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This article shows the mathematical method to determine the lateral stress on the shaft and toe resistance of pile using the new approach. The method was originally invented by Meyer and Kowalow for the static load test. The approximation curve was used for the estimation of both settlement curve and toe resistance curve of the pile. The load applied at the head of the pile is balanced by the sum of two components: the resistance under the toe of the pile and the skin friction. Therefore, the settlement curve is compilation of two factors: the skin friction curve and the resistance under toe curve. The analysis was based on the verification of the methods using laboratory experiments, that is, static load tests. The results of the research allowed to determine the relationship between parameters of the Meyer–Kowalow curve. On the basis of the relationships, it was possible to determine the skin friction and the toe resistance of the pile. Mathematical analysis of curve parameters allowed to determine the influence of the toe resistance on the settlement.

Statistic load test is the most commonly used method for estimation of the bearing capacity of piles. From the test we obtain the series a values: load-settlement, Q-s curve. In practice, it is extremely difficult to reach the critical load of the pile when the settlement turns out of control. The existing methods that allow bearing capacity to be calculated give the value which is very often 1/10 of the critical load. The question arises if it is possible based upon short series of load, i.e., 0÷0.4 critical load, to predict the critical value of the load, with accuracy which is sufficient for practical calculation. The paper presents a method how to calculate the critical load based upon short series of load in the static load tests.

The problem of consolidation of soil has been widely investigated. The basic approach was given by Terzaghi who assumed soil of constant physical and mechanical parameters. In the case of peat consolidation, the permeability coefficient of soil and the elasticity modulus are functions of the settlement which is an important additional factor. The model proposed here assumes varying the elasticity and permeability coefficients. Moreover, the settlement is described by the so-called elementary curve which was approximated empirically based upon laboratory tests. The model allows to consider the case when the filtration in the peat body goes in horizontal direction. It happens so when the charging layer does not receive outgoing water from the pores. The model includes also the case when the load involving consolidation varies in time i.e. the charging layer grows up gradually. The model has been applied practically in several cases and it comes that there is a good agreement between calculated and measured settlement of the consolidated peat layer.

In the work authors analysed possibility of obtaining static load tests curve for a pile in case of changed diameter, using load curve based on results of static load tests for given diameter. In calculation analysis authors used Meyer–Kowalów (M-K) method. A mathematical description was shown of determining new M-K curve for a pile with changed diameter, taking as a basis original M-K curve obtained from static load tests. Then an example of calculations is presented in which parameters of M-K model for a new curve were determined. Simulation calculations were carried out in the original computer program, the results of which includes load curves for piles with different diameters and relations between diameter changes, limit load capacity and settlement of a pile.