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Calcareous sand is widely used as fill material in island construction projects in the South China Sea. The mechanical properties of the interface between calcareous sand and geogrid under high temperatures and complex environmental conditions play a critical role in the long-term stability of such structures. In this study, interfacial pullout tests between calcareous sand and a geogrid are conducted under six temperature conditions (−5 °C, 0 °C, 20 °C, 40 °C, 60 °C, and 80 °C) and various normal stress levels. A database containing 1178 data sets is established from these tests. Based on the test data, four predictive models are developed: support vector machine (SVM), particle swarm optimization SVM (PSO-SVM), genetic algorithm optimization SVM (GA-SVM), and a deep learning long short-term memory network (LSTM). The results indicate that the LSTM model provides significantly higher predictive accuracy and robustness compared to traditional machine learning models, achieving an R2 value of 0.97 on both training and testing datasets and superior performance in RMSE, MAPE, MAE, and MSE. Sensitivity analysis using SHAP values shows that shear displacement has the greatest influence on shear strength, followed by temperature, normal stress, and particle size. Furthermore, based on the LSTM model predictions, an empirical formula for shear strength is proposed, enabling engineers without expertise in deep learning to estimate the shear strength of calcareous sand–geogrid interfaces effectively.