Proceedings Volume Cover
SOCIETY OF PETROLEUM ENGINEERS OF AIME  
6200 North Cen%ral Expressway  
Dallas, Texas 75206  
.,..  
THIS IS A PIWPRINT --- SUBJECT TO CORRECTION  
By  
Mahmood H. Rana, Queen’s University, Kingston, Ontario, Canada  
@
Copyrigh t  
1 9 6 7  
Am erican In st it u t e of Min in g, IMet ailu rgical an d Pe!roleu m En gin eers, hm.  
ABSTRACT  
It is well known that rocks behave in a  
viscoelastic manner. Therefore, the theory of  
elasticity does not provide valid answers to  
problems of rock behavior. Various theological  
models have been developed conforming to rock  
deformation. Most important of these is the  
The parameter has  
been experimentally determined in the labora-  
tory, using a number of independent tech-  
niques.2>3 ~is paper LS a step further in  
this direction and consists of theoretical  
development for determination of structural  
and rock-like materials.  
Some  
viscosity from mine stope measurements.  
data obtained in the laboratory are used to  
The model involves a  
Kelvin solid model.  
calculate some values of the coefficient of  
coefficient of solid viscosity, whtch appears  
to have the makings of a future criterion for  
rock fracture.  
The above are the  
solid structural viscosity.  
used in formulating the comments concerning  
exploitation of the directional properties of  
rocks in drilling reorientation of mine work-  
ings and oil well fracturing.  
The paper describes the evaluat~on of the  
Kelvin model and presents  
a few analytical  
.AN/YLYTICALCONSIDERATIONS  
developments concerning rock’s viscosity from.  
measurement in the mine stopes and the struc-  
tural ,volumeflow of rockk? Sotieexperimental  
results obtained in the laboratory are pre-  
sented. These results indicate the advisabi’lilz  
of using a Kelvin model and give an idea of  
the types of failure mechanisms operating in  
the rocks.  
in &alyLical developmeritpresented here  
i.tis assumed that the rocks behave like a  
Kelvin solid, represented by the equation;  
(rd%h’yt.!......dl]  
The solution of Eq. 1 is given by;  
In light of these and other developments,  
the directional properties of rocks are dis-  
cussed. The possibilities of exploitation of  
these properties in drilling in preferential  
directions, reorientation of mine workings, and  
oil well fracturing are briefly mentioned.  
..  
INTRODUCTION  
.
It is weld-known that rocks behave in a  
viscoelastic manner.. Among theological models  
applicable to rock beha~or, the most tiportant  
-is..tha$_.of..$&e_Ke&$&&J&~,~%13&?5@?_t&?t&?..  
Maxwell.atid.Burgermodels are-alsoapplicabl&””  
to some extent. One of the two constituents of  
a Kelvin solid deals with time-dependent  
. .. .  
-Ifflis”constant, Eq* 2’reduces to:  
-.  
.
.
m,  
J$$$  
,...,.... ...-,..- .-_”  
behaviorof rocks and involves the coefficient.  
.....+.  
..... ....  
t
of structural tisc@t.y,  
This solid-v~scous L  
. .  
.’.  
...  
. .  
-par@eter appe:ars-to”bea,”fut~e potential .-.... ~ -.,gi:,.+:+  
(’~’ +.”g>  
~
.’{?: ~  
-criterion-forstructui’aldesign involving”%ockb  
‘Refe~tincefi.$[hld@u6tra~~ogs”a$”epd.ofj.pape-x--  
.
. .  
,.  
.*.**  
. ......  
:-...*..;....--,-..-.,-.,#.e,...6&.,*.;-.;=.-.---  
.......,.e-  
.+1  
.. ...*  
. .  
.