Probability model for embedment of single pile into rock masses at building sites in karst terrain

In karst area, existing methods used to determine whether single pile is embedded into rock masses cannot ensure that there is no steep rock surface around the pile tip or that there is no cave within a certain range under the pile ending, and thus, there are great safety risks for the pile foundations. Based on the building foundation survey and the pile foundation engineering practice in karst terrain, this paper establishes a probability model for embedment of single pile into rock masses which considers the degree of foundation dissolution and the pile diameter, deduces the depth distribution formula for the rock-embedding probability of single pile, and verifies the rationality of the proposed probability model with a project instance. According to the results, the degree of ground dissolution and the pile diameter are the main influencing factors to the rock-embedding probability of single pile; the proposed model properly reflects the pattern that the rock-embedding probability of single pile decreases with the rise of the foundation dissolution degree and with the increase of the pile diameter. The project instance shows that, overall, the theoretical rock-embedding probability is 10% smaller than the actual rock-embedding probability of single pile, and this difference is less than 5% in the depth range with a small dissolution ratio; so, the proposed probability model for embedment of single pile into rock masses is of high engineering accuracy. All data used in the proposed rock-embedding probability model for single pile is only from site investigation, which contains cheap, abundant, and reliable available data sources; so, this model can be used to evaluate the reliability of the embedment of single pile into rock masses in the karst terrain.