**1. Introduction**

The underground plant of a hydropower station is a large, complex underground building structure, and its stability is affected by factors such as geological structure, carven span, in situ stress, and support strength [1]. As underground plants are located in different stress environments, the lithology and strength of the surrounding rock are different, and the strength of the support to maintain the stability of the surrounding rock varies. Insufficient support strength can lead to local instability, collapse, excessive deformation of the surrounding rock, or even integral damage,

while too much support strength can lead to unnecessary waste. Due to the complexity of the surrounding rock, scholars are still unable to fully grasp the deformation characteristics and reinforcement mechanism of the surrounding rock under complex stress conditions, which makes the theory and specification of surrounding rock reinforcement immature, and the support of underground plants still mainly relies on experience for design and construction. At present, the support design of underground plants is commonly based on the engineering analogy method, and there is insufficient knowledge of the deformation characteristics of the surrounding rock in high in situ stress areas. Because of the lack of relevant design experience, it is not sufficient to fully guide the design of the cavern support. The empirical method sometimes leads to safety problems due to inadequate design support strength or waste of resources due to over-support.

On the other hand, many successful examples of underground plants provide valuable data for the design of rock support. Through these data, the reinforcement measures and strength of the surrounding rock can be summarized, and the inherent laws of rock support and a new support design method can be proposed. For underground plants, the commonly used method is the system anchor and anchor cable support method, which can give good play to the strength and its own bearing capacity of the surrounding rock [2]. Through studying research papers and design data, a systematic summarization of sidewall support schemes for 29 underground plants with a span range of 18.0–34.0 m and a strength-stress ratio range of 2.0–14.55 was carried out, and the regression fitting relationships between the strength of the system anchor bolts and cables and the strength-stress ratio of the surrounding rock and the plant span were proposed. Based on the regression fitting relationship, an underground plant support strength index was defined, which can quantitatively evaluate whether the surrounding rock support is reasonable.

Neural network theory is recognized as a method for solving nonlinear problems, and it has been applied in rock mechanics parameter identification and stress analysis, parameter prediction, rock stability, rock deformation prediction, and rock engineering inverse analysis [3, 4]. One of the most popularly used neural network models is BP (back propagation) neural networks, which are multilayer feed-forward neural networks that are widely used in nonlinear modeling, function approximation, logic classification, etc. On this basis, an intelligent design model for the anchor support of the underground powerhouse is proposed based on a BP neural network. The model optimized the design of the system anchor diameter and spacing by inputting the plant span and strength-stress ratio. The different degrees of influence of the plant span and strength-stress ratio on the system anchor support scheme were analyzed according to the weights between the neurons.

#### **1.1 Underground plant and rock surrounds support**

#### *1.1.1 Underground plant*

According to incomplete statistics, more than 600 underground hydropower plants have been built worldwide, including more than 200 in Norway, which is the largest number of underground hydropower plants, and there are two underground power plants with an installed capacity of more than 1000 MW. As of 2015,
