1: As the degree of saturated of pore water decreases, the Poisson’s ratio also deceases. However, since the soil is cemented due to capillarity and adsorption as the saturation continuously decreases, Poisson’s ratio starts to increase as the internal stress increases.

2: the P-wave velocity increases to the velocity of compressional waves in water, whereas the S-wave velocity is largely unaffected by the presence of water

3: Poisson's ratio increases with depth, with increasing water saturation and with decreasing porosity.

Poisson’s ratio is controlled by two independent elements:

1) The solid rock,

2) The dry or wet micro fissures or microfractures.

1) Solid rock is influenced by the constituent mineral composition. The higher Poisson’s ratio of the rock-solid is the higher Poisson’s ratio of the rock. Poisson’s ratio of the solid rock may be roughly estimated from clay contents for clastic rocks.

2) Fissures or microfractures are defined as flat pores of low aspect ratios lower in the dry case or heightened, in the wet case, Poisson’s ratio of the rock. The magnitude of change depends on the volume concentration and aspect ratio of cracks. The higher the pore volume concentration and the lower the aspect ratio, the larger the amount of change in Poisson’s ratio.

I understand your question related to the role of Poisson´s ratio as input for geotechnical engineering applications involving stress-strain relationships. As a Geophysicist for E&D, essentially Poisson's ratio is one measure of a rock's strength that is another critical rock property related to closure stress.

Poisson's ratio is dimensionless and ranges between 0.1 and 0.4 in oil and gas wells. A low Poisson ratio, such as 0.1–0.25, means rocks fracture easier whereas a high Poisson ratio, such as 0.35–0.45, indicates the rocks are harder to fracture. The Poisson's ratio changes from layer to layer, and we can follow laterally these features by AVO analysis and forward modeling and prestack elastic simultaneous inversion, using not only two logs (P-wave and S-wave), but also three logs (P-wave and S-wave + density log).

As a Geophysicist, I use the FRM (Fluid Replacement Modeling) on Hampson & Russell software, for me the best software in Reservoir Characterization. Just to give you an example, please see below a simplified list of inputs and outputs:

Fluid Replacement Modeling:

Well name: Liverpool_x-1

Zone of Interest: Klopp

Zone of interest name: Salah Fm.

Start at top: Van Dijk Fm.

End at top: Alexander-Arnold Fm.

Domain type: Depth

Domain datum: Surface

Domain path: Measured

From top: Mané at depth: 312 m

To top: Henderson at depth: 1344 m

Input Logs:

P-wave log: P-wave_Klopp_x-1_fullstack_corr_0.760_ph_-85

S-wave log: S-wave_Klopp_x-1

Density / Porosity:

Density log: Density_1_Klopp_x-1

Porosity is calculated from density log and matrix density

Porosity threshold = 2 %

Input fluid parameters

---- Fluid Parameters: Brine -----

Density: Constant value = 1.09 g/cc

Bulk Modulus: Constant value = 2.38 GPa

Saturation: Constant value = 100 %

---- Fluid Parameters: Oil -----

Density: Constant value = 0.75 g/cc

Bulk Modulus: Constant value = 1 GPa

Saturation: Constant value = 0 %

---- Fluid Parameters: Gas -----

Density: Constant value = 0.1 g/cc

Bulk Modulus: Constant value = 0.021 GPa

Saturation: Constant value = 0 %

Patchy Saturation method: Homogeneous Mix (Reuss Average)

Petrophysical Parameters:

Matrix is user-defined.

Matrix Bulk Modulus: Constant value = 40 GPa

Matrix Shear Modulus: Constant value = 44 GPa

Matrix Density: Constant value = 2.65 g/cc

Patchy saturation not applied - Reuss Average used for fluid modulus

If saturation GOR is exceeded, free gas is used in calculations

Gas is default gas.

Gas Bulk Modulus = 0.021 GPa

Gas Density = 0.1 g/cc

Brine is default brine.

Brine Bulk Modulus = 2.38 GPa

Brine Density = 1.09 g/cc

Output Logs:

P-wave: P-wave_frm

Density: Density_frm

S-wave: S-wave_frm

Poisson´s ratio : Poisson_frm

Output Conditions :

Output porosity: Same as input porosity

Output temperature: Same as input temperature

Output pressure: Same as input pressure

Output GOR: Same as input GOR

Output fluid parameters

---- Fluid Parameters: Brine -----

Density: Constant value = 1.09 g/cc

Bulk Modulus: Constant value = 2.38 GPa

Saturation: Constant value = 100 %

---- Fluid Parameters: Oil -----

Density: Constant value = 0.75 g/cc

Bulk Modulus: Constant value = 1 GPa

Saturation: Constant value = 0 %

---- Fluid Parameters: Gas -----

Density: Constant value = 0.1 g/cc

Bulk Modulus: Constant value = 0.021 GPa

Saturation: Constant value = 0 %

Patchy Saturation method: Homogeneous Mix (Reuss Average)

I attach a paper “Dependency of Poisson’s Ratio on Water Content for Unsaturated Soils” by Y. Dong.

Best regards, Mario E. Sigismondi

Early in my career, I discovered that real world measurements contradicted the basic theory. We were able to measure P-wave velocities of ~1500 m/s and shear wave velocities of ~150 m/s while the theory said that Vs/Vp shouldn't go lower than ~60%. The problem of course is that the P wave velocities were in the water in saturated clean gravels and the S waves not passing in the water. Can someone explain how to calculate Poisson's ratio in this situation?

You may want to use a simple model to answer your questions. Refer to my paper A Petrophysical Interpretation of P & S Velocities (Full Waveform Sonic). Make use of the apparent linearity of the plot of squared P and S velocities.

The Gassmann fluid substitution of water by gas depends on the properties of the fluids (water, gas) and of the rock (porosity). The P velocity is first affected by the compressional effect (gas a much lower modulus than water) that becomes maximum around 10% gas saturation; afterwards the density effect is dominant: Vp decreases sharply first, then increases with gas saturation. The S velocity reacts only to the change in fluid density: Vs increases with gas saturation.