ON STRESSES IN OVERSTRAINED MATERIALS. 265 



In addition to these tests, another is carried out, which is no doubt the important 

 one from an engineer's point of view, to ascertain the shearing strength of the soil. 

 This is effected by means of a machine designed by Prof. Terzaghi (a description is 

 given in Krey's Erddruck und Erdwiderstand, pubUshed by W. Ernst & Sohn of Berlin). 

 The soil is not tested exactly as it arrives, but it is diluted with excess of water and 

 then put in a thin layer between sand-filtering discs under a known load. The 

 water is thus squeezed out until a stable condition is reached, which takes about a 

 fortnight. It is considered that the clay then contains the maximum amount of water 

 possible under that particular load. The load usually selected is that to which it is 

 subjected in situ, but the clay is sometimes tested after having been subjected to 

 other selected loads, and therefore contains more water, or less, as the case may be. 

 It is important to note that the shearing strength obtained represents the result of 

 combined cohesion and friction. 



While my new laboratory was being built I concentrated on the solution of 

 problems presented by a very simple model of sand. As I have previously stated, I 

 believe that sand pressures are essentially connected with the packing of the grains. 

 It appeared to be worth while to investigate the pressure of ideal sand made up in 

 uniform spheres. Rough experiments with HofiEmann steel balls showed that they 

 behaved very like sand. The mathematical solution of the equiUbrium of steel balls 

 in three dimensions appeared to be very difficult, so the two-dimensional problems 

 were attacked. The spheres (in two dimensions) can be replaced by cylinders and a 

 model was made with about 100 discs 1 in. dia. by J in. thick. These can be pOed 

 on edge and their motion examined as they slip. 



The results of the mathematical investigation of the forces between the discs 

 proved to be most interesting. This simple two-dimensional model will reproduce 

 all the phenomena of ' arching.' The arching over a hole in the bottom of the bin is 

 reproduced. The arching which supports sand in a silo (or vertical tube ) is reproduced. 

 The arching which is used in the latest Swedish method of building retaining walls, 

 anchored back at the top, is reproduced. The model shows all these actions and 

 the graphical solution of the forces gives numerical results. 



I regard arching as the most fundamental property of sand and, therefore, the 

 model appears to be valuable. 



The next problem was to find out how to use the model : how to apply the results 

 to real problems. One use of the model has akeady been found, which may be of 

 great importance. The model shows that there are limits which cannot be passed by 

 arching ; thus no arching can occur over a hole in the bottom of a box unless the 

 depth of sand is greater than a certain proportion of the diameter of the hole. This 

 appears reasonable. The same reasoning shows that sideways arching cannot occur 

 in sand if the depth of sand is small compared with the width. This at once indicates 

 how accurate measurements may be made on sand pressures — i.e. how arching may 

 be eliminated — viz. , by keeping the width of the wall on which the pressure is measured 

 large compared with its depth. All previous experiments have, I believe, been made 

 with approximately cubical boxes, and attempts have been made to avoid arching 

 by using larger and larger models. The solution appears to lie in the proportions, 

 not in the size of the model. 



A measuring apparatus was at once put in hand on these lines and is now nearly 

 completed. PreUminary experiments show that it acts satisfactorily, so far as can 

 be judged at present. The apparatus is designed to measure the force on a wall 

 (vertical or battered) and to give the horizontal and vertical components and the point 

 of application : in other words, to give the resultant force in magnitude, position and 

 direction. The ' wall ' is about two feet long and three inches deep. 



Since I reported to the Committee the fact that sand would bear loads proportioned 

 to the aibe of the dimension of the bearing surface (not square), Mr. Oscar Faber has 

 repeated my experiments with rather more accurate apparatus and has confirmed my 

 results. 



The clay experiments are held up at present till the new 3 -ton testing machine, 

 now nearly ready, is available. 



I should welcome a visit from the Committee to see my calculations and new 



apparatus. 



C. F. Jenkin. 



