The "Loughborough Loess" Monte Carlo Model of Soil Structure

S. C. Dibben, I. F. Jefferson and I. J. Smalley
Collapsing Soils Research Group, Department of Civil and Structural Engineering, Nottingham Trent University, Nottingham NG1 4BU, United Kingdom

The Loughborough loess is an ideal model material attempting to mimic the structure of a true loess. To produce a variant of the model, a simple Monte Carlo method has been developed, allowing a computer model to be created. Thus enabling various aspects of internal structures examined.

The evolution of the Monte Carlo approach to the collapsing soil problem has been gradual. The first application was to the problem of the closest random packing of spheres in one dimension (Smalley, 1962). These experiments have recently been repeated and the 0.78 packing value confirmed (Assallay et al., 1996). The method enabled the pseudo-regularity of contracting planar basalt systems to be explained (Smalley, 1966) and allowed model drumlinfields to be constructed (Smalley & Unwin, 1968). The method produced some initial soil structures for post-glacial marine clays (Smalley, 1978) but had its most successful application in determining the mode shape of loess particles (Rogers & Smalley, 1993).

Soil structure at the single particle level is difficult to represent and difficult to investigate. Loess is a relatively simple soil in which the structure is dominated by 20-30mm quartz particles of a 8:5:2 aspect ratio, giving blade shaped particles (Assallay et al., 1996). The major geotechnical problem is that this structure collapses when loaded and wetted; a hydroconsolidation process causing subsidence and possible damage. To study this hydroconsolidation process it is necessary to model or observe the soil structure, both during formation and prior to collapse occurring.

The application of computing to the model allows the scale of the model to be increased significantly and the time taken to produce a structure becomes negligible. This eliminates one of the main problems of all particle packing carried out manually. That is that the structures obtained are small and few due to the time consuming nature of the work. This causes a problem with the repeatability of results and the behaviour of the structure on a larger scale.

The original model, written in FORTRAN 90 sets up a two dimensional array. Rectangular blocks represent the quartz particles and have a dimension of one unit high by any value greater than two units wide. A random number generator is used to drop the particles into the array to form an open, random packing.

Due to the method of particle placement the array is only pseudo-infinite and thus side boundaries are used. A boundary is located at 80% of the height of the array to allow for "unfull" columns. The void ratio is calculated for the area within these boundaries. A particle size of 3 :1 gives a void ratio of 1 . 18 on average (a packing density of about 0.47), which is a sensible value for loess (Fookes & Best, 1969). As the particle width increases the void ratio also increases. For the first time it is possible to demonstrate the effect of particle shape on voids ratio for a model soil.

The program allows an on screen display of the structure, with file output to a CAD package to enable printouts. A series of remarkable sub-structures forms, the most characteristic of which is the staircase structure. This is similar to the stepped-face-to-face structure discovered by Smalley and Cabrera in 1969. A three dimensional version of the program will enable the aspect ratio of the quartz particles to be properly represented and give a more accurate void ratio. The model described above gives the initial formation of the loess. It is intended to study the bond formation in order to create a model of the metastable structure. The subsequent hydrocollapse mechanism will then be analysed.

As Assallay et al. (1996) pointed out, the basic Monte Carlo method can be useful for very simple applications as well as the very complex applications for which it was invented. Extremely simple tests can be done with random number tables but the application of computer modelling makes the method available for a whole range of geographical and geotechnical applications.