity with depth.

In a horizontally laminated geological medium, the measured gravity is expressed by the formula (Łukawczenko 1948):

$$ {\Delta g_{\text{p}} = \frac{\partial g}{\partial z}\sum\limits_{i = 0}^{n} {h_{i} } - 4\pi G\sum\limits_{i = 0}^{n} {\rho_{i} h_{i} } + \delta g_{i} }, $$

(2)

where ${\frac{\partial g}{\partial z}\sum\nolimits_{i = 0}^{n} {h_{i} } }$ change of gravity with depth, $4\pi G\sum\nolimits_{i = 0}^{n} {\rho_{i} h_{i} }$ sum of attraction of layers of density ρ _i, and thickness h _i , δg _i component corresponding to gravitational effect of existing heterogeneities beyond the shaft lining of limited horizontal size.

Component (3) (Fig. 1) corresponds to a change of gravity in a layer between its roof and the bottom. Graphically, this change (Fig. 1) is represented by inclined sections of (3) distribution. The inclination changes on the boundaries of the layer, which is connected with the density of the layer. Therefore, by measuring the vertical change of gravity between the roof and the bottom of an unlimited horizontal layer, one may determine the density of the layer, provided that suitable corrections accounting for the place of observation are introduced.

Fig. 1

Character of gravity changes with depth

The location of measuring points with respect to the boundaries of the layer is presented in Fig. 2. The calculation of density can be performed between the positions of the successive point. Only in the case of points located in the thickness interval of a layer, the density can be determined correctly, i.e., between points 2 and 3.

Fig. 2

Unlimited horizontal layer in vertical gravimetric survey

The gravimetric survey in a shaft can also be realized in such depth intervals which correspond to the location of the shaft girders. Frequently, the difference of gravity at points corresponding to the boundaries of the layers cannot be established. Therefore, the difference of gravity defined on the basis of gravimetric measurements is called interval density.

It is calculated from the formula:

$$ \rho_{i} = \frac{1}{4\pi G}\left( {\frac{\partial g}{\partial h} - \frac{{\Delta g^{\prime\prime}_{\text{p}} }}{{h_{i} }}} \right), $$

(3)

where $\Delta g^{\prime\prime}_{\text{p}}$ difference of gravity measured in the bottom and in the roof of a layer, taking into account suitable gravity correction (it look “Gravity corrections”). $\frac{\partial g}{\partial h}$ vertical gradient of gravity.

Apart from interval density, also average density can be calculated, on base of formula (3). For doing so, an average change of gravity Δg _N in interval h equal to a vertical distance between two extreme measuring points in the shaft is introduced to the formula. The average density is then calculated with a very high accuracy ±0.001 Mg m⁻³. The calculation error for interval density is much higher due to the small distances between measuring points Δh ≪ h.

It can be calculated for the formula:

$$ \delta \rho_{i} = \left| {\frac{1}{4\pi G}\;\;\frac{{\delta \left( {\Delta g} \right)}}{\Delta h}} \right|, $$

(4)

where δ(Δg) is a mean squared error of a single measurement of gravity.

The influence of the measuring error and distances between measuring points on the accuracy of determining the interval density is presented in Fig. 3. If the gravimetric measurements in a shaft were made with an accuracy of, e.g., ±0.02 mGal, the determined interval density of a layer 5 m thick is burdened with an error ±0.05 Mg m⁻³, which constitutes about 2% of average density of rocks (2.0–2.6 Mg m⁻³).

Fig. 3

Relations of error in calculated interval density δρ _i to error of gravimeter measurement δ(∆g) and vertical distance ∆h of test stands in the mine shaft

Gravity corrections

Gravity corrections are made to eliminate the influence of all factors associated with the place of measurement. When the gravimetric surveys are conducted in a mine shaft, the gravity correction is most important. Gravity correction means taking into account the effect of gravity exerted by the shaft lining, its shaft tube and accompanying workings.

The gravity influence of the shaft lining has a significance when the thickness or type of lining material changes. Much bigger influence is exerted by the shaft tube as it affects the shape of the recorded Bouguer anomaly, mainly interval density calculations.

