The primary goal of this research is to investigate the effect of spinal fusion on the fatigue properties of intervertebral discs. Discs are harvested from levels adjacent to levels which had previously undergone lumbar fusions (juxtafused) and from levels which did not undergo the procedure (normal). Methods of specimen preparation and testing are described. Load relaxation, static strength, fatigue to failure, and residual static strength tests are performed on over 110 specimens. Fatigue tests are performed under loading conditions representative of the variable amplitude nature of loads experienced in life. A wear out law (WOL) that reflects strength degradation with prior loading is modified. A data analysis methodology is developed to account for variable amplitude loading. Survival probability functions are derived for strength, life, and residual strength. The modified WOL and analysis methodology are applied to the normal and juxtafused data. Experimental results indicate that juxtafused discs may be more brittle than normal discs. Juxtafused discs exhibit significantly less load relaxation than normal discs. Juxtafused discs initially are stronger but develop damage more rapidly than normal discs. Finite probabilities of a damaging event occurring are predicted for normal and juxtafused discs for relatively minor activities.

The secondary goal of this research is to develop a method to explain the variation observed in the modulus of a composite material comprised of longitudinal fibers embedded within a matrix. The modulus is modeled using the rule of mixtures, wherein the contributions to the modulus from the fibers and matrix are weighted by their respective volume fractions. The constituent moduli and fiber volume fraction are assumed to be independent random variables. An analytical model, the probabilistic rule of mixtures (pROM), is derived for the joint density function of the modulus for specific values of the constituent moduli and volume fraction. A Monte Carlo representation of the PROM is developed which approximates the analytical model. A parametric study of each parameter in the individual density functions is conducted to determine their effects on the modulus distribution. The PROM is used to correlate with experimental data from ligament tests using physiologic values for the constituent parameters.