I'm not sure this is exactly what you asked for, but anyway it may be worth for you having a look on RETC http://www.pc-progress.com/en/Default.aspx?retc

The pore size distribution (PSD) is not related withe grain size distribution. If the texture of the sample is homogeneous, the PSD can be obtained from one grain.

X-ray scanning can be used fo rthe 3D determination of PSD

@ Karim

I think it should be related, if you have the grain size analysis (see the attached XLS file) then these grains if they are randomly and closely packed should form a certain pore distribution.

@ Fulvio

No I did not try Geo-Slope!!! Which module (Air/W. Seep/W)? Could you provide more details please?

@ Mohsin

You are completely true, this technique is quite good for 3D representation experimentally. If there is a module to predict the 3D pore distribution from grain size analysis then the comparison between measured and predicted would be great.

@ Laith

Are you talking about the pores among the spheres?. Supposing that these spheres are massives?. I was thinking in micro and mesoporosity, excuse me.

Have you methods in place to test your predictions?

There is conceptual relation between PSD and soil water retention curve. The derivative of soil water retention curve is pore size distribution. Please see pioneer work of Arya and Paris (1981):

Arya, L.M., Paris, J.F., 1981. A physico-empirical model to predict the soil moisture characteristic from particle-size distribution and bulk density. Soil Sci. Soc. Am. J. 45, 1023–1030.

and many papers published after this important paper.

If you retrieve your information on grain size from a 3D scan (microtomography), Pore3D is a good solution (see http://ulisse.elettra.trieste.it/uos/pore3d/)

Pore size relates to grain size.They have approximatly the same order. However in general case it is impossible to get more exact relation between them. Additional information is needed. Is it a rRegular (what type of regular structure) or random (parameter of random structure) structure? In other case you need to have nathematical model of your structure (you can borrow it from literature). in other case the experiment can give you the best answer.

As @Anatoliy says, there is a relation to get some idea of the PSD, newertheless much more information plays a role on it (packing density, homogenity of the materials, sorting of the particles, etc). You may use the RETC program to fit a generalized Water Retention Curve from your texture data (using the Neural Network Prediction) and bulk density. Take a look into http://www.pc-progress.com/en/Default.aspx?retc

As commented by Mohammad Reza Mosaddeghi, the model of Arya and Paris (1981) and following modifications (Arya, L. M.; Leij, F. J.; Shouse, P. J. & van Genuchten, M. T. Relationship between the Hydraulic Conductivity Function and the Particle-Size Distribution Soil Sci Soc Am J, 1999, 63, 1063-1070) based on the similarity of the grain size distribution and the corresponding voids, give good estimates of retention curves, especially in sandy soils.

We are developing a software that does that.

I think, the answer is No. Grain size distribution alone cannot determine the pore size distribution - it will also depend on the nature of packing, such as density, degree of homogeneity, stability of the structure etc.

I don't think it possible, provided many other soil properties such as bulk density, texture, organic matter and degree of homogeneity are not available. Computed tomography (CT) technology scans the thin soil slice and sufficient number of CT images may help to detect the soil pore size distribution and estimate some soil hydraulic properties.

Have a look at the works of Prof. Delwyn G. Fredlund of the Unversity of Saskatchewan. He has conducted a great deal of research on the subjet of unsaturated soil mechanics. His book "Unsaturated Soil Mechanics in Engineering Practices (D.G. Fredlund, H. Rahardjo, and M.D. Fredlund; John Wiley and Sons, 2012) is an indispensable state-of-the-art on the subject. He has developed an analytical model for the prediction of the soil-water characteristics curve (SWCC) that is based on a modelling of the pore size distribution.

Additionally have a look at Dr Leo Rothenburg's (University of Waterloo) work on "peanut mechanics". In the 1980's he studied the micromechanical behavior of granular material and was mathematically predicting the distribution of pore size - at that time.

@ Luis Alvarez

Very interesting, I look forward to hear about your software. Is it possible to give us a small hit about its capabilities (2D or 3D matrix, etc.)?

Please, when you finish the software post a web link here to generalize the benefit to other colleagues

Wish you all the best :)

Experimentally - Tomography techniques are used to find the PSD in 3D...

Simulations - DEM are generally used to find PSD...

