Calculation of pore water pressure? 1

[sphgeo]

Hi all,

I found a bit confusion about computation of pore-water pressure (or excess pore water pressure) when performing soil deformation analysis. In my understanding, we have to solve the Biot's consolidation theory for all problems. Are there any other ways, which may be simpler, to calculate the excess pore-water pressure when performing soil deformation analysis?

Could someone please help me to summarize ways to calculate excess pore water pressure in soil mechanics (static and dynamics analysis)?

 

[jester86403]

for the most part pore water is simply hydrostatic pressure in most cases. To solve for excess pore water pressure you can use bernoulli's equation

 

[dgillette]

jester86403 - I think the question is a lot bigger than that. sphgeo is (I believe) referring to Biot's coupled consolidation-deformation theory.

"The first truly coupled theory of consolidation was published in 1941 by Biot. In this theory, the continuity and equilibrium relationships are coupled so that, in three dimensions, the governing equations consist of three stress or displacement equations of equilibrium and a continuity equation." (Theories of Consolidation, R.L. Schiffman)

I must disagree strongly with your answer to sphgeo. One cannot get the proper pore pressures from fluid-flow considerations alone, as you imply. Volume change and undrained shearing affect the pore pressure also. This is why there is consolidation theory (beginning with Terzaghi's 1D infinitesimal-strain model, and extending on into 3d, finite-strain, etc.) and why we care about undrained shear strength.

BTW - Don't you mean Darcy, rather than Bernoulli?
____________________

sphgeo - Your question is huge, and not one that can be answered easily in this forum. Perhaps if you were more specific, someone could suggest a simpler solution to the problem at hand. A lot of dams, tunnels, and foundations have been built successfully using 1D consolidation theory, undrained shear strengths measured by vane or cone, etc., without resorting to higher-level theories, such as Biot or large-strain consolidation. I'm sure there are some, but off the top of my head, I can't name one existing structure where Biot or other coupled analysis was actually used in the design or a safety evaluation. Perhaps in the offshore petroleum industry, or some large tailings dam.

My old friend Schiffman, the consolidation theorist, would turn over in his grave to hear me say this, but sometimes we have to remember that we're trying to apply fairly sophisticated math to a pile of dirt, and our ability to do the math greatly exceeds our ability to characterize the materials and loadings.

 

[BigH]

dgillette: snaps to you on your last para!! Plugging first order values into 5th order mathmatical equations.

 

[sphgeo]

Hi dgillette and other,

Thank you very much for kindly reply. I could get some answers in your posts. Yes, my question is very general therefore could made other difficult in helping me. I will simplify my question:

When we conduct soil-liquefaction analysis, I means 2D or 3D computer modeling, we will need to solve the coupled theory of consolidation equations, so-called theory of mixture, and appropriate soil constitutive model. In such analysis, I will get information on the soil deformation, effective stress profile and change in pore water pressure.

However, when considering simpler problems such as bearing capacity analysis, bank construction analysis, or other soil deformation analyses. By solving soil constitutive models, I can also get information about the soil deformation pattern and stress (effective stress) profile. Without considering pore-water pressure, such results may not full fill demand of geotechnical applications and design. We will need to consider the effect of pore-water pressure in these problems. In such cases, I want to know methods to estimate the pore water pressure. Of course, we may also solve the coupled theory of consolidation in these cases but it seems unnecessary since it is very complicated. There must be some simpler ways to do this job. 1D consolidation analysis is one of them. Are there any suggestions?

Thanks in advance!

 

[BigH]

There are a number of variations in estimating the porewater pressure responses. First, is the simplistic one that change in porepressure = applied vertical stress. Skempton in 1954 put forth the "A" and "B" coefficients taking into account vertical and horizontal stresses where the horizontal stresses are the same in both directions of the plane. It is noted that these are not independent of soil stress history and characteristics - (i.e., not all stress paths to failure follow the similar path). Henkel expanded to the alpha coefficient taking into account the three-Dimensional point of view. You might wish to refer to Terzaghi Peck and Mesri (1995) section 15.5 and Section 25. Also you should refer to Henkel's paper (you'll find it referenced, say, in Wood's book on Critical State Soil Mechanics (and elsewhere). Head's book on laboratory testing has a good chapter on the use of stress paths.

As you are talking about "liquefaction" - the applicable values might be harder to come by given that you will have difficulty to obtain undisturbed samples to test in the triaxial apparatus - and varying percentages of silt in the samples will markedly effect the porewater pressure response and its dissipation.

As dgillette indicates, this is very complicated and not all that well understood (or used) by most practicing engineers - which leads me to believe that you are doing more "research" rather than practicing - not that that is a bad thing.

 

[jheidt2543]

Just for curiosity, here is a link to Henkel's obituary:

http://www.atypon-link.com/doi/pdf/10.1680/geot.2006.56.6.442?cookieSet=1