المحاظرة السابعة / الجيلوجيا هندسية / مرحلة اولى

Figure 7-1(A,B,C, and D) shows the most types of deformations occurs in rocks sample resulting from application of various loads.







(A): Deformations due to applied tension force







(B): Deformations due to applied compressin force






(C): Shear strain due to applied shear force








(C): Cylindrical rock sample subjected to tri-axial load
Figure (7-1): Deformation types in rock specimen
The relation between different types of Elasticity Modulus can be summarized as:
G=E/(2(1+?))
K=E/(3(1-2?))

Example 7-1:
A core rock specimen of (?=0.422), the sample height of 7.6cm, and diameter of 6.2cm. Subjected to uniaxial load which cause axial strain of -3.44mm/m. determine the change in sample diameter due to same load.
Solution:
?L=-4.33mm/m =-3.44?10-3
?=-?_T/?_L
0.422=-?_T/((-3.44×?10?^(-3)))
?T =1.452?10-3
?_T=?D/D
?D=D×?_T
?D =1.452?10-3?6.20 = 9?10-3 .
Example 7-2:
If the average of uniaxial load of (37.6kN) applied to rock specimen of (12.6cm in height) and (4.83cm in diameter). The modulus of Elasticity E is 35 GPa. Determine the change in rock sample height by the applied load.
Solution:
?=F/A
A=?/4 D^2
A=?/4 ?(4.83/100)?^2=0.00183 m^2
?=(38×?10?^3)/0.00183=20.74×?10?^6 N/m^2
?=E?
??=?/E=(20.74×?10?^6)/(35×?10?^9 )=5.93×?10?^(-4)
?_L=?L/L
?L=?_L×L=5.93×?10?^(-4)×12.6=7.47×?10?^(-3)cm
?Specimen subjected to "Contraction" due to compression load.


Example 7-3:
A limestone rock specimen with following data:
?=0.276
E= 63 GPa.
Estimate all other Modulus of Elasticity.