Abstract: In order to more accurately understand the creep characteristics of mud siltstone in the fro⁃ zen state，and to provide a solid and reliable theoretical basis for the construction of freezing method，the mud siltstone was subjected to three temperatures of unconfined compressive strength test and two loading levels of creep test，through the introduction of fractional order differential theory into the Abel viscous pot，then a fractional order Burgers model was established，which was compared with integer order model. The results show that under the uncon-fined compressive strength test，the peak stress of the rock gradual⁃ ly increases with the decrease of temperature，showing a significant increase in strength，and the speci⁃ mens at low temperature show more obvious brittle characteristics at the time of destruction. Under the creep test，the test curve of muddy siltstone can be divided into two stages of rapid creep and stable creep，the rapid creep stage strain grows rapidly，accounting for about 90% of the total strain，the rapid response of the initial stress makes the strain curve rise steeply at the beginning of the loading，and with the passage of time，the curve gradually becomes flat and enters the stable creep stage，which is almost constant，and the stabilized strain increases with the reduction of freezing temperature or increase of load⁃ ing level. The stable strain increases as the freezing temperature decreases or the loading level increases. By constructing the Abel viscous pot based on the R-L fractional order integral and introducing the Burgers model，the integer-order and fractional-order Burgers models were established to describe different load⁃ ing levels and different freezing temperatures，and the inversion of the model parameters yielded a good⁃ ness-of-fit of the integer-order model of only 0.918，while that of the fractional-order model reached 0.998. The fitting results were as follows，the goodness-of-fit of the integer-order model was only 0.918， and that of the fractional-order model reached 0.998，the fitting results and the test curve almost complete⁃ ly overlap，and the significance of the model parameters is clear，which is convenient for the direct appli⁃ cation in practical engineering. The study provides a theoretical basis for the long-term stability of rock en⁃ gineering.

Key words: rock mechanics, argillaceous siltstone, creep, Abel viscous pot, elemental modeling