土-機械系の相似性に関する研究 (第3報)

砂-モデル・シュー系の相似性

抄録

Dynamic and geometrical similarities were tested in a fine dry sand using three kinds of model shoes with similar configuration (Tab. 2). Each model shoe consisted of three plates combined in such a state as shown in Fig. 1 to investigate the effects of space e. Horizontal draft and slip sinkage of model shoes were determined as the dependent variables and the pertinent variables of them were selected (Tab. 1). Design or operating conditions were obtained by dimensional analysis. Experiments were done under the three levels of v, p and e (Tab. 3) in the test apparatus shown in Fig. 2. In the test apparatus, the model shoes were drawn always in a horizontal posture. Draft and sinkage were measured by means of a strain gage type force transducer and a differential transformer, and forward displacement of model shoe was also recorded.
Influences of independent variables to draft or sinkage of model shoes and similarity at four categories of II_s, were investigated mainly by the method of the analysis of variance. —ANOVA—.
The results obtained were as follows.
1. Effects of v to D or Z were negligible within the range of velocity designed in this test.
2. The outstanding effects of p to D and of e to Z were recognized.
3. As the ineffectiveness of v was cleared, similarity was tested supposing that the same experiments were carried out three times in three levels of II_p and II_e. Each combination of II_p was considered to be a specific model shoe-sand system, and then, ANOVA was adapted to each system.
3.1 Dynamic similarity
In most of the combinations of II_p and II_e, the existence of dynamic similarity was recognized (Tab. 7). However, beyond II_s=1.5, there were some cases that the similarity did not come into existence. It seems that the dissimilarity was brought from some differences of an initial condition of each shoe which were enlarged with its forward displacement
3.2 Geometrical similarity
Geometrical similarity was recognized when II_e was zero. In other words, the gradient of sinkage plane of model shoe was similar when space was not given (Tab. 11).
4. II_D or II_Z versus II_p and II_e
Significance was cleared through the inspection of ANOVA (Tab. 8) that II_D or II_Z varied with II_p and II_e, but interactions were not seen. Their relationships are presented as a plane in Fig. 4 and 5.