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Rock strengths and rock failure criteria 87

(2) Uniaxial strain test (Fig. 3.1B): the cylindrical rock specimen is only
loaded in the axial direction, and the lateral direction is constrained
(no lateral displacement);
(3) Tensile test (Fig. 3.1C): the cylindrical rock specimen is applied
tensional force (stress) in the axial direction;
(4) Hydrostatic test (Fig. 3.1D): the cylindrical rock specimen is
compressed with the same stress in all directions;
(5) Triaxial compression tests (Fig. 3.1E): the cylindrical rock specimen is
compressed in both axial and lateral directions. The axial stress (s 1 )is
greater than the lateral stress (s 3 , confining pressure);
(6) Polyaxial (true triaxial) compression test (Fig. 3.1F): three independent
and mutually perpendicular stresses (s 1 , s 2 , and s 3 ) load to the faces of
a rectangular prismatic specimen.

3.1.1 Uniaxial tensile test

Uniaxial tensile strength describes the capacity of the rock to resist tensile
stress. It is one of the most important parameters for hydraulic fracturing
design. The direct (Fig. 3.1C) and indirect (point load and Brazilian tests)
methods can be used to back calculate tensile strength. The direct
measurement of tensile strength can be performed by gluing both ends of a
cylindrical rock specimen to metal front plates that are fixed to the platens
of a load frame. The glue or cement has to be more resistant to tensile stress
than the specimen (Shang et al., 2016).
The indirect methods (e.g., the Brazilian test) have been dominant
in determining tensile strengths of rocks due to their ease in sample
preparation and testing procedure. The Brazilian test is performed by
applying a load by two platens diametrically compressed to a rock
cylinder (Fig. 3.2). The technique involves loading a disc-shaped
specimen in compression across its diameter. Such loading generates a
tensile stress at the center of the disc in a direction perpendicular to the
direction of the applied load. Failure occurs by an extensional fracture
in or close to the loaded diametral plane. The tensile strength is given
by the ratio of the peak load P to the diameter and thickness product
(ISRM, 1978):
2P
T 0 ¼ (3.1)
pDt
where D and t are the sample diameter and thickness in mm; P is the load at
failure in Newtons; T 0 is the uniaxial tensile strength in MPa.