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A deeper understanding of the coupling mechanical effect between a wholly grouted anchor and surrounding rock was achieved: the wholly grouted anchor was used to constrain surrounding rock deformation through the shear force transmitted by the interface layer, the support force of the wholly grouted anchor to the surrounding rock was equivalent to the additional volume force acting on the surrounding rock of the circular cavern, and the analytical solution of the stress and the displacement of the surrounding rock of the circular cavern under the support of the anchor was obtained [14-16].
The force at the surface can be expressed as a volume force using the divergence theorem.
[5] is incorporated as a source term by replacing the volume force ([??]) within the momentum equation, thus Eq.
It is sometimes convenient to use a volume force instead of the stress tensor for the electromagnetic induced stress tensor [T.sub.EM]:
where [X.sup.v] is the volume force and [[lambda].sub.0] and [[micro].sub.0] are the Lame elastic constants of the spacetime continuum, substituting for [[u.sup.v;[micro]].sub.[micro]] from (6) into (5), interchanging the order of partial differentiation [[u.sup.v;[micro]].sub.[micro]] in (5), and using the relation [[u.sup.v;[micro]].sub.[micro]] = [[[epsilon].sup.[micro]].sub.[micro]] = [epsilon] from (19) of [11], we obtain
The ensuing quantities {S,S,z,Z} have the meaning of generalized stress fields: S is a nonsymmetric stress tensor; S is the couple-stress tensor; z is the internal volume force related to the presence of the microcracks, playing the role of the force responsible for the internal changes of the system configuration [7,8], and Z is the microstress tensor.
In the end, however, the contents of the volume force us to deal directly with the relationship between Kendall and Strauss.
The volume force may thus be very small, but not exactly zero.
where F is a volume force, [rho] is the fluid density and v is the dynamic viscosity.
* In analogy with conventional theory, a local momentum equation including a volume force term is obtained from vector multiplication of equation (15) by B and equation (16) by [[epsilon].sub.0]E, and adding the obtained equations.
In this equation the contribution from the volume force is found to vanish in rectangular geometry, and to become nonzero but negligible in cylindrical geometry.