A theoretical formulation of dilatation/contraction for continuum modelling of granular flows
A theoretical formulation of dilatation/contraction for continuum modelling of granular flows
复制标题
DOI：
10.1017/jfm.2021.249
复制
发表时间：
2021-04
影响因子：
3.7
通讯作者：
Huabin Shi;P. Dong;Xiping Yu;Yan Zhou
中科院分区：
文献类型：
--
作者：
Huabin Shi;P. Dong;Xiping Yu;Yan Zhou
长期以来，颗粒物质的剪胀/收缩一直被认为是颗粒流中的一个重要过程，但目前还没有一个广泛的剪切速率范围内对这一过程的全面的理论描述。本文提出了颗粒流连续介质模型中膨胀/收缩的理论公式，其中膨胀/收缩效应由颗粒间持久接触力链重排引起的摩擦分量和颗粒间碰撞引起的碰撞分量组成。在该公式中，摩擦胀缩采用考虑剪切变形下接触力链重排的摩擦固体压力，而碰撞粒间压力采用已有的流变定律来解释碰撞胀大效应。提出的公式首先通过在扭剪流变仪中描述颗粒样品的剪切弱化行为，并通过捕捉干燥和浸没的颗粒边坡的早期破坏来分析验证。然后将所提出的膨胀/收缩公式积分为双流体连续介质模型，并将该模型应用于研究水下颗粒柱体的坍塌过程，进一步验证了所提出的膨胀/收缩公式，其中膨胀/收缩起着关键作用。
Abstract Shear dilatation/contraction of granular materials has long been recognized as an important process in granular flows but a comprehensive theoretical description of this process for a wide range of shear rates is not yet available. In this paper, a theoretical formulation of dilatation/contraction is proposed for continuum modelling of granular flows, in which the dilatation/contraction effects consist of a frictional component, which results from the rearrangement of enduring-contact force chains among particles, and a collisional component, which arises from inter-grain collisions. In this formulation, a frictional solid pressure, which considers the rearrangement of contact force chains under shear deformation, is proposed for the frictional dilatation/contraction, while well-established rheological laws are adopted for the collisional inter-grain pressure to account for the collisional dilatancy effect. The proposed formulation is first verified analytically by describing the shear-weakening behaviour of granular samples in a torsional shear rheometer and by capturing the incipient failure of both dry and immersed granular slopes. The proposed dilatation/contraction formulation is then further validated numerically by integrating it into a two-fluid continuum model and applying the model to study the collapse of submerged granular columns, in which the dilatation/contraction plays a critical role.