4.2 Normal and shear strength calibration for parallel bond

Normal strength and shear strength (σ<sup>c</sup> and τc) for parallel bond are the two major micro-parameters contributing to the material's compressive strength. Three typical calibration tests were carried out: varying normal strength, varying shear strength, and varying both with a constant relative ratio. The relationship between compressive strength and microstrength is shown in the Figure 10.

Figure 10. Relation between macro-compressive strength and micro-strength.

As illustrated in Figure 10, the macro compressive strength depends on both normal and shear strength of the contact balls, while normal strength contributes a little more. An important feature for this case is that it is the smaller one of these two micro-parameters controls the upper limit of the macro-strength, i.e. the compressive strength cannot increase when either one of the micro strengths stay at a constant level.

For Young's modulus and Poisson's ratio, neither the normal nor the shear strength of particles has much contribution in the normal range. However, when both these two micro strengths decrease to very small values, the Young's modulus and Poisson's ratio have a little more influence.

The empirical discoveries found in the above calibration test can be used to form concrete target with the required mechanical property, although the calibration still needs to be conducted step by step. This is because different micro-variable changes may result in similar macro-property, and the changing magnitudes probably vary widely as other parameters vary.
