ed Triaxial Conditions.
2.5 Deviatoric Sts=15M Pa (normalised).
C2.0 25MPa. Eff Mn Stress. 30MPa. 1.0 X 0.5 22MPa. URV (1000m m 3) r a n g e o f p r e s s u r e s
considered in this analysis. Also under the stress levels considered here the majority of pore volume change, 6p^,
will be a consequence of a deforming rock m atrix and not grain crushing, therefore
ôp^ is a fun ction of applied effective stress [S a ^ ). and
b u l k r o c k m a t r i x m o d u l u s ( K ) . p j g 6 . 2 . 5 .d. Normalised pore fluid pressure rise data
Since effective stress under ®
deviatoric stress of 1 5MPa. See text for details.
undrained conditions can
found from Skem pton's A & B co-efficients and applied stress,
JPp = (B[<73 -P A (t7i-< 73)].V ,)/(K (V o + URV))
where V, is the rock specimen volume, Vq is the initial pore volume of the rock under applied hydrostatic stress. Hence the change in pore fluid pressure as a function of urv under a more simplified stress regime of purely uniform mean stress, is.
or.
6Pp = (Kf.B.6(73.VJ/(K.(Vo -P URV))
6Pp = Q .ôgJ {\Jq -P urv)
Where C = (B.Kf.V,)/K. Curves of this form are fitted to all the data of a given stress condition and extrapolated to zero urv. More accurate data fitting is prevented by lack of datum points. The percentage pore fluid pressure increase from the initial starting pressure of 150MPa under a zero urv can be read from the vertical axis. These percentage pore fluid pressure increases under certain deviatoric and effective mean stress conditions map a 3-D surface on axes of effective mean stress, deviatoric stress, and percent pore fluid pressure rise.
The three dimensional plot can be visualised from the tw o dimensional plot (fig. 6.2.5.e.). Line a - a ' maps perpendicular to line B-B% w ith point a ' mapping
directly onto point b" . A 3-D representation of the results is shown in fig. 6 . 2 . 5 . f .
The plot represents the Pp
r is e u n d e r i n c r e a s i n g d iffe r e n tia l axial s tre ss separated into effective mean and deviatoric stress components. The effective me a n s t r e s s d a t a is truncated at a value of 20MPa
r e p r e s e n t i n g t h e c o m m e n c e m e n t of the 10 G roup A., C p = 1 7 0 , P p = 1 5 0 . C p '= 2 0 (s tt)M P a . . 9 i s N l-B '= D v @ 30M Pa Mn S tress.
Points interchange on 3 - D plot,
L 3 c In Stress' @ IS M P a Dev. 0 25 20 30 0 5 10 1 5
Deviatoric Stress or Mean stress (MPa).
experiment. It c a n be seen p;g 6 .2 . 5 .e . Surface p lo t represente d in 2-D space. Percentage increase in pore fluid pre ssure fo r increases in e ffe c tiv e mean stress and d e v ia to ric stress. See te x t.
how under triaxial stressing conditions the pore fluid
pressure rise is more sensitive to deviatoric stress induced crack closure than to effective confining stress induced isotropic compaction. This conclusion is, of course, valid only for the initial pre-dilatant stage of deformation, afterw hich different mechanism (New Dilatant Crack grow th - n d c ) , changes
the pp response markedly. The surface can be represented as;
%Pp =
0.
0 0 6.
6.
2.
5.a.
Which, in this simplified analysis shows both a a ' and b b ' going through the
origin. In the equation, %Pp represents the percentage rise in pore fluid
pressure, D^^ represents the axial deviatoric stress, and a ^ ', the effective mean stress. To calculate the compensation factor between the pore pressure rise for the minimum u r v obtainable experimentally and the pore pressure rise for theoretical zero u r v , a plane is plotted for actual pore fluid pressure rises
under a URV of 2 , i 0 0 m m ^ and the equation for the surface calculated.
By comparing the constants in each equation, the correction factor is obtained. Under a starting fluid pressure of i5 0 M P a the URV correction factor is 1.2 8 6. The validity of this factor relies on the extrapolation of the data to
By c o mp ar i ng the c on st a nt s in e ach eq u at i on , the correcti on f a ct or is o bt a in e d. U nder a starting fluid pressure of iBOiviPa the URV cor recti on f a ct or is 1.286.
The validity of this factor relies on the extrapolation of the data to zero URV in figs. 6 .2 .5 .C . & d. A
greater number of tests would provide more information for accurately extrapolating the data, and perhaps would give an improved reading for zero u r v .
b i f c c i i v o Moan S irc s s (MPa).
Fig. 6 . 2 . 5 . f . Three dim en sion al representation of percentage pore flu id pre ssure rise fo r increases in dev iatoric and e ffe c tiv e m eans stress for ex perim ental data g ro u p A.
To check the accuracy of the calculated surface, pore fluid pressure rises are calculated for the experiment which e m p l o y e d an u r v of
2 , i 0 0 m m T and the results are
t h e n d i v i d e d by t h e correction factor to yield the actual pore fluid pressure rise. The results are given in fig. 6 . 2 . 5 . g . It can be seen
h o w the results a c c u r a te ly a c c u r a t e l y d e t e r m i n e s p o r e f l u i d p r e s s u r e ris e f o r t e s t
0151 w ith in g roup A suite o f e x pe rim en ts , see te xt.
predicts the pore fluid
pressure rise until 6 = 0 .5 % , beyond which new dilatant crack growth causes
the pore fluid pressure curve to roll over, w h e r e a s the calculated curve continues in the same plane. This is expected considering the assumpti ons
and limitations of the analysis.
A ctu al and C alcu lated %Pp ns,e. U R V = 2 ,1 0 0 m m 3
Based on interpo lated d a ta analysis and
m easured stress values. Onset of AE.
un
Experim en tal d ata, te s t 0 1 5 1 .
CL
0.2 0.4
Axial Strain (%).0.6
In S u m m ary, the method of linearly extrapolating experimental pore fluid pressure rise data for deviatoric and mean stress com ponents of differential axial stress during the initial compaction stage of triaxial deformation can be used to determine pore fluid pressure for any given stress path under a known commencing mean stress.
6 .2 .6 .
Future Work.
Further w o rk to develop this investigation essentially involves a greater number of more complicated experiments. These are highlighted below.
► Conduct triaxial experiments under controiieci deviatoric and effe ctive m ean stress conditions. This would accurately isolate the effect of both deviatoric and mean stress on pore volume change and hence pore fluid pressure change. Improving control of these stress parameters w ould also provide more data points on fig. 6.2.5.e. & 6 . 2 . 5 . f . This could
be achieved by accurately controlling the confining pressure during triaxial deformation.
► G re ate r n u m b e r o f urv's. Conduct more experiments using a wider range of URV's. This would provide the extra data points on the curves in figs. 6.2.5.C. & d.
► In v e s tig a te d iffe re n t e ffe c tiv e confining pressures. Employ different effective confining pressure conditions during triaxial experimentation, (considering the above comments), to examine the effect of different com mencing effective mean stresses on the relationship established in this section. Under cataclastic flo w conditions ( C p '> lO O M P a ) ,
com paction and cracking occur simultaneously during initial triaxial deformation.
► D e velo p eq u ip m en t capable of removing the effect of the URV
com pletely during undrained triaxial deformation through the use of the pore fluid intensifier, see fourth bullet point in section 6.4.4., "Future W ork".