Dear Abada Dandachli

There are 2 meanings for cohesion that can be related to elasticity & elastic constants:

1. Cohesion (geology), the part of shear strength that is independent of the normal effective stress in mass movements

2. Cohesion (chemistry/physics), the intermolecular attraction between like-molecules

So I guess you refer to a correlation in geology-soil, & for that you can check the following work that gives the correlation or relationship between the two variables---soil cohesion & elastic stress

Article Relationship between soil cohesion and shear strength

I quote the paper: "...Cohesion of soil is an important factor of soil consistency. The word cohesion, however, has acquired two connotations. Soil physics defines it as "the cohesive force that takes place between adjacent particles". On the other hand, in soil mechanics, cohesion means "the shear strength when the compressive stresses are equal to zero". It is apparent that these two meanings differ...."

hi..the correlation for Young's modulus with respect to cohesion..for very soft clay (cohesion c = 0 to 50 kPa) the expected value of E = 0.5 to 5 MPa, soft clay (c=25 to 50 kPa), the value of E = 5 - 20 MPa, medium clay (c=50 to 100 kPa), the value of E = 20 - 50 MPa)..i suggest you to read the test book on Principles of foundation engineering and Geotechnical engineering hand book edited by Braja M. Das..ok all the best in your research..

In the plasticity theory cohesion is defined as yield stress at zero pressure (e.g. in Mohr - Coulomb theory, cohesion lies on the intersection between yield surface and the deviatoric plane at zero pressure).

Theoretically, Young's modulus and cohesion have no connection, but in practice, there is an experimental observation that Young's modulus and cohesion are (very roughly) linearly dependent, "cohesion ~ E/10",

The undrained cohesion of soil (cu) was directly correlated to the undrained secant modulus of clay soils as shown

E = β cu

Some typical values of β determined from full-scale field tests are given in the attached Table

Hi Abada Dandachli

There is n't any definite relevance between C (cohesion) and Elastic modulus (E) in soil and porous material. For example you can consider a poorly graded gravel (GP) with high density, without any finer soil (clay and silt) and in situ cementation, this soil could have high E and no Cohesion (C~0). In contrast you could find a soil with finer particle size and also insitu cementation, which it have high E and also high C.

Generaly Cohesion and Elastic modulus are gained with very different tests, and establishing a general correlation between them, may be deceptive. Any correlation is case sensitive, because C and E are affected by soil type, degree of cementation, aging, etc.

But in the case of information lack, the data base in the following books could be used:

Principles of foundation engineering by Braja M. Das.

Foundation analysis and design by Joseph E. Bowles

,etc.

The proposed data in these books must be used conservatively as an initial estimation.