Equivalent Cycle Load And Dynamic Damage Properties Of Q₃ Loess

Based on the Palmgren-Miner(P-M) cumulative damage hypothesis, the simplified procedure of seismic movement for evaluating the liquefaction of loose saturated sand was developed by the Professor H.B. Seed and his colleagues in 1975. The equivalent uniform stress and cycle number of seismic movement can be determined by this simplified procedure. It is an important basis not only for liquefaction evaluations of sand subjected to the earthquake motions, but also for exploring the strength,deformation and stabilization of soil under vibration loading. The simplified procedure has being widely used in soils dynamic properties exploration and bring into play very important function in soil dynamics progress, but the applicability of this method for structure Q3 loess need to be validated. At the same time, because of the distinct structure strength of unsaturated Q3 loess, the process of deformation development and breakage of Q3 loess under vibration loading is actually the development of soil structure damage. On the basis of the soil structure damage, it is not only very important theoretical meanings but also practical values to investigate the dynamic deformation and strength behavior of Q3 loess.In this paper, via dynamic tri-axial tests of Q3 loess under sinusoidal loading and random vibration loading, the applicability of Palmgren-Miner(P-M) cumulative damage hypothesis for Q3 loess has been validated and the procedure for computing equivalent number of uniform stress cycle of Q3 loess was proposed. First, by using the theories of random vibration, the rule of linear cumulative damage and the representative dynamic strength curves of unsaturated undisturbed loess, a formula to calculate equivalent cycle number was proposed. And the formula embodies the effects of the frequency of vibration load. The results is shown that, under the same standard of breakage, the range of equivalent cycle number calculated by this formula is consistent with the results of the tests under sinusoildal vibration when the equivalent uniform stress equal to 0.65 multiples of the maximal peak value of random vibration. Although the correctness of the formula is validated by the results of the tests, the equivalent uniform stress is less than the results testing under sinusoildal loading, the calculation results of the formula need to be modified in practice. Second, based on the alternative implementation of Palmgren-Miner hypothesis developed by R.A.Green, namely equatingenergy dissipated in the soil subjected to the actual earthquake motions and neq equivalent cycle number, another formula is proposed. And the non-liner stress-strain response of the material is properly taken into account in this method. The results is shown that the calculation equivalent uniform stress and cycle number by this formula consistent with the dynamic strength curves tested under sinusoildal loading.At the same time, based on the Miner's cumulative damage hypothesis developed for energy absorbed in the material under load, the deformation of Q3 loess under vibration load is discussed in this paper. According to the results of tests, the relationships between dynamic module,the ratio of damping,residual modul and accumulation of damage are discussed. Finally, the accumulation of damage is applied directly in equivalent visco-elastic model, and a calculating model contained residual strain is set up.