Adhesion and Bond Strength
In the context of steel reinforcement of rock or concrete materials, adhesion describes a bonding mechanism (Farmer, 1975; Littlejohn and Bruce, 1975) in which a pseudo-chemical bond develops at the steel/cement interface which is brittle (no residual bond after rupture) and independent of confining pressure (stress normal to the interface).
Typically, for regular carbon steel and cement grouts with W:C in the range of 0.35 - 0.5, this adhesion or shear resistance is equivalent to 1 to 3 MPa. Over the surface area of a 15.2 mm diameter cable, this is equivalent to a capacity of 10 kN over a 20 cm length of grouted cable. Unfortunately, this adhesion is exceeded after less than one fifth of a millimetre of relative slip (Fuller and Cox, 1975; Hyett et al., 1992; Nosé, 1993). As such, it is unlikely that adhesion can act simultaneously over any appreciable embedment (grouted) length and rarely accounts for any significant percentage of the instantaneous pullout resistance (bond strength). In fact, as the cable is loaded and begins to slip at the cable/grout interface, a wave of localized adhesion failure propagates down the cable away from the loading site.
Adhesion is thereby rapidly removed from the system as this initial bond is broken and is not considered hereafter as a load transfer mechanism. Slip, dilation, friction and bond strength The helical, multi-wire nature of the cable surface creates a negative relief of equivalent geometry in the hardened grout. After adhesion is removed from the interface, the cable slips with respect to the grout annulus. If rotation of the cable during pull-out is prevented, a geometric mismatch occurs between the cable flutes and the corresponding grout ridges. This mismatch increases with increasing relative slip as illustrated in Figure 2.6.4.
As the grout ridges must ride up and over the cable wires, the grout compresses in the confined borehole and thus generates a normal pressure on the grout/steel interface. Friction (pressure dependent shear strength) thus develops along this interface providing resistance to further slip. This interaction is called dilation. Dilation is limited in the extreme by the absolute scale (height) of the grout ridges. In reality, dilation pressures develop to the point where these ridges crush, reducing the maximum dilation to less than 0.1 mm for plain strand cable (Diederichs et al., 1993).
Dilation is the key to cablebolt performance and is a complex process which is dependent on grout stiffness, rock stiffness and grout strength. This relationship will be explored in the next section.
Bond Strength and Load Transfer
Before proceeding with a discussion of bond strength, it is necessary to understand the process by which load is transferred from the rockmass to the cable via the shear resistance at the cable-grout interface. As the rock slips with respect to the cable, shear stresses (load/unit area) are generated at the interface. As these shear stresses accumulate along the length of the cable due to the addition of incremental rock loads, the tension in the steel strand increases (for an unplated cable) from zero at the face to a maximum at some point into the borehole.
Beyond this point (i.e. in the "anchor" section of the cable) the shear stresses act in the opposite direction and can be considered as negative. In this region, the loads accumulated in the bottom portion of the cable are transferred back to the rockmass and the cable tension drops back to zero at the upper end of the grouted strand. The following examples illustrate this concept.
In this example, a slab or wedge of thickness, A (less than critical embedment length), displaces downwards under the influence of gravity. If the ultimate bond strength along segment A is less than the critical bond strength, the shear stress acting on the cable-grout interface in section A will become approximately constant as the slab slides along (and off) the cable. During slip, the tension in the steel cable rises linearly from zero at the face to a maximum at the separation plane between A and B. Segment A is called the pick-up length. Note that in the anchor length, B, the shear stresses act in the opposite direction as the cable tends to slip down with respect to the rock. Section B, in this example, is long enough to transfer the load from A back to the rockmass without significant slip (<10mm).
The end of the cable in B may or may not displace at all, depending on the length of B (if A=B, the amount of slip will be equal). The tension in the cable returnsto nil at the top of section B as all of the load is transferred back to the rock.
Load Transfer Example: Fractured Ground
The concept of bond stress and load transfer become slightly more complicated when dealing with a fractured rockmass, displacing under gravity or the influence of stress as in this example. Here the displacement profile (Bawden et al., 1995) of the rockmass is assumed to be non-linear, with maximum displacement at the face reducing to nil into the rockmass (at the top of section B). The boundary between the loading section, A, and the anchor section B, becomes undefined. In the lower section (A) the rock has displaced more than the cable (with respect to initial conditions). This generates slip and shear loading on the cable-grout interface and tension in the strand. At some point into the back, the relative displacement between the cable and the rock is zero. This is the neutral point (zero shear and maximum tension) and is the boundary between the pick-up length and the anchor length. Above this point the load is transferred back to the rockmass (Section B) as the shear reverses direction and the cable tension drops back to zero.
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