Page 72 - 2025年第56卷第8期

Research on local scour depth of tower foundation in sediment-laden
rivers based on stochastic process

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CAO Shuai ，LIU Lei ，ZHANG Hongwu ，ZHANG Qian

s

（1. People’ Government of Dongshiduan Town，Xushui District，Baoding 072550，China；

2. Ministry of Water Resources，Beijing 100053，China；

3. Yellow River Research Center，Tsinghua University，Beijing 101309，China；

4. Baoding Shangquan Municipal Engineering Co.，Ltd.，Baoding 071051，China）

Abstract：The problem considered in this study is the local scour depth of transmission tower foundations，for which

there is not yet unified calculation method in the sediment-laden rivers. Due to these problems，they are usually cal‐
culated by the formula of bridge pier scour at present，which lead to significant deviations with the actual results，

especially in sediment-laden river like the Yellow River. In order to reduce the potential natural hazards caused by
inaccurate calculations，this study has established a theoretical formula for the local scour depth of tower foundation

based on the fundamentals of stochastic process. As the forces acting on the sediment particle are uncertain during the

process of scouring around the tower foundation，the motion of each particle in the scour pit is also random，thus
forming a stochastic sediment motion field within the scour influence range. According to the sediment transport

theory，there are specific transport laws for both bed-load and suspended-load on the riverbed near the tower founda‐
tion. These laws provide the theoretical basis for determining the probability density of positional state transition
based on Markov random field and the statistical theory of sediment movement. The scour pattern of the tower founda‐

tion，positional state model，and transfer-probability are discussed，and then the analytical formula for local scour

depth is obtained by deriving the average dynamical equations of positional state. Meanwhile，by analyzing the physi‐

cal mechanism of transition probability density，this study has determined the expression structures for the probabil‐
ity density functions of time-averaged positional state transition. In light of the measured statistical data from natural
sediment-laden rivers and physical modeling experiments，the relevant parameters in the calculation formula for local

scour depth of tower foundation have been preliminarily determined. Finally，two sets of tower foundation scour model

tests can be used as evidence to verify the proposed analytical formula for local scour depth，and the result indicates
that the calculated values are consistent with the actual measurements.

Keywords：stochastic process；sediment-laden river；tower foundation；local scour depth；physical modeling
experiment
（责任编辑：鲁 婧 韩 昆）

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