Chapter 6 is an introduction to the importance and role of time in soil biogeochemistry. Time is one of the five major factors of soil formation, but many students are unfamiliar with the concept and terms of geological time, and with the concept and understanding of soil age. New developments in geomorphology and geochemistry in the last two decades have further added important insights into the concept and determination of age on hillslopes, which is also introduced here.

Chapter 10 focuses on what might be the most important reason for studying soil biogeochemistry: its importance for and interactions with us. First, the sheer magnitude of human disturbance of the soil mantle on Earth is introduced, especially the effect of farming. The impact of farming on soil C is examined in detail, and the effects of irrigated agriculture on soil geochemistry are used as an example of further comparisons that can be made by the reader. The uncertain and potential impact of our warming climate system on soil C, and potential feedbacks that might be ensuing, are considered. The recently renewed interest in accelerated soil erosion on managed landscapes is examined in light of new methods to measure the rates of erosion and also our emerging concepts and data on the true rate of soil production and regeneration.

Under certain conditions, a finite element may lose its ability to deform and become excessively stiff. This phenomenon is called "element locking." In this chapter we will consider three forms of locking, including transverse shear locking, membrane locking, and incompressibility locking. Approaches for alleviating or avoiding locking will also be described.

Truss structures are built up from individual slender-body members connected at common joints. The members are connected through hinge joints which are free to rotate and thus cannot transmit moment. Individual members carry only axial tensile or compressive force. In this chapter, the truss is comprised of uniaxial elements introduced in the previous chapter. However, in order to construct the global stiffness matrix of a truss structure in 3D space, it is necessary to construct the element stiffness matrices with 3 DOF at each node, corresponding to three displacement components in the Cartesian coordinate system. After developing the finite element formulation for 3D truss structures, the effects of thermal expansion and uniaxial members subject to torsional deformation are treated.

In this chapter, we consider time-dependent problems of discrete systems with N DOF. We will show how the finite element formulation is used to construct the element mass matrices, which are assembled into the global mass matrix. We will consider free vibration, to determine natural frequencies and natural modes of a finite element model through eigenvalue analysis, and numerical methods for integrating the equation of motion in time which can be used to determine dynamic response under applied loads and given initial conditions. The Lagrange equation will be shown to demonstrate how it can be applied to construct equations of motion. Once again we will consider slender bodies undergoing uniaxial vibration, torsional vibration, and bending vibration. A formal derivation of the Lagrange equation will be considered in a later chapter.