In discussing the stability of an underground excavation, determining on a failure criterion for the rock mass is the key problem.
A failure criterion for the rock depends upon the relationship between the strength of the rock and the stress in it. On the basis of the failure theories proposed by Griffith, Mohr and Coulomb, the authors have used the following empirical relationship between the principal stresses. It expresses a failure criterion for the rock in the uniaxial compressive strength of the intact rock and the material constants which depend upon the properties of the rock
“The failure criterion”
σ₁=σ₃+√mσ_cσ₃+sσ_c² (1)
where,
σ₁ is the major principal stress at failure
σ₃ is the minor principal stress at failure
σ_c is the uniaxial compressive strength of the intact rock
m and s are material constants which depend upon the properties of the rock
While, the failure criterion for a jointed rock mass may be determined by the same relationship to equation (1) to decrease the values of m and s according to the classification of rock masses.
In order to check the applicability of the failure criterion, the authors have mainly made a study of the material constants, m and s, to use about 1, 000 pieces of the results on uniaxial and triaxial tests.

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Toppling phenomena were observed along the cut of forestry road where rhyolitic welded tuff of the Nohi rhyolitic rocks is distributed. The rock mass of the welded tuff is separated into platy segments at the site by joints that strike parallel with the slope surface and dip 80° to 90°. The joints decrease in their number and the rocks near joints change in their texture with increasing vertical distance from the slope surface. These facts show that the joints have developed by weathering action from the slope surface.
The toppling phenomena are inferred to have developed through the following process. Firstly the development of joints separated the rock mass into platy segments with narrow width, and decreases the strength of segments against bending and buckling. Secondly segments began to topple when they are buckled mainly by their own weight or bended by the force exerted by adjacent segments.

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The discharge of groundwater from the catchment facility of Minafuku underground dam in Miyako island, Okinawa Prefecture, was calculated by solving the Sugio's equations and Manning's equation. The availability of the Sugio's equations in this case was proved by calculating the permiability of the Ryukyu limestone nearby the facility on the basis of the data of the 4th pumping test in this dam. The permiability which we calculated equals to 0.25cm/s and it is good accordance with that of ordinary Ryukyu limestone. The Manning's coefficient of the pipe in the catchment facility was calculated on the basis of the same data. The coefficient which we have gotten equals to 0.032 and it is extremely larger than that of the other ordinary steel pipe.
When H₀ (initial groundwater depth) and dH (drow-down of the groundwater level) are given, we can estimate the discharge of groundwater from the catchment facility of this dam by the use of Figure 5 in this report.

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