The discusser found it interesting to apply the equations provided by the principle of natural proportionality to the experimental data contained in this paper. The load–settlement response in Figs 19 and 22 are similar to the common load-settlement response of piles (Juárez-Badillo, 2005b). The general theoretical equation reads
where σ is bearing pressure, s is settlement, σf = σ at s = ∞, s* = s at σ = 1/2σf and (si, σi) is the initial point.
Figures 23 and 24 are the same as Figs 19 and 22 with theoretical points included. The parameter values appear in both figures. Observe the effect of ageing in Fig. 24 in some of the bearing pressure increments. They may also be mathematically described in a similar way as the ageing of G0 in clays (Juárez-Badillo, 2005a).
Comparison between MSD prediction and field measurements for load–settlement curve at Bothkennar
Comparison between MSD prediction and field measurements for load–settlement curve at Bothkennar
Comparison between measured and predicted load–settlement response of Kinnegar pad loading test
Comparison between measured and predicted load–settlement response of Kinnegar pad loading test
The stress–strain behaviour of Bothkennar clay in (a) CK0U triaxial compression, (b) CK0U triaxial extension shown in Fig. 18 may be mathematically described by the pre-peak normal function YN with v = 2 and the post-peak ductility function YD (Juárez-Badillo, 1999). The pre-peak normal function YN reads
where x = (σ1−σ3)/σc0,ea is the axial natural strain = ln(1 + εa), xf = x at ea = ∞, μ is the shear coefficient, and σc0 is the isotropic initial consolidation pressure. ea and εa are negative in triaxial compression and positive in triaxial extension. Equation (21) may be written as
and also as
The post-peak ductility function YD reads
where (σ1 − σ3)∞ = (σ1 − σ3) at ea = ∞, [ea1 (σ1 − σ3)1] is a known point, and ν is the ductility coefficient.
Equations (23) and (24) were applied only to the representative curves of Fig. 18.
Assuming a value of σc0 = 50 kPa, equation (23) for the pre-peak may be written as
where (σ1 − σ3/2)i is the initial stress at ea = 0, and equation (24) for the post-peak may be written as
Because of the small values of εa they were considered as equivalent to the values of ea.
The parameter values found were, for the CK0U triaxial compression,
and for the CK0U triaxial extension
Figure 25 is the same Fig. 18 with theoretical points included.
Soil stress–strain behaviour of Bothkennar clay (after Hight et al., 1992): (a) CK0U triaxial compression; (b) CK0U triaxial extension
Soil stress–strain behaviour of Bothkennar clay (after Hight et al., 1992): (a) CK0U triaxial compression; (b) CK0U triaxial extension
The discusser is confident that the above material might be of some use to the authors of this paper.
Authors' reply
The authors thank the discusser for his interest in the problem of predicting load-settlement behaviour using triaxial test data. The discusser shows that quasi-hyperbolic curves roughly fit both the reported field data from Bothkennar and Kinnegar and the associated triaxial test curves. However, it is not clear to the authors how the discusser uses the latter to predict the former; specifically, the prediction of s*, the foundation settlement at half the bearing capacity, is not mentioned. It is a central feature of the authors' new MSD method that the whole load-settlement behaviour can be predicted directly from a stress-strain curve without the use of any parameters.
