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A Brief Review of SF's Young Bay Mud: Part II

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: C_c = compression Index; C_r = 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 C_r 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 C_c 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 C_r to settlement is insignificant compared with that of C_c. 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 C_r values of 0.12, 0.14, and 0.15 and average C_c 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 C_c 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.

Figure 1. Empirical correlation between in-situ water content and compression index for Young Bay Mud

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 C_c is presented on Figure 1. Roughly speaking, the relationship indicates that C_c increases at a rate of 15% per every 10% increase in the natural water content. For example, the C_c 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 C_c becomes non-linear at higher consolidation pressure, the C_c 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 C_c and Liquid Limit due to the testing procedure described earlier. However, given the spread of the data, C_c 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.

See Next: Time-Rate of Consolidation

A Brief Review of SF's Young Bay Mud: Part I

Coming from the Upper Midwest to the San Francisco Bay Area, I get to deal with the Bay Mud, which resembles the soft and compressible characteristics of many of the Great Lakes clays except that its deposition is different. This technical note summarizes the findings from my humble effort in the literature review of available articles, a compilation of existing data, and correspondences with several friends and experts in the subject matter, to partially fulfil my personal curiosity and also for my work.

Introduction

The Young Bay Mud (YBM) is a marine-deposited clay commonly found along the margins of the bay, between modern shorelines and the historical limit of tidal marsh. The YBM is composed of alluvial gray silty clay, with thin layers of silt and fine to medium-grained, sands, small amounts of organic material, and shell fragments. Within developed areas and city limits, the YBM is generally buried under artificial fill; therefore, YBM is typically normally consolidated or slightly overconsolidated, i.e., OCR of between 1 and 3 (Bonaparte and Mitchell, 1979; Benoit and Clough, 1986; Koutsoftas et al., 2017). Where it is exposed at the surface, it can be desiccated and stiff, and its OCR can be higher. There are mainly two types of YBM commonly encountered in the San Francisco Bay Area (Johnson and Bartow, 2019). The first type is very soft to soft clay with organic content (CH, OH). This type of soft bay mud is generally characterized by higher plasticity, higher moisture content, lower density, and low shear strength. The second type is more notable in its granular composition: sandy/silty clay (CL, SC) and silty sand (SM). This type of mud deposit primarily consists of soft to medium sandy clay or medium dense silty sand, having lower plasticity, lower moisture content, higher density, and higher shear strength. This document provides a brief review of the engineering properties, primarily the indices and consolidation properties of the first type of YBM, as it is more geotechnically concerning and applicable to the type of work discussed herein.

Index Properties

The engineering properties of YBM vary across the Bay Area. Table 1 presents a compilation of several index properties of Bay Mud from limited existing literature and author's projects.

Liquid Limit

All data points, except the samples from the Bridge Oakland Mole and Yerba Buena Cove, have Liquid Limits ($w_{l}$) of greater than 50% that indicates a high-plasticity or high-compressibility soil. If plotted on the plasticity chart, many of these data points also fall slightly above the A-line, which is a characteristic of many marine clays. If there is a presence of organic matter, the data points are located in the region below the A-line, e.g., plasticity index of 45% and Liquid Limit of 90% in Benoit and Clough (1986). The Liquid Limit represents the mineralogy of a soil, and often time, and can be empirically correlated to strength and other properties of a soil (TPM, 1996). Soil with higher Liquid Limit or its natural water content ($w_{0}$) closer to Liquid Limit tends to behave as a vicious fluid when sheared. In other words, a soil with higher Liquid Limit is highly sensitive like those of Scandinavian marine clays.

