## 1 Introduction  
Gas extraction is an essential technical approach for ensuring coal mine safety [1; 2]. Conventional gas extraction drilling in broken and soft coal seam faces challenges [3; 4; 5; 6; 7; 8; 9]. Moreover, due to the low gas concentration, the extracted gas does not meet industrial standards for development and utilization, resulting in direct atmospheric emissions and environmental pollution. The gas extraction volume in Chinese coal mines in 2020 reached 12.8 billion cubic meters, with a utilization rate of only 44.8% [10; 11]. The average gas extraction concentration value in Panvie coal mine was 25.73%, which did not meet the lower limit of 30% for gas utilization concentration. The horizontal wells within the roof are an effective method to develop gas in broken and soft coal seams, and layer-penetrating fracturing is a key engineering method in the stimulating of horizontal wells within the roof of a coal seam [12; 13; 14; 15]. For broken and soft coal seams, both domestic and international studies have been conducted on the theory of layer fracturing in horizontal wells within the roof using methods such as physical simulation or numerical simulation. [PERSON] [16; 17; 18] and others utilized theoretical analysis and numerical simulation methods to study fragmented and low-permeability coal seams in the Huainan region of China. They compared the propagation characteristics of fractures under different stress states and concluded that the in situ stress is a key controlling factor for fracture propagation across layers. [PERSON] [19; 20; 21; 22; 23] and others found that under conditions of reasonable construction displacement and horizontal well spacing, fractures can extend from the high-stress roof into the low-stress coal seam. The effectively supported fractures formed in the roof can provide pathways for coalbed gas to enter the wellbore. Additionally, they observed that larger injection volumes of fracturing fluid led to greater depths of fracture propagation across interfaces, and during fracture propagation across layers, the height and length of fractures within the roof were greater than those within the coal seam. They conducted physical simulation experiments on layer fracturing in horizontal wells and studied the expansion laws of fractures and the sensitivity factors of layer fracturing effects. The results indicated that the horizontal well position, injection volume, perforation method, and vertical-horizontal stress differential are four important factors influencing the morphology of fractures during layer fracturing in horizontal wells. Previous studies often assumed that the roof of the coal seam is a single rock layer, and models were constructed in the form of \"roof-coal seam\". However, based on underground exposure and analysis of surface drilling cores, it is commonly observed that coal seams are not directly in contact with the immediate roof; instead, there is typically a layer of carbonaceous mudstone pseudo roof, forming a composite roof of the coal seam. Therefore, hydraulic fracturing must consider the influence of the mudstone pseudo roof on fracture propagation. The article was based on the combined rock mechanics characteristics of actual fractured and soft coal seams and overlying strata. It employed numerical simulation and physical similarity modeling methods to study the interlayer characteristics of hydraulic fracturing fractures in composite roof strata. The research was validated by using Panxie coal mine in Huainan Mining Area and Luling coal mine in Huaibei Mining Area as examples, providing a basis for the construction of horizontal well hydraulic fracturing in fractured and soft coal seam roofs.