The gravity activity of the shaft with its lining was accounted for by approximating these objects with a material line of constant density. Thus, calculated mining correction for a shaft does not allow for correct determining rock density beyond the shaft lining. This is connected with the varying lithology and so varying density of layers. For average values, we will obtain a shaft filled with rock material having density and location similar to that around the shaft.

To illustrate this, calculations of interval density were performed in one of the shafts in the Upper Silesian Coal Basin (USCB).

This shaft opens up a coal level 510 which is about 6 m thick and its bulk density equals to 1.35 Mg m⁻³. Two measuring points were located within the level; therefore, the calculated interval density should correspond to the bulk density of hard coal. The results are presented in Fig. 4. The curves Δg ¹, Δg ², and Δg ³ are distributions of Bouguer anomalies calculated without and with mining corrections made for the shaft, curves Δg ² and Δg ³, respectively. The significant difference in the course of last two distributions results from the way in which the correction for the shaft was calculated. In the first case distribution, Δg ² includes the correction calculated on the assumption that the shaft was approximated with a material line. The coal level 510 is deposited in the depth interval 262–268 m and the mining correction for this area equals to 0. Calculated densities of distribution Δg ¹ and Δg ² are identical and equal to 1.89 Mg m⁻³, which does not correspond to the density of hard coal. Therefore, it is purposeful to make a vertical cylindrical model, parts of which would represent the placement of particular layers. In this situation, the Bouguer anomaly distribution starts to resemble the actual picture. After applying the above procedure, the calculated density equaled to 1.36 Mg m⁻³ (densigram ρ ³ _i ).

Fig. 4

Example of calculating interval density: ∆g ¹, ∆g ², and ∆g ³ distribution of gravitational Bouguer anomaly calculated as follows: without gravity correction, with gravity correction by shaft assuming its constant density and with variable density; $\rho_{\text{i}}^{1}$, $\rho_{\text{i}}^{2}$, and $\rho_{\text{i}}^{3}$ interval densities calculated based on the distributions ∆g ¹, ∆g ², and ∆g ³

The second gravity correction does not necessarily have to be taken into account. It is a topographic correction Δg _t. The way of calculating it for points located under the surface is commonly known from the literature (Hammer 1939; Beyer 1979; Hearst et al. 1980; Fajklewicz 1980). Exemplary calculations of this correction for selected terrain models are presented in Fig. 5.

Fig. 5

Vertical distributions of topographic gravity for a selected terrain

The analysis of the distributions Δg _t reveals that for positive height difference in reference to the stroma shaft, the topographic correction is plus, and for negative, height difference is minus.

The shape and range of the topographic correction of gravity show that it influences only the calculated average density value (Madej 2002).

The sign of the change of average density, calculated without topographic correction, compared to the actual value is opposite to the sign of the topographic correction (Madej 1992).

Another correction to be necessarily taken into account in gravity measurements is the correction of gravity of drifts and workings leading to the shaft.

However, their gravity impact is limited to the initial section, as in the dependence shown in Fig. 6.

Fig. 6

Relative changes of gravity correction caused by sidewall in a function of its relative length and diameter

The dependence shows a relative gravity impact in the shaft axis depending on its relative length and related to its horizontal size. The presented plot reveals that the gravity impact of the working acts on an area covering five times its horizontal size.

Methodics of interval density calculation

The previously discussed method of calculating density of rock layers around the shaft referred to a situation when the course of lithostratigraphic profile in the place where the shaft was drilled is known. This profile could be used for constructing a depth model of rock layers around the shaft. This could guarantee that the calculated interval density values were congruent with the bulk density values. However, in a lack of any information about the lithostratigraphy of layers opened out through the shaft, the density is calculated in quite a different way, by iterations.

The cycle is initiated by calculating average and interval densities without accounting for the correction of shaft gravity. The correction is defined in the next step on the basis of previously calculated average and interval density values. Then, the density is determined for the second time, accounting for the mining correction, for the calculation of which densities established in the previous step were assumed. At the next stage, the calculation process is repeated several times to establish the density of rocks beyond the shaft lining.

