## 1 Introduction  
Underhand drift-and-fill mining provides a suitable solution for the extraction of fractured and/or highly stressed ore bodies [1, 2]. The strong selective mining capabilities, high ore recovery rates, and minimal void exposure have led to its widespread application in underground metal mines [3]. In this method, the stope is mined layer by layer in a top-down sequence, and each layer is further divided into a series of parallel drifts. The primary drifts are excavated and filled with cemented backfill first, followed by the excavation of secondary drifts. Once all the ore in the layer has been replaced by the cemented backfill that is capable of providing a stable artificial roof for working underneath, the excavation can proceed to the next layer. This process is repeated until the entire ore body within the stope is excavated. Except for in the initial layer, personnel and equipment consistently operate under the constructed backfill roof [4, 5]. Therefore, the key to successful implementation of this method lies in the roof's stability. Given the typically used primary-and-secondary mining sequence, interfaces will form between the backfill in adjacent drifts [6]. Since the interface generally has a lower strength than the backfill matrix [7], the presence of these interfaces can significantly reduce the continuity and integrity of the backfill roof. To mitigate their potential negative impact, the traditional aligned drift layout is often adjusted to a staggered drift layout, or the basket weave drift layout [1; 2], as shown in Figure 1. In practice, the basket weave drift layout is extensively implemented in numerous mines, including the Jinchuan Nickel Mine [8], the Maoping Lead-Zinc Mine [9], and the Wushan Copper Mine [10]. Due to its widespread adoption, it is imperative to conduct an in-depth stability analysis for the backfill roof with the basket weave drift layout. The stability of a backfill roof is intrinsically related to its strength. A reasonable evaluation of the required strength for roof stability is an integral part of backfill design [11; 12; 13; 14]. To achieve this, analytical methods and numerical simulation are commonly employed. Analytical methods generally model the roof as a beam or plate and utilize elasticity theory to calculate the stress components and derive the strength requirement of the backfill roof. Although analytical methods can rapidly evaluate the strength requirement, their underlying assumptions often limit their applicability. In the basket weave drift layout, the drift driving directions in the adjacent layers are alternating and perpendicular to each other, and the displacement distribution of the backfill roof will differ from those in cases with consistent driving directions, such as aligned or staggered drift layout. In such scenarios, the beam or plate models in analytical methods may fail to accurately capture the actual loading conditions of the backfill roof. Although some numerical simulations have been conducted to study roof stability, they have typically assessed stability based on stress or plastic zone distributions, resulting in highly subjective analysis outcomes [15; 16; 17]. There  
Figure 1: Drift layout commonly adopted in underhand drift-and-fill mining method: (**a**) aligned drift layout, (**b**) staggered drift layout, and (**c**) basket weave drift layout. is currently limited research on the displacement distribution and strength requirement analysis of backfill roofs with the basket weave drift layout. This paper introduces an iterative search method for assessing the strength requirement of the backfill roof in numerical simulations. This method can effectively eliminate the subjectivity in traditional roof stability analysis. The method is applied to determine the strength requirements of the backfill roof with the basket weave drift layout in the Maoping Lead-Zinc Mine. A comparison was also made between strength requirements obtained from the numerical simulation and those predicted by traditional analytical solutions.