Here are examples of methods for predicting sand outflow depth. An empirical formula of Ioroi and Yamamoto [1] could reproduce the outflow rate with acceptable accuracy. There are a few numerical models, which were designed for a specific shape of a structure. Maeno et al. [2] and Kotani et al. [3] proposed a numerical model to simulate cyclic water pressure, which could calculate the cyclic pressure acting on a simple seawall. Another model is a model of Nakamura et al. [4]. This model was able to simulate the outflow rate from the lowest edge of a rubble revetment.
References
[1] Ioroi, M.; and Yamamoto, Y. (2013). “Formula for Evaluating Suction Rate of Backfilling Materials from a Coastal Dike by Big Waves,” Proceedings of the Twenty-Third International Offshore and Polar Engineering Conference, Anchorage, AK, USA, 30 June–5 July 2013; pp. 1210–1216.
[2] Maeno, S.; Kotani, Y.; Hoshiyama, C. Outflow limit of backfilling sand of revetment under cyclic loading of water pressure. Annu. J. Coast. Eng. Journal of Japan Society of Civil Engineers 2000, 47, pp. 926–930. (in Jpn)
[3] Kotani, Y., Yoshimura, C., Maeno, S., and Nago, H. (2002). “Flow Out of Back-Filling Sand Behind Sea Wall Under Cyclic Water Pressure Variation,” Journal of Japan Society of Civil Engineers 2002, 712, pp. 97–106, doi:10.2208/jscej.2002.712_97. (in Jpn.)
[4] Nakamura, T., Hur, D.S., Mizutani, N. (2006). “Suction Mechanism of Reclaimed Sand Behind a Rubble Seawall,” Journal of Japan Society of Civil Engineers Ser. B2 (Coastal Engineering) 2006, 62, pp. 150–162, doi:10.2208/jscejb.62.150. (in Jpn.)