The author’s experience shows that such a complex calculation process requires 6–7 cycles to bring about density values close to the real ones.

An exemplary calculation cycle on a model of layers is presented in Fig. 7. It was assumed that a horizontal layer of rocks 2.6 Mg m⁻³ of density lies at a depth of 100–124 m. Above and below are layers of density 1.9 and 2.1 Mg m⁻³, respectively.

Fig. 7

Results of rock density calculations—different ways of accounting for mine shaft corrections (explain of symbols in text)

The generated gravity measurements in a shaft allowed for determining the Bouguer anomaly $\Delta g_{\text{B}}^{1}$ in Fig. 7a and the corresponding distribution of interval density changes $\rho^{\prime}_{\text{int}}$ in Fig. 7b.

Densities $\rho^{\prime}_{\text{int}}$ were calculated without mining correction for the shaft. The comparison of changes of density distribution with the model ones shows that the biggest differences between them were observed at the shaft and sump pit from 0.09 to 0.4 Mg m⁻³, respectively, and at the borders of the high-density layer from −0.1 to ±0.15 Mg m⁻³, respectively.

In the next step, the mining gravity correction for the shaft was determined, assuming that its density is constant and equals to the previously defined average value for the whole complex. This caused that only $\rho^{\prime\prime}_{\text{int}}$ values calculated in the area of the shaft outset and bottom stroma shaft and sump pit were congruent with the real values. At the border of the high-density layer, the distribution of density changes with depth was incorrect. Only the use of the iterative method of calculating influence of the shaft approached the calculated density values to the actual ones (Fig. 7c).

The distributions of mining correction for the shaft are presented in Fig. 7d. It was calculated on the assumption that the density of the shaft tube is constant distribution ${\Delta g_{\text{g}}^{\text{sz}} \left( {\overline{\rho }_{1} } \right)}$. The value of the correction increased in the area of stroma shaft and sump pit. Assuming the density of shaft sections in line with values calculated after ten iteration steps, the distribution of mining correction for the shaft took the form of a curve $\Delta g_{\text{g}}^{\text{sz}} \left( {\rho_{\text{int}}^{10} } \right)$.

By assuming end values of the correction, we can certainly obtain correct density values of the layers.

The results of calculation of interval density for these layers are presented in Fig. 8. The density could be determined after only seven calculation cycles to obtain results congruent with the real values. Most importantly, this method does not require knowledge about the rocks which surround the shaft.

Fig. 8

Interval densities determined in successive calculation cycles for selected depth intervals

Distributions of Bouguer anomalies from simple structural forms

In gravimetric measurements performed in a shaft, it is most important to evaluate density changes in the immediate neighborhood of the shaft, right beyond its lining. Such assessment can significantly help determine conditions of safe operation of equipment and shaft utilities.

Having assumed the simplest rock mass model, when the layer is localized horizontally at a certain depth, the vertical distribution of Bouguer anomaly represents the gravity of the layer. This distribution is presented in Fig. 9. Its analysis reveals that the anomaly distributions were drawn from an unlimited plane-parallel layer and from the limited horizontal one. Accordingly, the shape of the Bouguer anomaly can be used for differentiating between unlimited layers and limited horizontally. A qualitative relation can be observed between the results of measurements and the geological build of the rock mass.

Fig. 9

Distributions of Bouguer anomaly in a shaft caused by a horizontal layer: a unlimited, b horizontally

The gravimetric method used for vertical profiling is based on a regularity discovered by McCulloh (1965; Fig. 10).

Fig. 10

(Fajklewicz et al. 1986)

Relative vertical change of gravity caused by a heterogeneous zone outside of the shaft lining

This regularity indicates that about 95% of gravity effect from a horizontal, unlimited rock layer limited by measuring points from the top and from the bottom are generated by this part of the layer which adheres the borehole (or shaft lining) in an area five times as big as the thickness of the layer.

This dependence is illustrated by curve 8 in Fig. 10 (EDCON 1977). When the measurements are made in a mine shaft, this relation takes the form of a function of shaft radius and its proportion to the thickness of the analyzed layer (Madej 1988).