A useful ratio to indicate sensitivity of soil is Liquidity Index (LI), defined as $(w_{0}-w_{p})/(w_{l}-w_{p})$. If LI is greater than 1, remolding transforms the soil into a thick slurry (highly sensitive); If LI is between 0 and 1, the soil behaves like plastic; if LI is negative, the soil cannot be remolded or will have brittle fracture when sheared. Bonaparte and Mitchell (1979) reported that LI for YBM is slightly above 1, which as described earlier, is a sensitive clay. Based on several other studies, Bonaparte and Mitchell (1979) summarized that typical values of YBM are: Liquid Limit at ±88% and natural water content slightly higher at about ±90%. However, because water content in most soils falls between its Plastic and Liquid Limits in its natural state, the author would like to caution the use of such “typical” values, especially the Liquid Limit, including those listed in Table 1 where the upper limits of $w_{0}$ exceed the upper limits of Liquid Limit. Recall that the first type of YBM contains some amount of organic matter. When the soil sample is prepared in accordance with the ASTM standard, air- or oven-drying causes irreversible dehydration of organic matter, reducing the Liquid Limit (TPM, 1996; Holtz and Kovacs, 1981). Therefore, the reported “typical” Liquid Limit value of ±88%, if prepared per the ASTM standard, is likely underestimated, and it is very likely that Liquid Limit is slightly above the natural water content. Often, the laboratory Atterberg Limits results are used to correct the classifications as observed in the field (e.g., CH vs. CL), while preparing boring logs. If in doubt of laboratory results, the engineer or geologist should check with the laboratory standard procedure and refer to the descriptive color (dark brown, dark gray, or black) of the retrieved samples for indications of organic materials.

Specific Gravity and Unit Weight

Two other useful properties are specific gravity ($G_{s}$) and total unit weight. When evaluating consolidation test results or performing settlement analysis, specific gravity is needed to compute the void ratio. Bonaparte and Mitchell (1979) summarized that specific gravity of YBM is in the range of 2.69 to 2.73, with a mean value of 2.71. The specific gravity of a soil varies based on soil constituents, e.g., organic soil has a lower $G_{s}$ value. Denby (1978) reported specific gravities ranging from 2.52 at a depth of 5 feet to 2.65 at 50 feet; and 2.75 below 75 feet from samples obtained in Hamilton. Therefore, it is reasonable to use a lower $G_{s}$ value for those YBM with organic materials at shallow depths. Based on the typical $w_{0}$ of 90% and a $G_{s}$ of 2.7, the initial void ratio ($e_{0}$) is roughly 2.4 for YBM without organic content, or higher void ratio for YBM with organic content. This assumes that soil stratum is fully saturated, i.e., $e_{0}=w_{0}G_{s}$. It has been reported that the total unit weight of YBM is fairly constant with depth. At the Hamilton Air Force Base, Benoit and Clough (1986) reported a unit weight of 100 pcf in the upper 6½ feet and 94 pcf below that. Note that near-surface desiccation can cause denser soil state and organic soil tends to lower the total unit weight to around 90 pcf. For general engineering calculations, the author uses a total unit weight of 95 pcf for YBM, unless organic content is noticeable, then a lower total unit weight such as 90 pcf is used.

Drawing from the discussions above, readers can easily conclude that YBM is a highly sensitive and highly compressible clay. The sensitivity component is more prominent in stress or strength analysis, while compressibility is more noteworthy in seepage, consolidation, or settlement analysis. In soft ground engineering, it is always preferred to muck-excavate soft and compressible soil like YBM, and backfill with sand or engineered fill if it is practical and feasible to do so (also from the environmental standpoint). If a geotechnical engineer must deal with YBM, either ground improvement or deep foundations will be needed. It is important to note that the majority studies of the YBM’s engineering properties were originated from the Hamilton Air Force Base, and by now, the readers should know that engineering properties of YBM vary across the Bay Area. As a result, the author urges reader to exercise engineering judgement and perform supplemental laboratory or in-situ testing to confirm properties in question.

See Next: Consolidation Properties

Book Review: Globalization Paradox

I enjoyed this book although I admit that global trade and world economy are way out of my depth. Rodrik presents economic globalization as a trilemma. As the saying goes, "winners write the history." The post-war world economy system was penciled by policymakers and economists, laying a path for their own (in their self-interest) and the underrepresented nations. Rodrik presents economic globalization as a trilemma. That is, we cannot pursue democracy, national sovereignty, and globalization all at once. Pick two. There is no one-size-fits-all solution. A "thin" layer of international rules that leaves room for nations is better globalization.

Summary

Different societies have different needs and preferences in shaping their institutions, democratic pressures are likely to lead to a variety of different institutions across different territories. This diversity inhibits the global integration of markets by raising transaction costs across jurisdictions. As a consequence, a world which is fully responsive to democratic preferences will be unable to achieve full globalization. A "thin" layer of international rules that leaves rooms for nations is a better globalization.

