## 1 Introduction  
Kast terrain is extensively developed all over the world, covering about 12% of the planet's dry, ice-free land [1]. With the exponential growth of the world's population, the rapid urban expansion and increasing demand for transportation facility make engineering construction in extremely complex geo-conditions an inevitable choice [2]. For the architectures in karst area, the geo-disasters such as sinkhole collapse, subsidence, floods and landslides induced by the instability of soluble rocks are frequently encountered [2; 3; 4; 5]. Those typical karst geo-disasters have aroused researcher's attention, and the correspondent mechanism exploration and treatment methods are also investigated extensively. However, besides the geo-disasters mentioned above, the occurrence of water-sand inrush disaster during underground construction in karst area is becoming more frequent. In the first decade of the 21 st century, the underground accidents caused by water-sand inrush accounted for 77.3% of serious safety accidents in China's large-scale infrastructure construction process. China's karst landforms are widely distributed, with a total area of 3.44 million square kilometers, accounting for 15.6% of the global karst area [6]. Furthermore, karst landforms are also abnormally developed in 55 countries and regions along the \"Belt and Road\", covering almost the whole of Asia and half of Europe, accounting for about 2/3 of the total global karst zone [7], which makes water-sand inrush geo-hazards one of the biggest threats for the underground engineering, even for the successful implementation of globalization. Numerous investigations have been conducted concerned with this type of geo-hazards, mostly derived from the risk evaluation theories of water outburst disasters in the mining industry since the mid-20 th century. The \"water-inrush coefficient\" criterion, followed by the \"water-inrush index\" [6; 8] were initially proposed based on the geologic conceptualization model that the coal seam floor is assumed as a piece of \"resistance stratum\" subjected to hydraulic pressure with two ends anchored, the water outburst is supposed to occur immediately when hydraulic pressure reaches the threshold value. Subsequently, in consideration of coupling effects of mining-induced stress and hydraulic pressure beneath the confined aquifer, the hypothesis of \"three zones\" and \"zero fracture\" theory [8] were suggested to finely analyze the stability state of \"resistance stratum\". The bearing capability of confined aquifer was theoretically analyzed based on the elastic-plastic mechanics and fracture mechanics, and the critical energy release position was further identified by [PERSON] [9] through Hoek-Brown criterion. [PERSON] et al. [10] introduced the \"flow-stress-damage\" model into tracing the initiation, propagation and coalescence of the fractures during the whole water-outburst process. These research achievements mentioned above made significant explorations in the risk assessment of water inrush through coal seam floor and fractured rock masses. However, as indicated by engineering practices and literature research, a considerable number of water inrush accidents were induced by the instability of filling medium under hydraulic pressure in karst cavity during underground construction [11], as briefly shown in Figure 1. Moreover, quite a few were characterized with distinct hysteresis phenomenon due to the progressive seepage-erosion process [12], for which those theories mentioned above would lose reliability and rationality from the perspective of instability mechanism. In recent years, numerical methods and laboratory tests in consideration of particle loss were employed to explore the progress of water-sand inrush through granular soil. The nonlinear fluid-solid coupling model based on continuum medium mechanics were developed to depict the porosity evolution and expansion of seepage channels [13]. [PERSON] et al.