This dependence refers only to a situation when we analyze the distribution of measured gravity changes in a shaft without accounting for the mining gravity correction.

In this case, the vertical distribution of gravity for layers of limited horizontal range is presented in a plot in Fig. 11. This distribution reaches extreme values at points localized above and under the layer boundary by dz value. In vertical gravimetric measurements, the sign of vertical gravity changes at the interface of layers differing in bulk density. In other words, the location of point in which the anomalies distribution reaches extreme values is determined by the boundaries of layers. Therefore, to determine these boundaries, a suitable gravity correction for the presence of shaft barrel should be introduced to the measurement results. After doing so, the plot illustrating gravity changes takes the form, as shown in Fig. 11. The extreme values on anomaly curve determine boundaries of a layer which has different densities from the environment.

Fig. 11

Vertical distribution of gravity for a horizontal layer of limited size

The vertical distribution of gravity, denoted as ∆g _P in Fig. 12a, is the basic value and a source of information about the structure of the rock mass opened by the mine shaft. On this basis, the Bouguer anomaly can be calculated. For this purpose, the average change of gravity with depth ∆g _N is determined. This is a hypothetical change of gravity in a situation when the rock medium has a constant density. The Bouguer anomaly, i.e., ∆g _P − ∆g _N, constitutes a superposition of gravity impact of layers differing in density and heterogeneities in them, as presented in Fig. 12b. The distribution of this anomaly is a basic source material on the basis of which one may infer as to the geological build of the rock medium. This process is based on the documented relations of measured distribution with physical parameters of the analyzed structures and geological forms.

Fig. 12

Vertical distribution of gravity a and its Bouguer anomaly b, ∆g _P measured value of gravity ∆g, ∆g _N average value of ∆g, and ∆g _B value of Bouguer anomaly

One of the characteristic vertical distributions of Bouguer anomaly is the contact of two layers of different bulk densities. Two variants of such an interface are shown in Fig. 13. Extreme value of distribution is well visible at the layers’ boundary. The sign of the observed gravity anomaly is congruent with the sign of density contrast of the lower layer as referred to the environment.

Fig. 13

Vertical distributions of gravity for a system of two plane-parallel layers

The physical parameters of heterogeneous zones beyond the shaft lining can be assessed through gravimetric measurements performed in a shaft. The dependence between the amplitude of anomaly generated by the heterogeneous zone and its parameters in a function of the mean squared error of gravity is presented in Fig. 14.

Fig. 14

(Fajklewicz et al. 1986)

Distribution of boundary amplitudes of gravity anomalies real to measurement error in a function of parameters of heterogeneous zone around the shaft of radius 2 m

Curves 1–5 represent relative density of heterogeneous zone drawn every 0.5 Mg m within the range from −0.5 to −2.5 Mg m⁻³.

And so, e.g., a rock void of density −2.5 Mg m⁻³ extending to a 1 m distance from the shaft lining (2 m radius) in a layer 1.3 m thick generates a gravity change equal to 0.04 mGal. In a shaft of a 3 m radius, the same amplitude corresponds to a larger void: 1.4 m horizontal range of and 1.75 m thick.

Vertical gravimetric surveys could be performed as time changes of gravity anomalies. They are applied in both boreholes and mine shafts (Fajklewicz et al. 1986, 1988). The changing values of anomalies are caused by changes of physical parameters of the medium around the shaft, mainly density.

Time distributions of vertical gravity changes with the changing density in a plane-parallel layer are presented in Fig. 15.

Fig. 15

Relation of gravity changes with density changes in a plane-parallel layer

The analysis of these distributions reveals that regardless the original contrast of layer’s density in relation to its surrounding, the vertical gradient of gravity in the layer has the opposite sign to the sign of corresponding density changes. An analogous situation can be observed, while tracing density changes in a horizontally limited layer. The results are presented in Fig. 16, where a characteristic shape of distributions of gravity anomaly and its changes caused by the geometry of the horizontally limited layer is well visible, it look Fig. 9.

