The safest strategy, both from an engineering and environmental viewpoint, is not to fill a sinkhole. If the sinkhole is a hazard to livestock, put a fence around it. If filling the sinkhole is essential to your project or the sinkhole is a danger to people, there is a right way to do it. The sinkhole can be filled using a graded-filter technique (Reitz and Eskridge, 1977; Sowers, 1996). The purpose of the graded filter is to allow water to seep into the ground while the soil is held back.
Always consult a professional geologist who is experienced in identifying karst subsidence and an engineer experienced in sinkhole remediation when dealing with any structure threatened by a cover-collapse sinkhole.
Reitz, H.M., and Eskridge, D.S., 1977, Construction methods which recognize the mechanics of sinkhole development, in Dilamarter, R.R., and Csallany, S.C., eds., Hydrologic problems in karst regions: Bowling Green, Western Kentucky University, Department of Geology and Geography, p. 432-438.
Sowers, G.F., 1996, Building on sinkholes: Design and construction of foundations in karst terrain: American Society of Civil Engineers, p. 115.