Analytic and numerical methods of sinkhole prognosis - Abstract
Article applies to various methods of predicting sinkholes on the surface caused by shallow
underground excavations and the excavations in fault region.
In the article are listed the basic factors determining the area of sinkholes like: depth of the
seam, rock mass thickness, mechanical parameters of rock mass, seam thickness, time of void existence
etc. which were took into consideration by the researchers to determine the height of caving zone .
There are two main methods to do that  classic analytic methods and more contepmorary 
numerical methods.
In analytic methods there are great number of equations applied in order to determine the height
of caving zone made by different researchers (Ritter, Segal, Sułstowicz, Mohr). This methods are divided
to empirical methods, and transforming function methods.
This methods were used for many years to predict sinkholes in shallow excavation areas, but
when the popularity of using computer programs in geomechanics increased, scientists have tried to
find new methods of predicting sinkholes.
That leads to numerical methods which allows the engineer working on surface sinkholes to take
numerous important parameters into consideration, having a significant influence on the character and
quality of surface deformation. The numerical methods allow to describe more precisely, using the
mathematic equations, the behaviour of the rock mass and the behaviour of the fault.
These methods mainly depend on a selected numerical technique (i.e. Finite Element Method,
Discrete Element Method, Finite Difference Method, or Boundary Element Method) and also on the
boundary conditions.
At first the prognoses were based only on empirical and analytical methods, but with time
scientists started using numerical analysis, which allowed to take many other parameters into
consideration.
Article show how importent is to combine analytic and emperical methods with numerical one
to achieve the best equation of natural processes which are sinkholes, considering all variables. It is still
very problematic because every sinkhole is unique and determined by different factors.