Key Takeaways & Executive Findings
- •• A novel analytical model integrates strain-softening behavior and intermediate principal stress to predict ground reaction curves for reinforced tunnels, overcoming limitations of existing models. • Existing models overestimate reinforcement effects; deformation prediction errors can exceed 75% when using single geological material models. • Neglecting softening and residual zones in natural regions leads to errors over 50%, highlighting the need for accurate constitutive modeling. • Incorporating intermediate principal stress reduces tunnel deformation by at least 30%, offering significant cost savings in reinforcement and support.
Abstract
Ground reinforcement is crucial for tunnel construction, especially in soft rock tunnels. Existing analytical models are inadequate for predicting the ground reaction curves (GRCs) for reinforced tunnels in strain-softening (SS) rock masses. This study proposes a novel analytical model to determine the GRCs of SS rock masses, incorporating ground reinforcement and intermediate principal stress (IPS). The SS constitutive model captures the progressive post-peak failure, while the elastic-brittle model simulates reinforced rock masses. Nine combined states are innovatively investigated to analyze plastic zone development in natural and reinforced regions. Each region is analyzed separately, and coupled through boundary conditions at interface. Comparison with three types of existing models indicates that these models overestimate reinforcement effects. The deformation prediction errors of single geological material models may exceed 75%. Furthermore, neglecting softening and residual zones in natural regions could lead to errors over 50%. Considering the IPS can effectively utilize the rock strength to reduce tunnel deformation by at least 30%, thereby saving on reinforcement and support costs. The computational results show a satisfactory agreement with the monitoring data from a model test and two tunnel projects. The proposed model may offer valuable insights into the design and construction of reinforced tunnel engineering.
1. Introduction
With continuous advancements in underground engineering, the New Austrian Tunnelling Method (NATM) is gaining increased adoption. The NATM emphasizes the self-supporting capability of rock masses and the spatial constraints imposed by the tunnel face [1]. This theory can be effectively demonstrated through the convergence confinement method, a framework that comprises three essential components: The longitudinal deformation profile (LDP), support characteristic curve (SCC), and ground reaction curve (GRC). Together, these components provide a comprehensive assessment of tunnel responses induced by excavation and facilitate the selection of appropriate support measures [2−5].
Ground reinforcement techniques, such as curtain grouting, jet-grouting umbrella, and grouted anchors, have gained increasing attention in tunnel engineering projects due to their significant contributions to controlling rock mass deformation [6], as illustrated in Figure 1. The reinforcement enhances strength and stiffness of rock masses, thereby altering the GRCs and influencing the selection of subsequent support measures.
Extensive research has been conducted on the effects of ground reinforcement through various methodologies, including numerical simulations [7, 8], in-situ monitoring [9, 10], and laboratory tests [11, 12]. While these investigations have provided valuable insights into the aspects of reinforcement, their applicability often remains constrained by specific conditions, and the processes for data acquisition and computational analysis are time-consuming. Considering these challenges, analytical approaches are increasingly favored by researchers for their cost-effectiveness and flexibility [13−17], which facilitate convenient parameter analysis, rapid assessment of reinforcement effects, and optimization of reinforcement schemes.
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CHEN Xuan-hao, ZHANG Ding-li, SUN Zhen-yu, CHEN Wen-bo (2025). Ground reaction curves for strain-softening rock masses with ground reinforcement based on unified strength criterion. Journal of Central South University. https://doi.org/10.1007/s11771-025-6067-3
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Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a novel analytical model for predicting ground reaction curves in strain-softening rock masses with ground reinforcement, incorporating the intermediate principal stress. It provides more accurate predictions than existing models and highlights the importance of considering softening and residual zones.
Why are existing models inadequate for reinforced tunnels in strain-softening rock?
Existing models often use elastic-perfectly plastic or elastic-brittle constitutive models, which do not capture the progressive post-peak failure behavior of strain-softening rock. This leads to overestimation of reinforcement effects and significant errors in deformation prediction, sometimes exceeding 75%.
How does the intermediate principal stress affect tunnel deformation?
Considering the intermediate principal stress can effectively utilize the rock strength, reducing tunnel deformation by at least 30%. This can lead to cost savings in reinforcement and support measures.
What are the practical implications of this research?
The proposed model offers valuable insights for the design and construction of reinforced tunnels, enabling more accurate prediction of ground response and optimization of support systems, particularly in soft rock conditions.
How was the model validated?
The computational results were compared with monitoring data from a model test and two tunnel projects, showing satisfactory agreement, which confirms the model's reliability.
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