Small-scale testing under 1 g conditions as well as in the centrifuge presupposes that a model and prototype have comparative behavior. The chief condition for agreement between model and prototype is that the initial soil states of both must be at equal proximity to the steady state line. Then, when stresses are normalized to the initial mean stress, the model will in all aspects behave similarly to the prototype. Scaling rules are presented that indicate the relations between stress, strain, and displacement for the model and the prototype in terms of geometric scale and stress scale. An obvious limit of scales is imposed by that the soil in the model can be no looser than the maximum void ratio. Similarly, it must not be denser than a value that corresponds to a prototype soil at the minimum void ratio. Three main areas of application of the approach in engineering practice are identified: design of representative 1 g small-scale model tests; reanalysis of data from conventional small-scale tests; and improving the versatility of centrifuge facilities in recognition of the fact that the centrifuge test does not need to be performed at equal levels of stress, when designed according to the new approach. Key words : physical modeling, sand, scaling relations, steady state, centrifuge testing.

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A precast concrete pile was driven 11.0 m into a sand deposit and subjected to three compression and one tension static loading tests. By means of strain-gage instrumentation, the loads imposed in the pile during the tests were determined. The observed load distributions appeared to suggest the existence of a critical depth. However, when the load data were supplemented with the residual load acting before the start of the tests, the appearance of critical depth disappeared. Instead, the analysis of the tests showed that the load distribution was a function of the effective overburden stresses in the soil over the full pile length, with β-ratios ranging from 0.40 through 0.65 and a toe bearing coefficient of 30. The shaft resistance degraded slightly from test to test. The shaft resistance in tension was about equal with the shaft resistance in compression. The β-ratios and the toe bearing coefficient derived from the test were applied unchanged to the results of compression tests on a second test pile, a 15 m long identical pile, and the calculated capacity agreed with the capacity found in the static loading test. Key words : instrumented pile, sand, loading test, residual load, load transfer.

The authors analyzed the results from a static loading test on a 11.0-m, intrumented, precast concrete pile and presented the findings in two earlier papers. The findings are here extrapolated to verify the dependability of applying the results and analysis methods to predict the detailed behavior of a similar test pile driven 5 m away from the first pile and to a 4.0 m deeper embedment. This paper offers conclusions drawn from the analyses of both piles with regard to residual load and resistance distribution. A primary result of the analyses is the indication that the critical-depth concept is not valid. For full-length piles, the critical-depth concept originates because of neglects in analysis of test data, such as omission of the residual load and testing-sequence history. For tests on short piles and laboratory studies of model piles, a critical depth appears as a result of neglect of the influence of shallow-depth variation of the earth pressure coefficient. Key words : instrumented piles, sand, loading test, residual load, load transfer, finite element, constitutive modelling, critical-depth concept.