The Research on the Effect of Humidity on the Rheological Model of Swelling Rock

Table 2

Rheological elements in the humidity field.

Fundamental components	Symbols	Explanation
Hooker model		σ Is the stress; E and a are the elasticity coefficient and the humidity expansion coefficient of Hooker model, respectively; is the humidity difference of before and after two states; moreover, assume that the changes of the humidity have no effect on the Hooker law of the elastic model
Plastic model		When σ<σs, there is no strain changes; when σ>σs, the plastic model yield; σs is the yield limit of the material; when the stress meets the yield limit, the yield continues, no-slip in friction surface and have no relationship with the time; in the coupling of humidity and stress, the yield stress of the material is σs() and the yield surface is f (σs, ), both of them have the relationships with the humidity; moreover, assume that the yield stress is a given constant
Newton model		The stress and strain obey to sticky laws in the Newton model; there is a proportional relationship between the stress and the strain rate; the formulation is , η is the sticky coefficient; under the coupling of the humidity and the stress, the sticky coefficient is expressed by η() and it has the relationship with the humidity; moreover, assume that the sticky coefficient is a given constant