Fig. 16

Dependence of gravity changes and density changes in a horizontally limited layer

Selected practical examples

Authors presented results of nine (out of ten or so) gravity analyses of shafts. They are presented in Figs. 17, 18, and 19. There are distributions of Bouguer anomaly and the respective densigrams: average density ${\overline{\rho } }$ and interval density ρ _i . Bearing in mind the way in which the latter was calculated, it would be more appropriate to call it complex density. Here, the shape of distribution of the registered Bouguer anomaly can be divided into sections differing in vertical gradient of gravity. The previous analyses reveal that each change of the gradient causes a change of density. As it can be seen on the figures, the anomaly distribution was approximated with straight lines. Each change of direction corresponds to a boundary of the complexes.

Fig. 17

Vertical distributions of Bouguer gravity anomaly Δg _B, their generalized courses $\Delta g^{\prime}_{\text{B}}$, and the corresponding densigrams of complex density ρ _i in selected shafts

Fig. 18

Vertical distributions of Bouguer gravity anomaly Δg _B, their generalized courses $\Delta g^{\prime}_{\text{B}}$, and the corresponding densigrams of complex density ρ _i in selected shafts

Fig. 19

Ignacy shaft. Vertical distribution of Bouguer gravity anomaly ∆g and the corresponding densigram of interval density ρ _i

The results of analyses of three shafts with a similar geological structure are presented in Fig. 17. Carboniferous rocks are deposited under a small Quaternary overburden. The distributions of Bouguer anomaly and the corresponding densigrams in neighboring Wirek and Nowy Wirek shafts differ very little. A distinct density boundary can be observed between the Quaternary and Carboniferous strata. The successive density boundaries between rock complexes are also encountered in the Carboniferous at a depth of 200 and 530 m.

In Wschodni shaft, also in the Carboniferous complex, two density boundaries were found at 100 and 330 m of depth. Numerous coal seams are present between them hence the diversified picture of gravity changes in this interval. Attention should be paid to a zone between 300 and 305 m, where the vertical gravity was anomalous. It corresponds to a coal bed of much lower density than the rocks in the roof and the bottom.

Much bigger lithostratigraphic and density diversification can be observed in the successive examples, as presented in Fig. 18. They represent distributions of Bouguer anomaly and densigrams corresponding to the geological build, i.e., Quaternary sediments, Triassic, and Carboniferous rocks. In the first two closely neighboring shafts (MI and MII), the first density boundary from the outset was observed in the Triassic at a depth of about 50 m.

Above are rocks of density ranging from 0.2 to 0.4 Mg m⁻³; these were smaller values than the underlying Triassic rocks. This loosening of the Triassic strata has an effect on the direction of geotechnical conditions at this depth, which may have significance for the safe extraction of these shafts.

It seems that equally important is the density boundary between Triassic and Carboniferous (both shafts at about 150 m of depth). Below, there is a layer of too low density ca. 0.5 Mg m⁻³ as compared to the density of rocks lying under and above this layer. The loosening was observed in the Carboniferous, and the loose material was probably strongly soaked with water.

Another low-density layer was also discovered in a Carboniferous interval in MII shaft at 350–375 m.

The distribution of Bouguer anomaly in Ignacy shaft (Fig. 18) provides many interesting pieces of information, e.g., that the low-density rock boundary reaches to a depth of 50 m, i.e., deeper than the boundary between Quaternary and Triassic marls. Hence, the conclusion that the density of the latter layer is lower than values given in the table. However, the most important result of analyses refers to the depth interval 80–200 m. This fragment of anomaly distribution is presented in Fig. 19. In this interval, the most important part of analysis of gravity changes is conducted for 160 and 180 m of vertical profile. The thickness of this zone has low complex density equal to 1.7 Mg m⁻³. Originally, in view of measurements conducted prior to sinking the shaft, the lower density zone was deposited in an interval 175–180 m; this was quicksand. The gravimetric surveys revealed that the quicksand zone increased by 15 m upward.

All of the examples presented in Fig. 20 deserve equal attention. And so, in Maciej shaft, the low-density rocks of the Carboniferous overburden are not only of Quaternary but also of Triassic origin. This generates considerable hazard for the stability of the shaft, especially that an intensified water flow was observed at the shaft lining (Fajklewicz et al. 1986) resulting in the washing out of rock material.