Two takeaways from the book:

Market and government are complement to each other, they do not substitute each other. As contrary to the popular belief to free market, market are most efficient and developed when they are blended with governmental institutions. Long distance market exchange does not exist without rules. In today's globalization world, government provides legal framework to conduct international trade. Therefore, governmental bodies are largest in those economies most exposed to international markets.
Capitalism does not come with a unique model. Economic stability and prosperity can be achieved through combinations of institutional arrangements in labor markets, finance, corporate governance, social welfare, and other areas.

Who should read the book:

Those interested in globalization and free market.

* * *

Unlike the last two books, this book is very much thought-provoking. Of particular interest to me, is how Rodrik describes the phenomenal rises of Pacific and Southeast Asian economies, including South Korea, Taiwan, Hong Kong, Singapore, Malaysia, Indonesia, and Thailand, since the early 1960s. Citing the examples from South Korea and Taiwan, the two of the "East Asian Tigers" adopted strategies to reduce frictions between government interventions and private investment and grant tax holidays to foreign investors, fueling the private sector. Corruptions, poor infrastructure, and high inflation are greatly emphasized. The goal was to create new, modern industries by diversifying the domestic market and less reliance on natural resources. When these "infant industries" became capable in the world market, these governments lowered the trade barriers, inviting international competition. China did something different. They pulled off a miracle with a series of experiments tailored to their needs and societal preferences like the Special Economic Zones and Township and Village Enterprises. By the time China joined the WTO, it had already created a strong industrial base. For this reason, globalization --- exporting --- plays a crucial role in these countries.

On the contrary, the East Asian countries' counterparts in Latin America, the Middle East, and Africa adopted a completely different strategy, called "import-substituting industrialization." These nations shut off their borders and gradually replaced import goods with domestic productions, by heightening governmental interventions. Most adopters did well; others, not quite. Brazil, Mexico, Turkey, and others saw the highest economic growth in their histories. Globalization does not work well in these nations. This diversity inhibits the global integration of markets by raising transaction costs across jurisdictions. Consequently, a world that is fully responsive to democratic preferences will be unable to achieve full globalization. As a side note, Rodrik pointed out the underlying force for ambitious economic growth comes from determined leaders.

Another interesting point is the labor market, the only market that is still highly protected. Rodrik proposes rich countries to loosen their immigration quota with a temporary visa program. These visa holders come in for 5-year, then return to their homes; replaced by new waves of foreign workers. The trained returnees would spark positive economic and social dynamics in their home countries. This does not only fill the void of labor shortage in rich nations but also produces a substantial gain in these developing countries, arguably the poor countries. That is a smart proposal. But I argue that it only works for early-career workers, who are ironically relatively inexperienced. Who in their mid- or late-career would venture out of their norms? I may be missing a point. Someone in the room, please advise.

PD Model: Curve fitting with Python

With a set of data, we will see how we can fit the data the phenomenological model by using $A$ and $b$ parameters with Python. A sample PD data can be downloaded on Github. The curve fitting process in Python is fairly easy. It uses a non-linear least square method to fit a function. We will need to import the Scipy libraries to perform the fitting. The code snippet is provided as below:

Lines #1-4: Read the .csv file. We see that there's a total of 251 lines of data with each line contains permanent strain in percent, number of load cycle, deviatoric stress, and shear stress ratio. Obviously, in this exercise, we are only interested in the accumulation of permanent strain due to load cycles. Therefore, we are going to ignore the effects of stress state for now.

	P_Strain_%	Load_Cycle_N	dS_psi	SSR
0	0.17	1	16.03	0.25
1	0.32	41	16.19	0.25
2	0.35	81	16.11	0.25
3	0.37	121	16.27	0.25
4	0.38	161	16.11	0.25
...	...	...	...	...
246	0.52	9841	16.19	0.25
247	0.52	9881	16.11	0.25
248	0.52	9921	16.19	0.25
249	0.52	9961	16.19	0.25
250	0.52	9996	16.03	0.25

Line #7: explores the correlation between each feature. This is a quick way to see any correlation between each feature or variable. For example, we see that the strongest relationship exists between P_Strain_% and Load_Cycle_N, i.e. 0.792972. Another strong positive relationship also exists between dS_psi and SSR. This is expected because deviatoric stress (dS_psi) is directly computed from shear stress ratio derived from the Mohr-Coulomb envelope. Again, we will come back to the effects of stress state later.

