Modelling the lateral behavior of trunk-root-soil systems with representative branching patterns using a combined p-y framework

The Beam-on-Non-linear-Winkler-foundation (BNWF) model using p - y formulation is widely used on laterally loaded structures (e.g., piles) due to its computational efficiency. However, its applicability to branched structural systems (e.g., trunk-root-soil systems) remains highly uncertain given their intricate branching geometries and proclivity for substantial deflections, which contrast with conventional pile structures. This work tries to address this issue through developing a combined p - y framework. Initially, physical model tests were conducted using four 3D-printed representative branched root architectures—tap, herringbone, dichotomous, and T-shape patterns—under dry and saturated sand conditions, thereby providing a comprehensive dataset for numerical model development. Subsequently, the p - y framework was established by considering the large deflection response of parent roots and the push-in/uplift behavior of branch roots during tree overturning. For modeling large deflection response, two types of p - y formulations were critically evaluated: the commonly used Reese p - y curve within previous studies and the hyperbolic p - y curve. For push-in/uplift behavior, the deep flow mechanism and a bilinear softening trend were considered, respectively. The proposed p-y framework was integrated into an efficient hybrid beam-FE model to predict the lateral response of the trunk-root-soil systems. Model validation demonstrated that the Reese p - y curve inadequately captures large deflection responses due to its inherent assumptions. Conversely, the hyperbolic p - y curve effectively predicts lateral resistance and root behavior in branched root systems. Compared to other analytical models, the proposed model enhances the capability to predict the overturning behavior of tree structures and enables the modeling of complex 3D root system geometries and root material variability, offering a potentially effective method for evaluating tree stability in practical applications.