'Memory stress' : physical and mathematical modelling of the influence of water-working on sediment entrainment and transport

Recent research has indicated that variability of antecedent flows is a fundamental control on the entrainment and transport of sediment in river systems. Specifically, the low flows between successive floods appear to have a far greater influence on the stability of a river bed than previously assumed. Increased durations of low flows increase sand-gravel bed stability so as to delay entrainment and significantly reduce transport. Although a degree of quantification of “memory stress” effects has been attempted by previous researchers, their applied methodology precludes development of appropriate mathematical relationships implicit to correcting existing sediment transport equations. The overall aim of this thesis is therefore to address this deficiency via robust physical and mathematical modelling. In total, 84 flume experiments were carried out in a flume. Two poorly sorted (g ≥1.6) sand-gravel mixtures of unimodal and bimodal distribution were compared and contrasted for sensitivity of modality to memory effects upon bedload and entrainment threshold. Five memory timescales (10, 30, 60, 120 and 240 minutes) were tested and contrasted with baseline data obtained for runs performed without any memory. Experiments employed a stepped discharge hydrograph covering sub-threshold to fully mobile conditions. A reference transport based approach was employed to determine entrainment threshold, and to develop mathematical descriptors of memory effects. Results show that increasing memory timescales up to 240 minutes increases entrainment thresholds ( ) by up to 49% whilst subsequent transport decreases by up to 97%. The memory effect prevails non-linearly for the range of low flows of non-dimensional transport between 10-6 to 10-1. Using these flume data, novel mathematical functions for bedload are developed to account for the influence of memory timescales. Here, memory is described via rising exponents of the function to quantify degree of non-linearity of transport to shear stress, and changes in the structure of the bed due to memory are represented within a lumped coefficient. Trends in the suite of exponents and coefficients indicate that changes in bed structure are of greater importance than the shift in non-linearity of bedload. Hence, the first framework for correcting existing graded sediment formulae for memory stress has been effectively developed using a scaling of the granular scale roughness parameter, An. Predicted results are calibrated and validated against available memory stress datasets from both field and laboratory based studies. Results show that without memory correction, over 80% of estimates fail to predict measured bedload effectively; once An based correction is applied, 100% of data are predicted effectively.