Environmental Public Goods

Chapter 8 considers the conservation of environmental public goods. The nonexclusive and nonrival nature of public goods provide an incentive to free-ride on the efforts of others. The result is that such public goods are systematically undervalued and the underlying environmental assets—such as watersheds, habitats, and ecological communities—are underconserved. It shows how individuals determine their contribution to public goods (via a Nash-Cournot reaction curve), and compares the result to the contribution that would be made if resources were being allocated efficiently from the perspective of society. Types of environmental public goods considered include additive (climate change), best- and better-shot (defence), weakest- and weaker-link (infectious disease control), and local public goods (common pool resources). The chapter also shows how strategic behavior by the beneficiaries of public goods may lead to socially undesirable outcomes (such as prisoner’s dilemmas).

Analysis of Support Reaction Curves considering Time-Varying Effect of Shotcrete

The core content of the convergence constraint method is to determine the reasonable support time and support stiffness. The stiffness of shotcrete in supporting structure is dynamic. The support stiffness of shotcrete is roughly calculated in engineering, which results in a waste of materials and increases the risk of construction. Therefore, in this study, considering the time-varying characteristics of shotcrete, combined with the elastic-plastic theory and the space effect of excavation surface, the calculation equation describing the support reaction curve is given. An example is given to show that the stiffness of shotcrete considering time-varying effect is lower than that of shotcrete without time-varying effect, and the difference is the most obvious in the age of 0–3 days. However, in the later stage, the stiffness growth rate of shotcrete considering time-varying effect is higher than that of shotcrete without time-varying effect. This study can predict the whole process of the support reaction curve, which can make the application of the convergence constraint method in tunnel support design more accurate, and provide a theoretical basis for the design of supporting structure in the process of tunnel construction.

Numerical Verification of the Concentric Arches Model for Geosynthetic-Reinforced Pile-Supported Embankments: Applicability and Limitations

In this study, a series of 3D FE simulations of a geosynthetic-reinforced pile-supported embankment (GRPE) design were conducted. The effect of the subsoil stiffness, friction and dilation angles of the fill, the fill height, the pile spacing, the surcharge load on the embankment, and the anisotropic tensile stiffness of the GR, the ground reaction curve (GRC), and the interfacial responses between the fill material and geosynthetic reinforcement (GR) were scrutinized. The numerical results showed how transfer of the vertical load towards the piles (load part A) and the related soil arches change with the subsoil stiffness, geometric parameters, and the vertical pressure on the embankment. Furthermore, the vertical load transferred through the GR (load part B) is reduced significantly with increasing subsoil stiffness, while the load part carried by the subsoil increases (load part C). The numerical results showed that the vertical stress distribution on the GR changes from an inverse-triangular shape for low subsoil stiffness to a uniform shape for high subsoil stiffness. This matches perfectly with the Concentric Arches model. For low subsoil stiffness, the tensile strains of the GR are concentrated at the corner of a square pile cap.

Time influence of tunnel support on the factor of safety

Before taking any measures to build a tunnel, the rock (soil) is in a primary stress state, which means that the stress state is a function of the thickness of the overburden. At the moment when the measures necessary to excavate a tunnel are taken, the rock state changes from primary to secondary, leading to stress concentration, especially in the tunnel abutments. If the rock is capable of accepting these stresses, a state of equilibrium is reached after certain deformations. Plastic deformations can occur if the stresses are larger than the strength of the rock mass. To avoid excessive deformations or collapse of the rock and the tunnel excavation, it is necessary to place a support. The achieved factor of safety is a function of both the support type and the time when the support is installed. This paper shall present a numerical example of different pressures considered in order to obtain the rock’s reaction curve.

Research on Influence of Road Tunnels with Different Lanes on Surrounding Rock Characteristic Curve

Convergence confinement method is an important guidance method for tunnel construction and support design. Numerical simulation method was used to comparatively analyze the ground reaction curve and the plastic zone under different rock grade and roadway tunnel size. The results show that the change of tunnel size has different effects on the maximum deformation of the tunnel arch crown, the ground reaction curve and the plastic zone range. Finally, some suggestions were put forward for the construction and optimization of the large span arch tunnel support structure. The research results may provide some guidance for related engineering