In my opinion the problem is that pores may have very complicated shapes and it is next to impossible to find the volume of every individual pore in a given sample. Having grain distribution one should be able to compute its volume, at least in principle, thus the remaining volume of the sample must be pores. This however says nothing about pore distribution. Indeed, some of them extend across the whole sample, don't they?

@ Marek

The gains are assumed to be spherical. As you nicely indicated that the pore space is resulting from subtracting a certain volume from a certain grain arrangement. Kindly attached find a PhD thesis which touches this subject.

Hi Al-Taie

I think you can assume the spherical shape for all soil grains, but it is not enough to solve this problem. you should also assume that the diameter of all soil shapes are the same. so, you can calculate the whole volume of specific numbers of the grains and the volume of the soil having the minimum volume in lozenge arrangement of grains. finally, the difference between two volume can be assumed to the volume of all pores of the soil. you should note that the accuracy of this method is not significant, because of aggregation, organic matter and other colloids and . . .

@ Darvishan

If we assume that the soil grains are the same, then we only need three grains to validate the pore between them on 2D basis. If you go back to previous discussions at the very beginning, you will see an XLS file that will give you a clear picture. Also take a quick look at Gunnar Hellstrom PhD thesis just above your post.

Thank you very much for your contribution.

I'm not sure this is exactly what you asked for, but anyway it may be worth for you having a look on RETC http://www.pc-progress.com/en/Default.aspx?retc

@ Thomas

Thank you. The steps below are an approach to determine the PSD for a certain soil:

1- Determine the grain size analysis (Lab work)

2- Predict or determine the SWCC (model=D. Fredlund equation or Lab work)

3- Predict the PSD from SWCC by RETC.

I have just skim through the various comments and suggestion (very enlightening) and not sure whether comments will help you anymore. I have spent some time with a related topic earlier. My understanding is-one cannot estimate total pore size and its distribution from the grain size distribution of a real soil. Because, this depend on particle arrangement and their orientation/fabric in the soil element. However, the xls file you have shared that has limitation in having a good understanding-all the particles on xls figure can be fitted in a smaller circle (or a larger circle) and in that case the total pore space would be smaller or larger i.e. how they are distributed with in a space is important.

Now, if someone tries to achieve minimum pore space i.e. minimum void ratio then this can be done as a numerical optimization problem as particle size and their relative amount affecting them. For an simple example, I have attached a Fig from my earlier publication [CGJ 45(10), 1439-1455] on a relative topic where you can see their effects from an experimental data. For 2D and 3D, this is a very old mathematical problem on achieving maximum density. You may google “Apollonius problem”. I have shared link that I have quickly found-

1. http://en.wikipedia.org/wiki/Problem_of_Apollonius

2. http://www.jensilvermath.com/2013/06/29/apollonius-sphere/

To get a good flavour on how particle fabric affects pore size of a soil element, you can use Discrete Element Method, DEM. They are capable of providing information on total pore size, their distribution related to particle orientation. Currently, I am using OVAL (open sourced) and capable of doing all of these.

I believe it is not possible. Please consider chapters 4 and 5 and especially Fig. 5.7 and Table 5.1 of “Fundamentals of Soil Behavior” [third ed.] by Mitchell & Soga.

Assuming all grains have a spherical shape , you can roughly calculate pore size as follow: pore size= (grain size*phi)/(1-phi) which phi is porosity

Nice, simple formula. But I see a small problem with it: use grain size expressed as its volume and compute average volume of the pores, then find average diameter of the pores. Now use the same formula for pore and grain diameters directly. Both results will be identical only when porosity is null.

In addition to assuming particles as spherical, one has to assume a 'packing' such as 'cubic', 'Orthogonal ... etc. See papers by Wang, Pande & Pietruszczak.

Ali Mohammad Bagheri , I would like to ask if there is any literature regarding the pore size formula you have mentioned. Also would like to ask if the grain size is in mm in the formula.

Additionally consider reviewing work done by Dr Leo Rothenburg (University of Waterloo). In the late '80's and early '90's he was doing research on matters which relate to your query.

Sudeep Hada , Please refer to SCA2007-49 as an example document which s/v in this paper is pore size. Generaly grain size is micrometer and calculated pore size is also in micro meter.