**7. Numerical modeling**

od, namely the interpretation of measured normal stress acting across arbitrary orient‐

In this method the shut-in pressure Psi is used to measure the normal stress component under the assumption that the vertical stress is a principal stress axis and the vertical stress magnitude

The analysis program *GENSIM* was used to calculate the magnitude and the direction of

Where, l, m, n is the cosines of the direction of the induced fracture plane related to the principal

The calculations involve obtaining the best fit based on using all shut-in pressure data derived from the measurements in the boreholes and varying the ratio σH/σ<sup>h</sup> and the strike direction

**Principal Stresses**

σV MPa σH MPa σh MPa Rock Cover Depth m

**Principal stresses** *184 ML 124 ML 64 ML* Rock cover *195m 184 m 530 m*

Maximum Horizontal principal Stress (σH ) in MPa 21.78 22.78 23.94 Minimum Horizontal principal Stress (σh) in MPa 10.89 11.39 15.96 Maximum Horizontal principal Stress direction N 800 N 800 N 900 K = σH/σ<sup>v</sup> 2.35 2.30 1.71

6.97 8.4 5.6 203 7.88 8.89 5.93 268 10.7 12.65 7.7 364

**Table 1.** Pre mining stress tensor as revealed by hydrofrac stress

**Table 2.** Post mining stress tensor as revealed by hydrofrac stress

Table 3 shows the comparison of pre and post mining stress gradient

The pre-mining and post mining stress tensors as revealed are given in tables 1 and 2

h si V H h σ = P - n .σ / m + l .( σ ( ) /σ ) (1)

9.28 9.89 14.02

2 22

ed fracture planes.

922 Effective and Sustainable Hydraulic Fracturing

stress axis.

Vertical Stress (σV) MPa

loose rocks respectively)

( 2.7 gm/cc + 1.4 gm/cc density of solid and

of σH.

σV is equal to the weight of the overburden.

principal stresses on the basis of the following equation:

A numerical modeling was carried out using the boundary element method to understand post mining induced stresses vis a vis mining. The initial stresses gradient of the pre mining stage was used with gravity loading as the surface topography is hilly. Three observation points were monitored for stress change in mining, due to excavation effects. The stress contour of the model is shown in figure 5

**Figure 5.** Major principal stress contour of the modeled stope.

The results of the stress output as revealed by the numerical model are given in Table 4.


**Author details**

Govinda Shyam

**References**

Smarajit Sengupta, Dhubburi S. Subrahmanyam, Rabindra Kumar Sinha and

[1] Whyatt-JKWilliams-TJ, Blake. W ((1995). In-Situ Stress in Lucky Friday mines W Reference:U.S. Department of the Interior, Bureau of Mines, Report of Investigations

Estimation of the Impact of Mining on Stresses by Actual Measurements in Pre and Post Mining Stages…

http://dx.doi.org/10.5772/56017

925

[4] Cornet, F. H. (1986). Stress determination from Hydraulic Tests on Pre-exiting Frac‐ tures- the HTPF Method. Proc. Intl Symp, Rock Stress and Rock Stress Measurements,

[5] Hubbert, K. M, & Willis, D. G. (1957). Mechanics of Hydraulic Fracturing, Petroleum

National Institute of Rock Mechanics, Bengaluru, India

9582. NTIS stock (PB96-131685)

CENTEK Publ., Lulea, , 301-311.

Transactions AIME, T., 210, 4597.

[2] Hindustan Copper Limited Internal Notes

[3] Dasguupta, B. (1965). Khetri Copper Belt. GSI memoirs, , 98

**Table 4.** Stress magnitude and orientation as revealed by numerical model

The modeling studies reveal that the measured value of the stresses agree reasonably with the computation values which is compared in Table 5


**Table 5.** Stress magnitude and orientation as revealed by numerical model

#### **8. Discussion and conclusion**

The availability of stress results during pre - mining stage and subsequent measurement of stresses at the post mining stage has refined our understanding of the in-situ stress vis a vis mining. The change in the orientation of the major compression from a favourable N10-20 0 (Strike of ore body N 300 and crown pillar oriented parallel to ore body) during pre- mining stage to unfavourable N85-90 0 at the post mining stage has prompted to redesign the stopes and support systems below the mined out area.
