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TCON is a computer program for computing consolidation settlements caused by surface loadings, and rates of these settlements. The computations consist of three steps and can be stopped after any of these steps. Thus the program can be used:

1. To compute the vertical stress increments at one or more locations due to arbitrary surface loads;

2. To compute the final consolidation settlements at these locations;

3. To compute the rates of settlement at these locations assuming vertical and/or radial drainage.

The general capabilities of the TCON program are illustrated in Figure 1. Three kinds of surface loadings can be applied: areal loads, semi-infinite loads and finite loads. Areal loads may consist of placement or removal of fill, or raising or lowering of the water table. The various semi-infinite and finite load options included in TCON are illustrated in Figure 2. The current version also allows uniform loading for arbitrary polygons; these loads are not discretized and give good results. Note that these are all pressure loadings. If you wish to accurately model the stresses under a rigid foundation, you must use a combination of load increments to represent non-uniform contact pressures. The quadrilateral and triangular loads are discretized into point loads and can be used to represent fills or cuts of arbitrary shape and height. Vertical stress increments, final settlements, or final settlements and the rates of settlement can be computed at multiple locations. Any one of several specified soil profiles can be assigned to a particular location.

This program, like all computer programs, is no smarter than the engineer who uses it. We have tried to make the program reasonably simple to use and to provide clear instructions. However, if you have not previously attempted analyses of the kind performed by the program, you should probably seek advice from someone who has experience with this kind of analysis. You will not obtain the correct answer to the problem you are studying unless the field conditions are adequately represented. Even then you should not assume that you have computed the correct answer. The purpose of analyses such as are conducted with this program should be to obtain insight into an engineering problem, not to obtain numerical values which are taken at face value. For this reason, we have built various options into the program so that you can explore the effects of varying the assumptions made in modeling your problem as well as the effects of varying material properties. However, we cannot guarantee that the program works for all analyses that you try to conduct. We have taken special care in developing the program, but you should run your own check problems before conducting particularly unusual or critical analyses.

Figure 1: General Capabilities of TCON

Figure 2: Finite and Semi-Infinite Load Options

As discussed subsequently, the accuracy of the solution obtained using TCON is increased by using smaller load increments and thinner soil layers. Thus if the user wishes good accuracy and specifies multiple soil profiles and locations for calculation, quite large problems can be created. Good judgement is therefore required in deciding just how much to attempt in each execution of the program. We have made it possible for you to do a lot at once but you are warned that the program can generate considerable output. Note also that TCON has been designed primarily to handle problems with complex loadings and/or problems in which the rate of settlement is important.

In TCON vertical stress increments generated by finite and semi-infinite loads are computed using the Boussinesq formula which implies that there is an isotropic, homogeneous, linear elastic half-space below the loaded area. In reality this is never the case but the stress distribution below a loaded area is not highly sensitive to stress-strain relationships of the materials involved, and so the Boussinesq assumption is generally considered to be an acceptable simplifying assumption. The resulting settlements and the rates of settlement are, however, somewhat sensitive to nonlinearity of the relationships between compressibility and permeability and effective stress. While the classical consolidation solutions were usually forced to adopt constant values for the resulting coefficient of consolidation over the entire compressible layer, numerical schemes such as those employed in TCON allow the user to define pressure dependent properties for each layer in the numerical model. While the same material type must be assumed throughout each horizontal layer, in problems with radial flow the properties can be made to vary as a function of the current vertical effective stresses in each column of the numerical model.

In problems with finite or semi-infinite loads, there will, in general, be immediate settlements, which result from distortion, as well as consolidation settlements, which result from compression. TCON computes only consolidation settlements for primary consolidation. For a discussion of the computation of immediate settlements the user is referred to the paper by Foott and Ladd (1981). Foott and Ladd indicated that the values of initial settlement obtained using the usual methods tend to be small in comparison to the consolidation settlement, at least for soft ground conditions where the clay is loaded into the virgin compression range. This is particularly so when the loaded width is several times larger than the clay layer thickness. Also, when an estimate of initial settlement is made, the conventional one-dimensional computation of consolidation settlement should logically be modified to incorporate a correction as described by Skempton and Bjerrum (1957). This correction accounts for the fact that the pore pressure increments immediately after loading are not equal to the vertical stress increments as assumed in the conventional one-dimensional computation because of the shear deformations which cause initial settlement. However, in all cases, except perhaps for very sensitive soft clays loaded to low factors of safety, this correction will result in values of the pore pressure increments that are less than the vertical stress increments, with a corresponding reduction in consolidation settlement. This reduction in consolidation settlement can compensate for most, if not all, of the initial settlement. Additionally, the uncertainties in the computation of consolidation settlements are such that the range of computed consolidation settlements may be greater than the initial settlement. Thus Foott and Ladd concluded that separate computation of initial settlements is usually not justified. The exception to this rule occurs when organic or highly plastic clays are loaded in virgin compression. Then initial settlements may be significant and they can be computed using the simplified procedure described by Foott and Ladd or by numerical analysis. Indeed, when initial settlements are significant it is questionable whether the usual approximation of assuming a single value of Young's modulus to compute the stress distribution below loaded areas is satisfactory, so that use of finite element programs in which the modulus varies from element to element becomes attractive.

