Settlement - Consolidation

In geotechnical engineering, one of the challenges encountered regarding soil behavior is settlement. In this article, I will first explain the fundamentals of the settlement concept, and then I will highlight the critical points that must be considered in design and analysis. Rather than a lecture-like explanation or a simple example solution, I will point out the main logic, and demonstrate the solution to a real-world example step-by-step, and I will also solve the same example using Settle3D, a software commonly used for settlement calculations. Let's begin!

What is settlement?

First and foremost, it is crucial to understand what the settlement is and its concept correctly. Settlement is described as the reduction in void ratio and the increase in relative density of the soil under various influences. The most significant of these influences include engineering embankments built on the soil, structures foundations, and changes in the groundwater level within the soil. Under these influences, the compacted particles gradually expel the water in the voids and move downward over time. One of the key aspects of this point is that the size of the particles does not change -at least that's how it's accepted-, the placement of the particles changes instead.

Settlements are analyzed under two main categories: immediate settlement and time-dependent consolidation settlement. Theoretically, immediate settlement stands out in coarse-grained soils. Consolidation settlement, on the other hand, is more prominent in fine-grained clay soils. But what about a vice-versa situation? Although time-dependent settlement can also occur in coarse-grained soils, water easily escapes from the voids between the particles at the time of loading, and the majority of settlement in these soils happens quickly. In clay soils, although immediate settlement may be observed at the time of loading, the main concern is consolidation settlement, as the expulsion of water from cohesive soils takes time. In this article, I will focus primarily on consolidation settlement.

About consolidation settlement

Consolidation settlement in cohesive soils occurs due to the long-term expulsion of water from the voids caused by additional vertical stress. The mechanism of consolidation settlement is illustrated in Figure 1 below by the U.S. Department of Transportation. I strongly suggest reading this document to deeply understand the spring-piston model.

Figure 1. Consolidation mechanism in fine-grained soil (Department of Transport, 2006)

I don't want to skip this part without mentioning it briefly because understanding the consolidation mechanism is really important. When any load is applied to a stable saturated soil, at t=0, no stress occurs in the soil grains, but the pore water between the grains carries the load and this creates an additional pore water pressure. This water, whose stress increases, tends to leave the soil over time and transfers the stress to the soil. At t=∞, the additional pore water pressure in the soil becomes zero and the applied load is completely carried by the soil grains. This mechanism symbolizes the behavior of a loaded soil over time.

As I mentioned before, the primary concern here is the increase in effective stress in the soil. Effective stress increases can occur under loading as well as changes in the groundwater level. The construction of an embankment or the foundation of a structure is a major cause of these stress increases. An important point to note is that clay soils have a load memory. If excavation is to be done for the foundation of the structure, the effect of the excavated soil must be deducted from the load memory at the relevant depth. Solely accounting for the load from the superstructure will yield incorrect results. However, the same is not true for fills, as no excavation occurs during their construction.

If the effective stress at point A of a clay soil is the highest effective stress that point has ever seen, in other words, if it has not previously encountered a higher effective stress, these clays are called Normally Consolidated (NC) clays. Contrarily, if a soil is subjected to a stress greater than the effective stress at point A and this stress has decreased for some reason, such clays are called Over-Consolidated (OC) clays. Why is this difference important? If the soil is in a normal consolidated state, it will undergo rapid consolidation under increased effective stress compared to OC clays. If it is in an over-consolidated state, it will first consolidate more slowly to the over-consolidation point, while its consolidation will accelerate after this point. Knowing the loading status of the soil to be analyzed is critical in this respect. There are various approaches in the literature for the calculation of this over-consolidation point, but I will not touch on them here. In summary, the history of the clay soils to be analyzed for consolidation and the procedures to be implemented must be thoroughly examined.

For the calculation of consolidation settlement, we will use the equation suggested by Bowles and given below in Equation 1.

Here:

• Sc is the total amount of consolidation settlement for the layer being calculated,

• mv is the coefficient of volume compressibility of the clay soil,

• Δσ' is the total vertical stress increase at the midpoint of the layer being calculated,

• H is the thickness of the layer that can be consolidated.

How to obtain parameters?

In consolidation calculations, it is necessary to determine the volumetric compressibility coefficients (mv) of clays. Various experimental and empirical approaches exist for this purpose. The first of these are laboratory experiments conducted on samples obtained from the soil and this test is called the Oedometer test. In this test, undisturbed and saturated samples obtained from various depths of the soil are subjected to various loads, and their void ratio changes are examined. With the help of different equations, volumetric compressibility coefficient and consolidation coefficient values ​​are obtained according to certain effective stress ranges as a result of the test. The coefficient of compressibility is the ratio of unit volume reduction to unit stress increase. This is determined by the changes in the initial void ratio and volume of the test sample under loading. According to the approach presented by Craig in 2004, the mv value can be obtained using Equation 2 below. In addition to laboratory experiments, the mv value can also be obtained using SPT data. This approach, introduced by Stroud in 1974, is given in Equation 3. The f2​ value found in this equation can be obtained from the graph in Figure 2.

Figure 2. Plasticity index and f2 value correlation (Stroud, 1974)

In analyses, while laboratory results obtained from actual samples are primarily considered, there are times when reliable data cannot be obtained, or laboratory measurements produce results that contradict engineering understanding. At these times, the importance of empirical approaches increases. Using the average of both data types obtained in the analyses can also be a reasonable approach.

