The stiffness analysis of an air-supported structure for an excavation pit primarily evaluates the membrane's ability to resist deformation under the influence of internal air pressure, external wind loads, self-weight, and other construction-related environmental loads. This assessment determines whether the structure can maintain its intended shape and stability as required by the design. Unlike traditional steel structures, these air-supported systems utilize flexible composite membrane materials for their enclosure. Since the membrane itself possesses negligible bending stiffness, its overall form and load-bearing capacity are maintained through a combination of in-plane tensile stiffness, pre-tension, and the pressure differential between the interior and exterior. Consequently, the membrane cannot be treated as a conventional rigid plate; instead, a mechanical model must be developed that accurately reflects the specific structural configuration. For air-supported (pneumatic) systems, the analysis must focus on the support provided by internal pressure, the relationship between membrane curvature and stress distribution, and membrane displacement induced by fluctuating wind loads. For air-ribbed or air-cushioned (pneumatic-cell) structures, it is also necessary to account for the local stiffness of individual inflatable units, the constraints at connection nodes, and the load-sharing behavior among these units. The deformation trends of the membrane under external loads are typically analyzed using parameters such as the material's elastic modulus, Poisson's ratio, thickness, and the structural pre-tension. The in-plane tensile stiffness is directly related to the material's elastic modulus and thickness, while the overall structural stiffness is influenced by factors including the span, surface geometry, boundary conditions, internal pressure, and anchorage methods. For large-span or complex air-supported structures, non-linear finite element analysis is generally required to evaluate stress, displacement, and stability under various load combinations, ensuring that the structure does not become unstable due to excessive local deformation, insufficient pre-tension, or pressure imbalances.
The fundamental parameters-including the structural configuration, geometric dimensions, mechanical properties of the membrane material, design internal pressure, and site-specific wind and snow loads-must be clearly defined. Based on these, a computational model is established, incorporating the boundary constraints at the membrane edges, anchorage nodes, and support points. For preliminary analysis under small-deformation conditions, structural stiffness can be understood through the relationship between load and displacement-specifically, as the ratio of a load increment to the corresponding displacement increment along a given direction of force. However, for flexible structures like air-supported membranes used in excavation pits-which exhibit significant geometric nonlinearity-the actual stiffness varies with deformation, pretension, and internal pressure; therefore, a fixed linear stiffness value cannot be used for a comprehensive assessment. Analysis should focus on key parameters such as maximum membrane displacement, principal stresses, localized stress concentrations, forces at anchorage connections, and the impact of internal pressure fluctuations on the structure's geometry. Furthermore, safety assessments must account for scenarios including extreme wind loads, pressure instability, and potential fan system failures. For projects analyzed using finite element software, it is essential to select appropriate membrane or structural elements, input accurate material constitutive parameters, and account for initial geometry, pretension, and large-deformation effects. Computational results should be validated against material test data, structural experiments, or field monitoring results to ensure the model accurately reflects the actual structural behavior. It should be noted that there is no universal stiffness value applicable to all air-supported membrane projects; rather, calculation methods and control criteria must be determined based on the specific structural configuration, design loads, membrane material properties, and relevant technical standards. Moreover, as stiffness analysis is only one component of the overall structural design, a comprehensive evaluation-encompassing strength, global stability, anchorage safety, and emergency air-supply reliability-is required to ensure the air-supported membrane system meets the practical operational requirements for excavation pit applications.