As noted above, TCON computes only settlements due to primary consolidation. For the same organic and highly plastic clays in which immediate settlements are significant, secondary consolidation or creep, may also be significant (again, see Foott and Ladd, 1981). With TCON rates of settlement can be computed assuming vertical and/or radial drainage. For standard consolidation problems single or double vertical drainage is assumed. All other things being equal, this will tend to lead to an underestimate of rate of settlement, since in practice, horizontal drainage will generally speed up the rate of consolidation (see for example, Schiffman, et al. (1969), Davis and Poulos (1972), Koppula and Morgenstern (1972)). Nonetheless, in addition to providing a simple solution, the assumption of vertical drainage provides the basis of much experience that has been accumulated to date in comparing computed and measured settlements and rates of consolidation. However TCON does allow the user to simulate three-dimensional drainage by including infinitely permeable sand layers, if desired. Additionally, TCON includes an option to simulate the use of sand or wick drains by allowing radial drainage into the vertical line along which stress increments are computed, in addition to, or in lieu of, allowing vertical drainage. Use of this option requires the assumption of locally homogeneous soil layers and the complete three-dimensional array of drains cannot be modeled - rather, the user specifies the equivalent radius of influence for a single drain.

In computing consolidation settlements, TCON makes at least two more simplifying assumptions: that the stress distribution and consolidation problems can be uncoupled, and that the consolidation problem can be formulated in terms of infinitesimal strains rather than finite strains (Schiffman, 1980; Znidaric and Schiffman, 1981, 1982).

The adequacy of the first of these assumptions, that the stress distribution and consolidation problems can be uncoupled, was discussed by Davis and Poulos (1972) who compared uncoupled solutions with coupled solutions obtained by the Biot theory and concluded that the assumption is generally reasonable. Note that the Biot theory also requires use of a single value for the Young's modulus and that coupled solutions using nonlinear soil properties may not give quite the same results.

The effect of formulating the consolidation problem in terms of infinitesimal strains instead of finite strains is of course moot, if the consolidation settlements are small, but may become significant if the settlements are large. Gibson et al. (1981) indicated that for thick homogeneous layers use of the conventional infinitesimal strain theory will seriously overestimate the time of consolidation but can underestimate the excess pore pressures at a given time. If numerical analysis procedures such as those used in TCON are employed, it is possible to account for large strains by discretizing thick layers into thin layers for computational purposes and by adjusting the layer thicknesses at the end of each timestep. While some workers argue that even numerical solutions should be formulated in terms of finite strains, such arguments are misleading as the finite strain formulation leads to a nonlinear differential equation for which there is no stable solution. It is therefore necessary to resort to various simplifying assumptions in order to obtain a solution and the effect of these assumptions is not usually obvious. It seems preferable to use the conventional infinitesimal strain formulation with updating of co-ordinates to account for large strains (Olson and Ladd, 1979; Yong et al., 1983; Pyke and Beikae, 1985). The user can then approach the "exact" solution as closely as is desired by using smaller and smaller load increments and layer thicknesses. Self-weight consolidation problems, as described by Schiffman, et al. (1984), Carrier, et al. (1983), Koppula and Morgenstern (1982), Been and Sills (1981) and Lee and Sills (1981), can be analyzed using the theory employed in TCON and the general procedure described by Yong, et al. (1983). A separate program called TAILS is available for this class of problem.

The user should note that TCON does not solve the real problem that the engineer faces, but rather it solves the problem as modeled by the engineer. While we have tried to provide as many flexible options in the program as we can, consistent with maintaining simplicity of the input and the output, there will still normally be some constraints imposed by the program on the user's ability to model the real problem and appropriate judgement must be applied to offset this. Likewise, this manual does not cover the whole subject of evaluating consolidation settlements and the user is referred to standard textbooks and manuals for guidance on such subjects as conduct and interpretation of laboratory tests, the effects of sample disturbance, the effects of smearing on the walls of sand drains, and so on. An excellent review of one-dimensional consolidation problems is given by Olson and Ladd (1979) who noted various shortcomings of classical consolidation solutions and suggested that numerical solutions have the attraction of simplicity and versatility. They noted that lack of well documented case histories makes it difficult to determine the accuracy of these numerical solutions but concluded that recent studies for inorganic clays indicate that the major error in prediction of the primary time-settlement curve probably lies in the measurement of the appropriate soil properties. A good example of the use of vertical drains and the analysis of this problem is given by Olson et al. (1974) and additional references may be found in Geotechnique, Vol. 31, No. 1, March, 1981. A useful summary of previous work and recommendations regarding settlements of buildings is given by Wahls (1981). The volume "Sedimentation/Consolidation Models" published by ASCE, 1984, contains many useful contributions on these subjects.

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