• Proposes a novel analytical model combining a multi-layer parabolic soil arch and a lower friction arch to predict vertical earth pressure on deep rectangular pipe jacking tunnels.
• Explicitly incorporates tunnelling-induced ground loss distribution, enabling more realistic assessment of soil arching effects.
• Derives closed-form solutions for key arch parameters (B, H1, lateral pressure coefficient Kl) based on principal stress rotation characteristics.
• Validates predictions against experimental and numerical results and quantifies parameter sensitivities, facilitating reliable jacking force estimation and lining safety design.