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Critical state soil mechanics is a framework used to describe the behavior of soil under shearing conditions. It posits that soil behavior can be predicted based on critical state lines in stress space. Factors are void ratio, soil composition, and confining pressure.

Resilient modulus ($M_R$) is a measure of soil's elastic response under repeated loading, such as traffic loads. It's important for pavement design and depends on factors like soil type, moisture content, and the magnitude of the applied load.

Dynamic soil properties include parameters such as shear modulus and damping ratio, which define the soil's response to dynamic loading. Influencing factors are soil type, void ratio, effective stress, and strain amplitude.

Seismic site response analysis is the evaluation of soil response to earthquake ground motion. The analysis can predict amplification of seismic waves and site-specific ground motion. Influencing factors include soil stratigraphy, bedrock depth, and seismic wave characteristics.

Atterberg limits are a basic measure of the critical water contents of fine-grained soils. These limits define the boundaries between different soil states: liquid, plastic, and solid. The limits are influenced by mineral composition, temperature, and organic content.

Liquefaction potential refers to the likelihood that a saturated soil will lose strength and stiffness under an applied stress, often due to earthquake shaking, causing it to behave like a liquid. Factors affecting liquefaction include soil composition, level of saturation, confining pressure, and seismic intensity.

Soil amplification is the increase in seismic wave amplitude as waves move from bedrock to softer soil layers. Factors that affect it include soil type, depth to bedrock, and the frequency of the incoming seismic waves.

Shear wave velocity is the speed at which a shear wave travels through a medium, and it's used to gauge the stiffness of that medium, in this case, soil. Higher Vs indicates stiffer soil. It's affected by soil density, elasticity, and confining pressure.