Fig. 20

Vertical distributions of Bouguer gravity anomaly Δg _B, their generalized courses $\Delta g^{\prime}_{\text{B}}$, and the corresponding densigrams of complex density ρ _i in selected shafts

In the roof part of Tadeusz shaft, there was observed a layer of considerably lower density (by ca. 0.5 Mg m⁻³) as compared to the Triassic rocks above it and the Carboniferous bed. This shaft was commissioned and the gravimetric surveys performed during the closing operations turned out to be useful.

The liquidation of a shaft starts with backfilling of workings in the immediate neighborhood of the shaft. The quality of the backfilling was analyzed with the use of gravimetric methods employing measurement of the vertical gravity before and after backfilling.

The results are presented in Fig. 21. The observed time difference of gravity $\Delta g^{\prime}_{\text{p}}$ corresponds to distribution Δg _M. It is equal to the gravitational impact of mass, the geometry of which is shown in the model of filling. The liquidation of the pit has not been obviously done well.

Fig. 21

Results of gravimetric modeling in the area of level 430 in Tadeusz shaft, $\Delta g_{\text{P}}^{\text{I}}$, $\Delta g_{\text{P}}^{\text{II}}$ measuring series, Δg _M model schedule of gravity

The last presented object is Morcinek shaft. The results of gravimetric measurements performed to a depth of over 900 m reveal a slightly varied shape of distribution of Bouguer anomaly (Fig. 20). The extreme of the distribution defines the Neogene/Carboniferous boundaries. The plot and the densigram show that the density of rocks systematically increased to this boundary 2.3–2.5 Mg m⁻³. Anomalies related to the presence of many coal seams strongly manifest themselves in the Carboniferous complex. This can be observed in the depth interval 660–750 m deep.

Special attention should be paid to the analysis of distribution of gravity in depth interval 210–310 m. This distribution is presented in Fig. 22 as a residual anomaly.

Fig. 22

Results of gravimetric measurement in Morcinek shaft

During complex density calculations (curve 2 in Fig. 22), a density difference of 0.04 Mg m⁻³ was found on the interface of layers at the depth of the girders, i.e., ca. 260 m. Extreme values of interval density determined for the successive measuring points (curve 1 in Fig. 22) are 2.35 Mg m⁻³ in the layer limited by girders 55 and 57 and 2.44 Mg m⁻³ in a layer between girders 61 and 63. Attention should be paid to the fact that the average density of the complex within which these two layers occur equals to 2.40 Mg m⁻³.

To solve the problem, a high weight was attributed to determining complex densities as being much more accurate than the interval density. Complex densities were determined with accuracy to ±0.007 Mg m⁻³, whereas interval densities were burdened with an error of ±0.013 Mg m⁻³, i.e., twice as high.

The two layers contacted at a depth at which a damage in the shaft lining was observed. The increase of density in the entire range between girders 59–66 over the lithological boundary between the on lying silts and the underlying siltstones could be explained by higher side pressure of the complex. This also explains the small vertical deformation in this depth interval, discussed by Podgórski et al. (1993).

Concluding remarks

The presented rudiments of use of the vertical profiling method in mine shafts guarantee results, on the basis of which geotechnical conditions around the shaft can be assessed.

The method for calculating interval and complex densities is considered to be particularly useful. In this method, it is the mining correction for the shaft barrel which decides about the correct determining of density of rocks beyond the shaft lining. When the lithostratigraphic profile is known, the shaft barrel is built of parts which correspond to the location of layers, for which the mining correction has been calculated. Otherwise, the iteration method has to be involved for calculating density values.

The vertical distributions of Bouguer anomalies for simple structural forms are indicative of a relation between these distributions and the geological build.

The time analyses of vertical gravity changes provide significant pieces of information about the dynamics of effects taking place beyond the shaft lining.

The presented examples of use of the vertical gravimetric method confirm its high efficiency for evaluating the state of rock mass beyond the shaft lining.