The stress in a granitic rock mass has been measured by hydraulic fracturing tec

Question

The stress in a granitic rock mass has been measured by hydraulic fracturing technique. Two tests were conducted in a vertical borehole. The results from the test are provided in the table below. The tensile strength of the rock was determined to 10 MPa in lab testing from cores extracted from the measurement zone. Determine the values of ?, ?2, and ?3. For each depth determine the k values (min, max, avg). Assess the results and comment with regards to the believability of the computed stress states. Shut-in pressure, Ps MPa) 8.0 16.0 Depth (m) Breakdown pressure, Pc MPa) 14.0 500 1000 24.5

Explanation / Answer

for 500mt depth,

Pc=14mpa,Ps=8mpa,T=10mpa

?max=3Ps-Pc+T=(3*8)-14-10=20mpa=?1

?3=Ps=8mpa

?2=? g h=0.027*500=13.5mpa

k=((?hmax+?hmin)/2)/?v=1.03

for this0.3+100/z= 0.3+(100/500)=0.5

0.5+1500/z=3.05

as k=1.03 its stable

for 1000mts depth,

?max=3Ps-Pc+T=3*16-24.5+10=33.5=?1

?2=0.027*1000=27mpa

?3=16mpa

k=((?hmax+?hmin)/2)/?v=((33.5+16)/2)/27=0.91

for this 0.3+100/z=0.4, 0.5+1500/z=2

in this also k=0.91 is stable

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