Abstract：Based on the analysis of nonlinear dynamics to time series of strain and stress which are tested by MTS to lots of joint systems of sandstone specimens，a new rule to find the largest Lyapunov exponent is established by introducing LE1-m mathematical model and unit-step function. The new rule involves step feature that confirms theoretic condition of finding the largest Lyapunov exponent even more. Value of the largest Lyapunov exponent erected by the new rule is very different to that of the old rule，which will lead to a very different valuing conclusion of chaos to stability of a system. Meanwhile，different sign of the largest Lyapunov exponent will produce different conclusions of system state of which the characteristic has been changed completely. Conclusions of the paper improve robustness to erect LE1 by old rule and are useful to basic theoretic research of chaotic dynamics.
