Based on the thought of limit equilibrium equition of granular medium, this paper makes an effort to study the caving rules of the roof of the undercut stope deep buried in granular medium, and furthermore, connected with the calculation of the collapse of the powder ore of Jinshandian mine, the result of this paper is compared with that of pomogb kob's theory. So far, most of problems which are being studied in granular mechanics are such as bearing capacity of foundations, stability of slope engineering and earth retaining structure. etc. There has been hardly one who paid his attention on the collapse of roof of underground opening deep buried in granular medium so much as he done in foundation and slope engineering in granular mechanics. The current method concerned with this problem is still the pomogb kob's theory which was put forward as early as 1908. This theory is based on the granular structure mechanics and supposes the arch which is formed after the collapse as parabola, so, it is gained by primary method on the basis of some hypothesis. Compared to this, we try to solve this problem by numerical method for partial differential equitions based on the limit equilibrium equition of granular medium which has been widely used in soil mechanics.
The characteristic method for solveing limit equilibrium equitions In granular mechanics, the limit equilibrium state of a point can be determined by the characteristic stress σ and the characteristic angle θ, their physic meaning are such as fig (l). By difference method, we can get M" first, and then M', and then M, so as to gain M from the known M1 and M2.
The classify of surrounding area of undercut stope by the velocity of slip. According to plastic theory, the slip field surrounding a rectangular cave in an infinit area is such as figer (4). In this paper, the slip lines are logarithmic spiral within the curve zone. There is no sense in talking about strain when the limit equilibrium state has been reached, because that all points must have been plastic flow state then, and their strain will expend continuouslly without the increasing of stress. So, the velocity of strain makes sense rather than strain itself. In fact, the true solution of our problem must make the velocity field satisfy the boundary condition of velocity· It will be very difficult to do so, most of us haven't done so up to now. To the problem of this paper, the gravity will produce tensile stress due to the vacancy below the roof, and the roof must be collapsing when the stress exceeds its ultimate capacity. So, it is enough to do only qualitative analysis in the velocity field. Generally, plastic potential function f can be assumed as the same as yield condition according to Von-Mises hypothesis. In the point of view of plastic theory, the boundary line or the envelope of slip lines denotes the interface of strain speed.