No matter how big or small a construction project is, it must stand on the ground, through the so-called Foundation (probably the dictionary took the image of a chicken’s leg). If the foundation is not stable, the project can collapse (photo). Therefore, construction engineers must study a minimum number of hours about soil and foundation. This series of articles hopes to popularize this difficult knowledge, for as many people as possible who need it 🆗
2. Parameters of Soil
(next)
2.1. Why is there Soil mechanics?
As the name suggests, this is a branch of mechanics, posing problems about the equilibrium and movement of the ground. The ground is where people live and build structures on it (houses, bridges, dams, etc.). The task of the engineer in this subject is to predict the behavior of the ground under the impact of these activities.
This science is also quite new, born in the early 20th century. The reason for its birth, also comes from practical needs, has had to pay the price for many damaged works related to the ground: landslides, foundation destruction, etc., so people need to find knowledge about this issue, regardless of the country or land. Any construction project needs a solid foundation to transmit the load to the ground.
Soil mechanics became an independent branch of mechanics, because soil has specific properties compared to other materials:
💎Soil stiffness depends on the state of stress:
Many materials work elastically, at least under a certain internal force range. Elasticity means that when the force increases by 2 times, the deformation also increases by 2 times, the stress-strain relationship is a straight line.
Soil does not follow this linear way of working: under compression, the soil becomes more compact and harder. That is why the deeper the soil goes, the harder it is, due to being pressed by the weight of the soil layers above it.
💎Soil failure is shear:
When subjected to compression, the soil becomes stiffer, but when subjected to shear, the soil gradually falls apart. Failure occurs when the shear stress is large enough to exceed the compressive stress.
💎Dilatancy:
Shear deformation of soil often leads to volume change. Loose sand tends to decrease in volume, while dense sand tends to increase. The reason is due to the increase or decrease in volume of voids between soil particles when sliding over each other due to shear:
Shear deformation of soil in construction design
A close-to-life example to visualize this phenomenon: when walking on the beach near the water surface, the sand around the feet is pulled dry. The reason is that the sand on the beach, which has been compacted due to being soaked in water, bears the weight of the person stepping on it, causing shear deformation, increasing the volume of the sand mass. In turn, it absorbs water from the surrounding sand mass.
On the other hand, loose sand tends to collapse when subjected to shear, accompanied by a decrease in volume. This phenomenon becomes even more dangerous if the sand is flooded, causing an increase in pore water pressure. For example, when there is an earthquake, the flooded sand is compacted in a short period of time, greatly increasing the water pressure. This causes the sand grains to begin to float, which is called soil liquefaction.
💎Creeping:
This is a phenomenon where the load remains the same for a long time, although it does not increase in magnitude, it causes the soil deformation to increase. Clay and silt show this property very clearly. Therefore, a road built on a weak clay foundation can continue to sink for decades.
💎Groundwater:
A special property of soil is that water can be present in the pores between soil particles. It contributes to the distribution of stress in the soil. Because it takes time for water to drain from the pores, the presence of water prevents the volume from decreasing too quickly.
Lowering the groundwater level often leads to an increase in the effective stress between soil particles, increasing the settlement of the foundation. This happens in many large cities (Mexico city), or in structures around the foundation pit that are digging basements that need to lower groundwater and are sinking and cracking.
💎Low homogeneity:
Unlike wood, steel or even concrete, soil is a very heterogeneous material. Its properties change with depth, horizontally: even at two points close to each other on the ground, the properties of the soil can be completely different. Therefore, survey work is indispensable to determine soil properties for foundation problems.
2.2. State of stress
First is the Stress in soil. Defined as the force per unit area, the concept of stress is similar to pressure. Note that for soil, the area represents a plane that cuts through both the soil particles, the voids between them, and the contents of the voids (water, air – see photo below). This allows the mechanical calculations to be applied to soil as if it were a continuous body.
In the soil, there are both external and internal forces acting. External forces include, for example, the weight of the soil itself and the load of the structure acting on it. These forces divided by the unit area A are called the total stress σ=F/A.
Internal forces are represented by the following types of stress:
– pore water pressure uw
– air pressure in the pores ua
Sign convention of stresses:
– σ has a positive value when there is a tendency to push soil particles closer together (compression). With soil, σ>0 is always present and
– ua is positive when there is a tendency to push soil particles away from each other. In normal cases, pores in the soil are interconnected so ua is equal to the atmospheric pressure on the ground, so consider ua=0
– negative uw tends to pull soil particles closer together (water is tensile). Soil above the groundwater level uw<0, water always tends to pull soil particles closer together. Soil below the groundwater level (saturated) uw>0, water tends to push soil particles further apart.
