Nonlinear model of constant pressure expression is proposed for semi-solid materials and filter cakes. In this model the compressive pressure P_S is replaced by the special power-law pressure function $\theta ={\left(1+\frac{P_S}{P_a}\right)}^{1-n}$considering constitutive equation for the specific cake resistance $\alpha ={\alpha }_0{\left(1+\frac{P_S}{P_a}\right)}^n$, where ${\alpha }_0$, $P_a$ and n are the constants. The linearized form of obtained equation has analytical solution, which is similar to the solution of classical Terzaghi equation, but in terms of the proposed power-law pressure function$\theta$. Consequently, pressure profiles and local characteristics of compressed semi-solid materials can be better described. Constitutive relations for the compressibility modulus G and consolidation coefficient C are presented as power-law functions of the compressive pressure P_S and used for the approximative analytical and numerous solutions of the obtained nonlinear consolidation equation. Consolidation coefficient (filtration diffusivity) of highly compressible filter cakes can vary little with compressive pressure increase or even remain constant due to the concurrency between G and α, which are both rise with higher compressive pressure P_S.

Several examples of the application of proposed model are presented for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO₃, silica, activated sludge, water treatment (WT) plant residue). The profiles of local compressive pressure P_S and local cake characteristics (specific cake resistance$\alpha$ and solidosity ε_S) are simulated and compared for different filter cakes based on the analytical and numerical solutions of this model. The values of apparent consolidation coefficient C_a are simulated based on the adjustment of numerical and analytical solutions of the proposed model. These values can be used for better prediction of solid–liquid expression behavior.

提出了半固体物料和滤饼的恒压表达非线性模型。在该模型中，压缩压力P _S被特殊的幂律压力函数代替$\theta ={\left(\mathrm{1个}+\frac{P_{\mathrm{小号}}}{P_{\mathrm{一种}}}\right)}^{\mathrm{1个}--ñ}$考虑本构方程的比抗性 $\alpha ={\alpha }_0{\left(\mathrm{1个}+\frac{P_{\mathrm{小号}}}{P_{\mathrm{一种}}}\right)}^{ñ}$， 在哪里 ${\alpha }_0$， $P_{\mathrm{一种}}$和n是常数。所得方程的线性化形式具有解析解，该解析解与经典Terzaghi方程的解相似，但在拟议的幂律压力函数方面$\theta$。因此，可以更好地描述压缩半固体材料的压力分布和局部特征。可压缩模量G和固结系数C的本构关系作为压缩压力P _S的幂律函数表示，并用于获得的非线性固结方程的近似分析和众多解。高压缩性滤饼的固结系数（过滤扩散率）随压缩压力的增加而变化很小，甚至由于G和α之间的并发而保持恒定，而G和α的并发性都随着较高的压缩压力P _S而增加。

对于不同的中等和高度可压缩的滤饼（HK高岭土，CaCO ₃，二氧化硅，活性污泥，水处理（WT）植物残渣），提出了应用该模型的几个示例。本地压缩压力的轮廓P_小号和本地滤饼的特性（具体滤饼阻力$\alpha$和solidosityε_小号）被模拟和用于基于该模型的分析和数值解不同的滤饼进行比较。表观固结系数C _a的值是基于所提出模型的数值和解析解的调整而模拟的。这些值可用于更好地预测固液表达行为。