How do you calculate shear modulus from shear wave velocity?
The velocity at which shear waves propagate through bulk matter is called the shear wave velocity. It depends on the shear modulus and density of the material. Mathematically, that’s: Vs = √(G / ρ) .
What is dynamic shear modulus of soil?
Dynamic shear modulus gives information about dynamic soil response and deformability characteristics. Dynamic shear modulus is defined as the ratio of the shear stress to the shear strain in the literature. Resonant column method is used to determine dynamic shear modulus of the soils in the laboratory.
What is shear wave velocity of soil?
Since Shear wave velocity is closely related to Shear strength and stiffness of material, It is used to evaluate engineering properties. In general. Soft soils : 100m/s – 200m/s (Avg. 150m/s) Stiff clays and sandy soils : 200m/s – 375m/s (Avg.
What does shear modulus tell you?
The shear modulus is the earth’s material response to the shear deformation. It is defined as the ratio of shear stress and shear strain. This valuable property tells us in advance how resistant a material is to shearing deformation.
What is maximum shear modulus?
The maximum shear modulus (Gmax, or shear modulus at very small strains) is an essential property of soils determining deformation characteristics and dynamic response of soils (Ku and Mayne, 2013); thus, the estimation of in-situ shear wave velocity or maximum shear modulus is very important.
What is Poisson ratio of soil?
The Poisson’s ratio represents a change in shape of a material while the volume is maintained constant. In soil mechanics, Poisson’s ratio, also known as the coefficient of lateral expansion, is affected by the following factors: a) The soil is a discrete and stratified medium, mostly not elastic and anisotropic.
What is the relation between Young’s modulus and shear modulus?
Where, K is the Bulk modulus. G is shear modulus or modulus of rigidity….Elastic constant formula.
| Formula | SI Units | |
|---|---|---|
| The relation between Young’s modulus and bulk modulus | E=3K(1−2μ) | N/m2 or pascal(Pa) |
Why is shear wave velocity important?
The shear wave velocity of soil and rock is one of the key components in establishing the design response spectra, and therefore the seismic design forces, for a building, bridge, or other structure. The shear wave velocity can be measured from in-situ field tests, such as cross-hole or downhole testing.
What is shear wave velocity test?
MASW is a geophysical method of mapping the stiffness properties of soil in an 2D profile. The method is based on measuring the lower frequency surface waves in the range 3-30 Hz (Park et al., 2007). Execution of the test is easy and quick which makes it very economical compared to other field methods.
What does the shear modulus depend on?
The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M1L−1T−2, replacing force by mass times acceleration….
| Shear modulus | |
|---|---|
| SI unit | pascal |
| Derivations from other quantities | G = τ / γ G = E / 2(1+n) |
How does the shear modulus change with temperature?
Shear modulus changed from 960 to 140MPa as temperature increased from 25 to 250°C. The shear modulus is the earth’s material response to the shear deformation. It is defined as the ratio of shear stress and shear strain. This valuable property tells us in advance how resistant a material is to shearing deformation.
Why are shear moduli greater than strength tests?
Seismically derived shear moduli are typically greater than those measured by in-lab strength tests because seismic measurements are made under elastic, low-strain conditions. Even though the shear modulus is a property closely connected to viscosity, it is insensitive to temperature and composition.
How is the dry bulk modulus related to shear?
The derived dry bulk modulus must be positive and greater than 2/3 of shear modulus to insure a positive lame constant and Poisson’s ratio. Otherwise, either Vp is too low or Vs is too high.
How are shear moduli used to define linear elasticity?
The Lame’s constant and shear moduli are the only two elastic constants to define the linear elasticity in an isotropic system through Hooke’s law. Similarly, working through the inverse Hooke’s law, Poisson’s ratio ν and Young’s modulus E are the only two requirements.