It is well known that oedometer moduli M are not constant, but vary with the applied vertical load. In particular the oedometer modulus increases up to the maximum past pressure p_{c}. At p_{c }, break point in the e-log p curve, the modulus decreases, to increase again at higher loads. Therefore the average modulus to be used for predicting settlement should in principle be chosen as the average modulus in the interval between the initial and the final vertical load. This can be done if the e-log p curve from the oedometer is available, but cannot be done if only the constrained modulus at geostatic stress is available. Since the target of DMT is specifically the 1-D modulus at vertical geostatic stress, and since DMT does not provide information on modulus at stresses higher than geostatic, predicting settlements using M_{DMT} involves approximation. Fig. 4 shows schematically two typical e-log p oedometer curves, and the values of the moduli M at various applied vertical load p. In many natural soils, with the exception of highly structured clays, where the break is sharp, the variation of the modulus across p_{c} is moderate. Hence the error in assuming M≈constant is often relatively acceptable for practical purposes. This assertion is supported by the large number of case histories in the recent decades indicating good agreement between observed and DMT-predicted settlements. On the other hand moduli estimated by alternative methods are not rarely affected by errors (e.g. disturbed samples) much larger than the mentioned approximation.
It is reminded that M_{DMT} provides an estimate of the operative modulus during the consolidation. Hence the predicted settlement is the primary settlement, and does not include the secondary settlement.
In clay, the expansion of the membrane occurs in undrained conditions. Therefore the dilatometer modulus E_{D} is an undrained modulus. Thus, according to logic, the correlation to be investigated should be between E_{D} and the undrained modulus E_{u}. Attempts of this kind were carried out in the early days of the DMT development. However a big obstacle, precluding such possibility, was the high variability of the undrained moduli provided by different laboratories, at least in part due to the high sensitivity of E_{u} to the disturbance. Hence, as a second attempt, the correlation E_{D} – M was investigated. This correlation involves many soil properties, including material type, anisotropy, pore pressure parameters etc. Hence no unique E_{D }– M correlation can be expected. On the other hand the DMT provides, in addition to E_{D}, also the parameters I_{D} and K_{D} , containing at least some information on material type and stress history. This availability provides some basis to expect at least some degree of correlation E_{D} – M , using I_{D} and K_{D} as parameters. Moreover, while the correlation E_{D} – M is, at least in principle, weaker than E_{D} – E_{u }, at least E_{D} – M can be tested, because M by different laboratory have much less variability than E_{u}.
Obviously the final word goes to real world observations. Large number of case histories have generally proved the favorable comparisons between observed and DMT-predicted primary settlements, thereby supporting the use of M_{DMT }as operative constrained modulus.
Note also Lambe et al. (1977 Jnl Asce GE, 106, GT3): “Drained moduli of saturated clays are typically about one-third to one-fourth the undrained values”. Hence a broad connection drained-undrained stiffness has already been invoked in the past.
Settlements calculations are generally carried out using the 1-D elasticity formula in 1-D problems, say large rafts, or the 3-D elasticity formula in 3-D problems, say small isolated footings. The well known formulae are respectively:
However the general recommendation is to use in all cases the 1-D formula, for the following reasons (Marchetti, 1991):
Since the above two formulae give similar answers, it appears preferable to use the 1-D formula, simpler and avoiding elusive n or σ_{h.}