Consider a clay layer drained at the the top and bottom as shown in figure. For the case of constant initial excess pore water pressure (ui=u0) and Tv=0.4 ,determine the degree of consolidation Uz at z/Ht.For the solution, start from eq.(6.32). U_z = 1 - \sum_{{m=0}}^{\infty} \frac{2}{M} \sin\left(\frac{Mz}{H}\right) \exp(-M^2 T_u) \quad (6.32)This equation represents a mathematical expression involving an infinite series. The terms include trigonometric and exponential functions. Here, \(U_z\) is a function defined by the infinite summation from \(m = 0\) to infinity. The summand involves parameters \(M\), \(z\), \(H\), and \(T_u\). The sine function \(\sin\left(\frac{Mz}{H}\right)\) introduces an oscillatory behavior, while the exponential term \(\exp(-M^2 T_u)\) describes a decay dependent on \(M^2\) and \(T_u\). The image depicts a schematic diagram for a fluid flow scenario, labeled as "(a)". The diagram presents a rectangular flow domain with the following features:1. **Axes and Dimensions**: - The vertical axis is labeled as "z". - The vertical distance in the diagram is marked as \( H_t = 2H \). - The horizontal velocity of the fluid across the section is denoted by \( u_0 \).2. **Boundaries**: - Both the top and bottom boundaries of the rectangle are labeled "Pervious," indicating that they are permeable surfaces. - The presence of tiny dots near these boundaries suggests the movement or interaction of particles or fluid through these pervious surfaces.This diagram might represent a simplified model in fluid dynamics to study the behavior of fluid flow through permeable structures or media.

The degree of consolidation refers to the extent to which a soil has undergone settlement or compression due to the expulsion of water from its pore spaces. It is a critical concept in geotechnical engineering and soil mechanics , particularly when dealing with the design and analysis of foundations for structures.Double drainage condition is givenwe know- Tv= d= H ,For single drainage d= ,For double drainage (GIVEN)There are two conditionsIF u 2. IF uwhere u= degree of consolidationwe have to determine uFirst condition-0.4=So u=0.713 which is greater than 0.6so second condition appliedwhen u0.4= 1.7810.4+0.085 = 0.933 u=1.67%Degree of consolidation u=1.67%