before and after the Sinking of a Bon-hole. 801 



Effects of a Bore-hole. 



§ 18. The existence of a bore-hole may profoundly inrlu- 

 ence the conditions in its immediate neighbourhood ; but 

 clearly it will not produce an appreciable effect at distances 

 from the hole which are a large multiple o£ its diameter. 

 Over the cylindrical surface of the hole the normal stress 

 must vanish, /. e. the horizontal pressure must be nil, sup- 

 posing the hole vertical. Thus if we suppose an imaginary 

 cylindrical surface coaxial with the bore-hole, but of relatively 

 large diameter, the material within it will be practically in 

 the state of the hollow cylinder of § 8 when we suppose a 1 ja 

 very small. From this conclusion we must exclude the 

 material immediately surrounding the extreme foot of the 

 hole, whose condition will be somewhat modified. Excluding 

 this very limited volume, we infer from (27) and (28) that 

 the maximum stress-difference S at depth /?, which was 

 gph~jj before the hole was bored, is, subsequent to the 

 boring, the greater of the two quantities 2p and gph. Here 

 ji denotes the horizontal pressure at depth It at a distance 

 from the hole. 



If p vanishes, i. e. if the material is in the condition of 

 an isolated pillar, the presence of the bore-hole makes no 

 difference. 



On the hypothesis of a compressible crust on an incom- 

 pressible nucleus, after the hole is formed S equals gph so 

 long as 7] does not exceed 1/3 ; thereafter it increases with rj 

 to a maximum of 2gph when rj equals 0'5. Particulars on 

 this hypothesis are as follows : — 



Value of &/gph. 



n = 0-2 -25 -o -o" -4 45 -5 



Before hule made 1 0"75 0*6 0-57 0"5 ; o 018 -00 



After „ „ 11 11 113 164 200 



AVhen a bore-hole is formed the engineer may thus 

 anticipate over its surface a stress-difference varying from 

 l> to 2p according to circumstances, where jj represents the 

 hydrostatic pressure at the same depth in a liquid of the 

 same mean density as the superincumbent material. 



From the identity in type of the results in §§8 and 10, 

 the probable behaviour of the tube-walls may be deduced 

 from experiments in which a circular cylinder of the material 

 with a coaxial hole of small bore is exposed to the combined 

 effects of uniform pressures over its flat ends and curved 

 surface. The former should equal the pressure in a, liquid, 



