Consolidation Properties during Primary Compression
The topic of consolidation properties of a soil normally encompasses the discussions of hydraulic properties, void ratio-effective stress relationship, and compressibility of a soil. This is because the void size, pore channel, and mineralogy of a soil directly control the drainage characteristics of a soil stratum, which drives the time-dependent consolidation process used in conventional settlement or even strength-gained analysis. In this section, we will mostly focus on the generalized primary consolidation parameters of YBM along with time-rate relationship used in settlement analysis.
$$\ S = \frac{C_{c}}{1+e_{0}}H_{0}\left(\frac{C_{r}}{C_{c}}\log\frac{\sigma^{\prime}_{p}}{\sigma^{\prime}_{v0}}+\frac{\sigma^{\prime}_{vf}}{\sigma^{\prime}_{p}}\right)$$
The equation above describes the primary settlement based on vertical effective stress (i.e., excess pore water pressure, \(\Delta u = 0\)). In this equation, a few consolidation parameters that we need are: Cc = compression Index; Cr = recompression Index; \(H_{0}\)= initial thickness; \(e_{0}\) = initial void ratio; and \(\sigma^{\prime}_{p}/\sigma^{\prime}_{v0}\) = Overconsolidation Ratio (OCR). This equation is useful because Cr can be estimated from an empirical database for \(C_{r}/C_{c}\). The void ratio of soil stratum can be estimated using natural water content and Gs discussed earlier. Therefore, the important consolidation properties to be evaluated for settlement analysis are Cc and \(\sigma^{\prime}_{p}\), which are best determined from oedometer tests.
The ratio of \(C_{r}/C_{c}\) typically falls within the range of 0.02 to 0.20 with lower values corresponds to highly structured and bonded soft clay and silt deposit and higher values corresponds to fissured clays and shales (TPM, 1996). Other mentions of typical \(C_{r}/C_{c}\) values are between 0.05 and 0.10, with the lower values corresponding to lower plasticity and low OCR clays (Holtz and Kovacs, 1981). In many practical problems, the contribution of Cr to settlement is insignificant compared with that of Cc. This is especially true for YBM that we know is mostly normally- to slightly-overconsolidated. Unfortunately, there are not many mentions of reliable \(C_{r}/C_{c}\) in existing YBM literature. Nguyen (2007) reported \(C_{r}/C_{c}\) of 0.08 with considerably scattered data. By compiling data from three other studies, Bonaparte and Mitchell (1979) reported average Cr values of 0.12, 0.14, and 0.15 and average Cc values of 1.2, 1.52, 1.6 to 1.8 along the initial portion of the virgin compression curve, respectively. Based on these average values, the derived \(C_{r}/C_{c}\) ratios are 0.10, 0.10 and 0.08 to 0.09, respectively. As we can see, although the ratio falls within a narrow range, it is highly dependent on the interpretation of Cc values that will be discussed shortly. Despite that, for designing problems, it is reasonable to neglect recompression and assume virgin compression at an OCR=1; for backcalculation or verification problems, consideration for recompression must be paired with accurate determination of preconsolidation pressure, \(\sigma^{\prime}_{p}\) that is primarily derived from available laboratory or in-situ testing data.
The mineralogy and structure of soil directly determine the
natural water content and compression index of the soil. In salt-rich or marine
environment, the flocculation or aggregation of clay particles causes more void
spaces within the soil, allowing for higher water content to come at
equilibrium. This is the case for YBM, whose higher natural water content leads
to proportionally higher compressibility compared to low plasticity clays. When
there is presence of organic content, the compression index is also higher
given the higher water content. The empirical relationship between natural
water content and Cc is presented on Figure 1. Roughly speaking, the
relationship indicates that Cc increases at a rate of 15% per every 10% increase in the natural water content. For example, the Cc values
are at around 1.3 for YBM with \(w_{0}\) of 90% and about 1.5 for organic
YBM with \(w_{0}\) of 100%. Because Cc becomes non-linear at
higher consolidation pressure, the Cc values in the figure were
determined from the range of \(\sigma^{\prime}_{p}\) to \(2\sigma^{\prime}_{p}\) The use of natural water content to estimate compression index for YBM is
useful compared to other known relationships between Cc and Liquid
Limit due to the testing procedure described earlier. However, given the spread
of the data, Cc is still best obtained from oedometer tests
performed on high quality samples. As a note for determining \(\sigma^{\prime}_{p}\) or OCR, the author generally finds that Casagrande’s method works well.
