MULTIVARIATE PREDICTIONS OF GEOMECHANICAL PROPERTIES OF ROCKS BY
ULTRASONIC VELOCITIES, PHYSICAL AND MINERALOGICAL PROPERTIES UNDER
DIFFERENT DEGREES OF SATURATION
Hasan Karakul1, Resat Ulusay2
General Directorate of Mineral Research and Exploration, Feasibility Studies Department, Ankara, Turkey
2
Hacettepe University, Department of Geological Engineering, 06800 Beytepe, Ankara, Turkey
1
ABSTRACT
Determination of P-wave velocity (Vp), which is closely related to intact rock, is a non-destructive, easy and less
complicated procedure. Due to these advantages, there is an increasing trend to predict the geomechanical
properties of rocks from Vp. Geomechanical properties of intact rocks depend mainly on mineral content,
cementing material, porosity and degree of saturation. However, up to the present, in the studies on the
prediction of geomechanical properties of rocks from V p, the effect of degree of saturation has not been
investigated. Consideration of saturation in these predictions is important for the use of empirical relationships
when the evaluation of the parameters at different saturation conditions is necessary in rock engineering
applications. By considering this issue, in this study, it was aimed to correlate strength properties (uniaxal
compressive and tensile) and Young’s modulus with Vp of various rock types under different degrees of
saturation. In addition, effect of physical properties of rocks on V p was also investigated and strength properties
were estimated from theoretical P- and S-wave (Vs) velocities, which were calculated based on mineralogical
compositions of the studied rocks. For this purpose, fourteen different rock types were collected from several
parts of Turkey and a comprehensive laboratory testing program, including determination of strength and
deformability properties at different degrees of saturation, and physical properties and mineralogical composition
of the rocks, was conducted. In the statistical analyzes, a series of different prediction relationships were
developed by using independent variables such as Vp, degree of saturation and effective clay content. In the
statistical analyses, in addition to experimentally determined Vp values, theoretical Vp and Vs values calculated
were also employed.
Simple regression analysis results indicated that although prediction of the strength properties of rocks directly
from Vp at different degrees of saturation was possible, the equations developed would yield some under- or
over-predictions. On the other hand, the multivariate equations developed have very high prediction
performances and are very useful tools to estimate the strength and deformability properties from the measured
Vp at any degree of saturation. In addition to mineralogy, the variation in the strength and deformability
properties with increasing degree of saturation is also associated with the combined effect of porosity and clay
content, which is first described in this study by the term Effective Clay Content (ECC). It was found that there
are relations with high coefficients of determination between ECC and Vp, which is the difference between the
saturated and dry Vp values (Figure 1). It is also noted that when experimental determination of sonic velocities
is not possible, strength properties of rocks at any degree of saturation may also be estimated using the empirical
relations suggested in this study based on the theoretical Vp (Figure 2) and Vs values, which are calculated from
mineralogical compositions of rocks. According to the experimental results, Vp has inverse and positive
correlations with porosity and density, respectively. Based on this, by considering porosity and grain density,
statistically significant multivariate empirical relationships to predict V p from physical properties were
recommended.
ECC (%)
18
16
14
12
10
8
6
4
2
0
-400
-200
0
Vp (m/s)
200
400
Figure 1. Relationship between ECC and P-wave velocity difference (Vp)
7.00
6.00
Vp (km/s)
5.00
4.00
P wave velocity
(experimental)
3.00
2.00
P wave velocity
(theoretical)
1.00
0.00
Rock type
Figure 2. Comparison of experimental and theoretical V p values for the studied rocks
KEYWORDS
Ultrasonic velocities, Degree of saturation, Geomechanical properties, Effective clay content, Multivariate
prediction equations