中国地质大学：《构造地质学》课程PPT教学课件（英文版）Lecture 23 mechanical behavior of rocks

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