	P_Strain_%	Load_Cycle_N	dS_psi	SSR
P_Strain_%	1.000000	0.792972	-0.096899	-0.036616
Load_Cycle_N	0.792972	1.000000	-0.079329	-0.040335
dS_psi	-0.096899	-0.079329	1.000000	0.764572
SSR	-0.036616	-0.040335	0.764572	1.000000

Lines #9-29: This is where we define the phenomenological model and run the curve fitting method. Note that we call "curve_fit" from the scipy.optimize library, then fit the "phe_model" with the xdata and ydata, which respectively, are number of load cycle and permanent strain. Note that "curve_fit" includes several other useful parameters, including uncertainty (sigma), initial guess (p0), and bounds etc. You do not need to input these parameters if you do not know any. The breakdown of the next few lines are as below:

Line #22 returns an array of the model parameters $A=0.25561268$ and $b=0.0786587$. The $b$ value is reasonable as discussed in the previous post.
Lines #23 &24 provides a covariance matrix with respect to $A$ and $b$; all of which are near zero.
Lines #27-29 is a further step to find out the $R^2$ value of the fitting. In this case, $R^2 = 0.965$. This high $R^2$ value should not be a surprise for a power relationship.

Now, let's plug back $A$ and $b$ to the model and plot the graph. An easy way is to create an empty array, p_strain, using Numpy and parse in $A$ and $b$ to the "phe_model" function. The computed permanent strain are stored in the p_strain array. Following that, we plot both original data and model results against the number of load cycle.

Read more about scipy.optimize.curve_fit

Download sample file from Github

Permanent Deformation (PD): Phenomenological Model, Part I

Part of my graduate research study aimed to incorporate the shear stress component into various predictive models for permanent (plastic) deformation under cyclic loading in granular materials. In particular, granular materials referred, herein, are aggregate base and subgrade materials constructed under pavement or roadway subjected to repetitive vehicular loading as opposed to saturated sand and silt subjected to cyclic loading during seismic shaking events (i.e. undrained response). In that context, total stress was used instead of effective stress to simplify the problem.

One should expect accumulation of permanent strain (or deformation) plotted as a function of load cycle (or time) as above. Note that the curve resembles a highly nonlinear relationship between plastic strain and load cycle; a phenomenological model that describes empirical relationship of each parameter. In one of the early studies, Monismith et. al. (1975) describes the power relationship to best fit the data by least sum of squared errors. Taking log at both sides, the power relationship becomes a linear relationship, shown in the figure below, where $\epsilon_{p}$ = permanent strain; $N$ = number of load cycle; $A$ and $b$ = experimentally determined coefficients.

$$\epsilon_{p} = AN^b$$

$$log(\epsilon_{p}) = log(A) + b\cdot log(N)$$

It now becomes obvious that coefficients $A$ and $b$, respectively, represent the "intercept" and "slope" of the data. The exponent $b$ is a material constant; the exponent $A$ must be a function of other factors such as stress level, previous stress history, placement conditions, etc. Furthermore, the exponent $b$ is typically around 0.1, and $A$ is harder to define due to other various factors. However, other studies have shown that $A$ is strongly dependent on repeated stress state and material strength (Khedr, 1985; Garg et. al., 1997).

Using the laboratory test data obtained in my study, we will write a Python code to curve fit the data next.

See Next: Curve Fitting with Python

Reference:

Gard, N, Tutumluer E, Thompson, MR, 1998. Structural modeling concepts for the design of airport pavements for heavy aircraft. Proceedings of the 5th International Conference on the Bearing Capacity of Roads and Airfields, Trondheim, Norway, 1998.

Khedr, S, 1985. Deformation characteristics of granular base course in flexible pavement. Transportation Research Record: Journal of the Transportation Research Board, 1043: 131-138.

Monosmith, CL, Ogawa, N, Freeme, CR, 1975. Permanent deformation characteristic of subgrade soils due to repeated loading. Transportation Research Record: Journal of the Transportation Research Board, 537: 1-17.