Mechanical Behaviors of rocks
Mechanical Behaviors of Rocks
stress g astic failure Yield stress oy elastic e2 e strain General relationship between stress and strain for rock deformation
General relationship between stress and strain for rock deformation Yield stress elastic plastic failure strain stress
Linear elasticit Hooke's law =E8 e=o/ctan a Where o is stress s strain and e the Youngs modulus or elastic modulus
Where is stress, strain and E the Young’s modulus or elastic modulus Hooke’s law Linear elasticity = E E= / =tan
u=u(y) 0 Sketch shown viscous flow layers The flow speed is the function of y
Sketch shown viscous flow layers The flow speed is the function of y
Linear viscous law (Newtonian viscous law) Shear stress is proportional to speed gradient Viscosity (Pa'S i- Flow speed di The variation of flow speed along the y direction, called speed gradient t Shear stress. or frictional force between the adjacent flow layers
dy du = —粘度，其单位为帕• 秒（Pa • s） u —流速 dy du —u 在 y 轴方向的变化率，称为速度梯度 —剪应力 Linear viscous law（Newtonian viscous law） Shear stress is proportional to speed gradient Viscosity (Pa·s) Flow speed The variation of flow speed along the y direction, called speed gradient Shear stress, or frictional force between the adjacent flow layers
did du_d du_dr dy dy( dt)dt( dy)at r Shear strain rate y--shear strain
—剪应变速率 = = = = dt d dy du dt d dt du dy d dy du Shear strain rate dy du --shear strain
Another express for Newtonian viscous law I=ny In--viscosity of material Shear stress is proportional to shear strain-rate o Stress o, dsdt For longitudinal deformation train-rate
= Another express for Newtonian viscous law Shear stress is proportional to shear strain-rate --viscosity of material For longitudinal deformation: = d/dt d/dt Stress Strain-rate
Viscosity of some materials materials viscosity Air(20°C 1.8×10 water(20°C 1.00×10 Pitch(50°C) 10 13 Glacial ice 15 Rock salt(20°C) 3^10 18 Glass(20°C) 1018。~1 0 Limestone(20°C) Lava(1100°C 10 (1200°C) 1300°C) 30 ithosphere 3 Asthenosphere 1019~1020
Viscosity of some materials 材料 粘度(Pa.s) 空气(20℃) 水(20℃) 沥青(50℃) 冰川冰 岩盐(20℃) 玻璃(20℃) 灰岩(20℃) 熔岩(1 100℃) (1 200℃) (1 300℃) 岩石圈 软流圈 1.8 10-5 1.00 10-3 106 1013 3 1015 1018~1021 1021 4 103 3 102 30 1022~1023 1019~1020 materials viscosity Air (20◦C) water (20 ◦ C) Pitch (50 ◦ C) Glacial ice Rock salt (20◦C) Glass (20◦C) Limestone (20◦C) Lava (1100 ◦ C) (1200 ◦ C) (1300 ◦C) Lithosphere Asthenosphere
a Ideal elastic strain b∽0o= B Ideal viscous strain strain, e strain-rate, e C Ideal elastoviscous strain at constant Stress: an VISCOUS Instantaneous oc元 bn0 vIscouS yield stress elastic strain is elastic elastic followed by viscous time. t strain, e strain for a stress of longer duration Mechanical behavior of materials D Ideal elastoplastic strain: elastic strain at low values of stress is replaced by viscous strain above the yield stress
Mechanical behavior of materials A Ideal elastic strain B Ideal viscous strain C Ideal elastoviscous strain at constant Stress: an instantaneous elastic strain is followed by viscous strain for a stress of longer duration D Ideal elastoplastic strain: elastic strain at low values of stress is replaced by viscous strain above the yield stress
Simple rheological models Elastic Strain-time E: Young's modulus (a) spring e= tan -1E Viscous dashpot F 8=tan-In t2 Visco-elastic n:Ⅴ scosity(Pas) F
Simple Rheological Models E: Young’s Modulus : Viscosity (Pa s-1 ) dashpot spring