Water in the pores between soil particles plays an important role in the mechanical properties of soil. This phenomenon can be related to the children’s game Sand Castle. If the sand is very dry, it is impossible to build a sand castle because the sand will melt when molded. When a little water is added (not too much), the water creates an attractive force that binds the sand particles together so that they can be molded.
The cohesive force between soil particles changes when the amount of water (humidity) in the soil changes as follows:
– When humidity increases: Pore water pressure decreases in magnitude (less negative), soil particles are separated, soil volume increases. With sandy soil, the volume increases very little, clay increases a lot.
– When humidity decreases: the process is reversed.
Then, after considering the soil from a discrete environment to a continuous solid object, start considering a Soil Element. Like a box of dimensions dx, dy, dz, at a depth z below the ground. The stress state is represented by a 3×3 matrix of stress values on each face of the soil element (google what a matrix is if needed). This matrix is called the Stress Tensor.
Stress Tensor in Foundation Design
Each surface has 3 stress components acting in 3 directions, the direction perpendicular to the element surface is called normal stress (normal), denoted by the letter σ at the beginning. The normal stresses are arranged in the diagonal of the matrix. The 2 components in the plane are tangential stress (tangential), causing shear, denoted by the letter τ.
Water pressure, pore gas, according to the theory of fluid mechanics (liquid, gas), only have normal components and have the same value of ua or uw in all directions. Therefore, their representation matrix has the form as shown above.
2.3. Principal stresses
In the special case of the stress state, when the element has only normal stress in 3 directions, the contact stresses are all equal to 0. These normal stresses are called Principal stresses, denoted by σ1, σ2, σ3.
This special case is quite common in soil mechanics situations. For example: The initial ground has not yet been subjected to any construction load, when the ground is horizontal, each soil element will have a principal stress state as shown above. With K being the coefficient of static horizontal pressure of the soil, 0.5≤K≤0.85.
principal stresses in foundation design
2.4. Soil strength
Strength is the limit stress at which an object has not yet been damaged. Soil damage is mostly due to shear stress. Shear failure: The easiest to visualize in practice is the collapse of a dam or roadbed due to a mass of soil sliding on the soil below it.
The shear failure of soil occurs on a plane with a shear stress large enough compared to the normal stress. The easiest illustration of this phenomenon is the classic problem of general physics about a solid on an inclined plane as shown in the figure:
Due to the equilibrium condition, the ratio of shear force to normal force: T/N = tgα. This ratio is smaller than 1 limit, called the coefficient of friction f, the solid is still in equilibrium. The slope angle α increases to tgα=f, the solid begins to slide down the slope. The larger the slope angle, the solid can never stand still on the slope. This is the basic theory of friction.
Based on that phenomenon, Coulomb (1736-1806) gave the classic formula for the strength (shear resistance) of soil:
τ = σ’tgϕ + c
where σ’ is the normal (effective) stress on the plane under consideration. c is the cohesion force, ϕ is the internal friction angle; these are the two most important parameters related to the load-bearing capacity of soil.
Meaning: If the shear stress on that plane is less than this value τ, the shear deformation can be limited, if it exceeds τ, the deformation cannot be controlled, then the soil is in a state of failure. The presence of c shows that even if there is no normal stress σ (roughly speaking, there is no force pressing on the sliding surface), there must still be a certain shear force to pull the soil into a state of failure.
2.5. Mohr circle of stress
A lot of information about the stress state in the soil and (c,ϕ) can be represented visually by the circle drawing method created by Mohr ().
Of course, the Mohr circle is not drawn for fun, Western science always has practical purposes. I will slowly explain its application, now the method of drawing a circle as shown below:
How to construct Mohr’s circle in soil mechanics
– Step 1: Construct the coordinate system (σn, τn)
– Step 2: Locate 2 points A(σy, τxy) and B(σx, -τxy) from the known stress values σx, σy, τxy (measured from the experiment)
– Step 3: circle with center at midpoint O of AB (located on the horizontal axis σn, diameter is AB.
===============================
(continued in part 3)
References:
1. TCVN 9362:2012 Standards for designing foundations of houses and structures
2. Design and calculation of shallow foundations – Vu Cong Ngu
3. Basic Soil Mechanics – R.Whitlow
4.SOIL MECHANICS– Arnold Verruijt, Delft University of Technology, 2001, 2006
5.Introducing Unsaturated Soil Mechanics to Undergraduate Students through the Net Stress Concepts– Eddy F. Ramirez
6. Mohr’s circle –Wikiwand.com