Once the coefficient of volumetric compressibility is determined using these methods, the compressible layer thickness (H) value can be obtained from the soil profile.

The final value in the equation is Δσ', which represents the increase in stress. It is important to understand the term "stress increase" correctly. The stress increase value is not the effective stress value. The current effective stress at a specific point is important for determining the coefficient of volumetric compressibility, and the value of stress increase is quite different from this. Stress increase occurs due to the load from the superstructure or changes in the groundwater level. It can also be referred to as a new load that will cause settlement. As I mentioned before, if a foundation for a structure is being constructed, the weight of the excavation should be deducted, and if it is a fill, the direct load of the fill should be taken. One critical aspect to consider here is the distribution of stress. That is, the stress beneath the foundation or fill decreases with depth in the soil and reaches a different value at a certain point of the clay being analyzed for settlement. Various approaches such as Boussinesq's method, Westergaard's method, and the 2:1 method exist in the literature for stress distribution. I will not explain these approaches in detail, but let me give bite-sized information. The 2:1 method provides a more general approach and often yields results that are more distant from reality. In the Boussinesq approach, the soil is considered as a homogeneous layer for stress distribution, whereas in the Westergard method, soils with different moduli of elasticity provide the stress distribution. Conducting detailed research on these methods will be useful for understanding the calculations. A common point of confusion usually concerns whether loads such as train and truck loads are considered in the consolidation settlement calculations. As I have mentioned before, consolidation settlement is a time-dependent settlement that occurs in compressible soils due to an increase in stress. The primary concern is with loads that are spread over time and are permanent. Instantaneous loads applied by vehicles, which do not affect pore water pressure, are not considered in consolidation settlement calculations. Such loadings can be considered under the category of immediate loading.

Final calculations

In conclusion, we have obtained all the data needed to calculate consolidation settlement. Subsequently, the total settlement is determined using Equation 1. Yes, we can obtain the total settlement but what is the limit value for this settlement and how can we assess what we got? In our codes, the limit value for total settlement is set at 5 cm in railway projects -of course, you have to make sure that the 5 cm seating is completed before the train is put into service- and any settlement values above this limit are considered for alternative solutions. These solutions include replacing with rock fill, compaction, and for more significant settlements, advanced methods like deep soil mixing (DSM) and stone columns. I will discuss these methods in detail in another article. In my research, although there is no consensus, the Federal Highway Administration document requires that the settlement under the fill be limited to 2 inches (51mm) when giving an example about DSM. I would appreciate it if you could share what limit your specifications set for this matter.

Once the consolidation settlement has been determined, it is necessary to ascertain how long it will take for the soil to complete this settlement. This determination is made using the experimentally determined consolidation coefficient, the length of the drainage path, and time with using Equation 4. The time required for consolidation to complete is obtained from the value derived from the graph of the percentage settlement with the dimensionless time factor (See video below).

Here,

• Tv is the time factor,

• cv is the coefficient of consolidation,

• t is the time measurement,

• Hdr is the drainage path.

I will not go into detail about the calculation of the consolidation coefficient obtained with the consolidation percentage and Tv time factor tables. The cv value is a concept that does not affect the amount of consolidation and only provides information about the percentage of consolidation completion over time.

To prevent the problem

Railway projects are long-term and complex, and progress depends on various factors. Phases such as design processes, expropriation time, and prioritization of critical constructions are considered. In this context, if a settlement issue is encountered in the location through which the route passes and there is sufficient time, you need to find a solution.

One of these solutions is preloading. A fill is constructed over the route to create the necessary conditions for consolidation settlement, and the soil is expected to settle under this load. Using the cv values ​​we obtained before, it is analyzed what percentage of consolidation has been completed in periods such as 3 months, 6 months, and 12 months. After reaching the desired limits, this fill is removed, and the real road fill and railway superstructure are laid according to the standards specified in the specifications using the appropriate methods and materials. Again, I want to underline that although this method may seem mandatory on paper, attention must be paid to criteria such as the condition of the construction area, the time schedule, critical constructions, and the conditions for bringing fill material to the area. Sometimes you may be doing modernization on an existing railway and you need to close one of the two operating lines and do work there. In such a case, it may not be possible to bring in fill material and do preliminary consolidation.

Another method to prevent consolidation settlement is to install sand drains. Sand drains are a method that facilitates the rapid removal of excessive pore water pressure within the soil, thereby accelerating the consolidation process. Although it is assumed in consolidation calculations that water drains in one direction, lateral drainage is actually an existing situation. When we consider this, it is necessary to make sand drains at certain intervals so that the water reaches a channel where it can drain easily and accelerate the consolidation process. As we will remember from Equation 4, the drainage path is a parameter that plays a very critical role in terms of time - and its square is taken. Reducing the drainage path in half means shortening the time by 1/4. However, the construction of these drains is a long and costly process. It would be good to evaluate it on a project basis.

Last but not least, sometimes we have encountered examples where there is not much difference between the settlement that occurs in 3 months and 6 months depending on the consolidation coefficient of the soil. In these cases where deep improvement alternatives are still needed, waiting 3 months longer may not be very efficient in terms of the economy and duration of the work. Again, such situations should be evaluated on a project and region basis.

Recap

I have tried to explain the mechanism of consolidation settlement as clearly as possible above. Below, I would like to share an application and calculation step by step. Thank you for reading this far. Please share your views and suggestions with me, and your own experiences. See you in the next article.

Arifcan Yilmaz, MSc

Civil Engineer