Consideration of soil consolidation is an important factor in the design of industrial, hydraulic, transport and civil structures, since incorrect calculation of soil foundations can lead to the destruction of technical objects. The phenomenon of consolidation is associated with the multiphase structure of the soil. Theories describing this process and other rheological properties are the basic concepts of engineering forecasting.
General concept
Soils, which are the most common building materials for building foundations, by their properties do not belong to any of the traditional phase states of substances (solid, liquid, gaseous), since they consist of many separate particles. Their strength and other physical and mechanical properties depend on the combined interaction of these elements and vary over a wide range.
The definition of soil consolidation is associated with the phenomenon of their compressibility under the action of the load. This is mainly due to the approach of solid particles to each other. At the same time, the water contained in the pores of the soil is filtered. This phenomenon is due to the fact that at different points in the reservoir, pore pressure is different. Water tends to migrate to less stressed areas. At the same time, a restructuring of the soil composition takes place. The process of changing the moisture flow with sufficient accuracy is described by Darcy's law.
The main tasks for which the theory of soil consolidation is intended is to calculate the amount of soil precipitation under the influence of the load and the time for which it will occur.
History of the theory
Consolidation (compaction) of the soil layer proceeds under conditions of transient filtration. For the first time, an equation describing this process with variable porosity and permeability was proposed by the Russian hydraulic scientist N. N. Pavlovsky. The solution to a particular one-dimensional problem in 1925 was made by the Austrian geologist Karl Terzagi.
In the 30s. Soviet soil scientist N. M. Gersevanov developed a system of equations in an incomplete form for solving a spatial problem. The theory of filtration soil consolidation was further developed in the works of the Russian scientist V. A. Florin. His ideas and calculations formed the basis of modern soil mechanics.
The three-component model proposed by Florin was subsequently used in the works of Yu. K. Zaretsky, L.V. Gorelik, M. Yu. Abelev, P.L. Ivanov and other scientists. The techniques developed by them are used in the design of hydraulic structures, offshore oil installations and other facilities on βweakβ soils.
Varieties
The following types of soil consolidation are distinguished:
- Natural, due to the pressure of the overlying layers. After a certain period of time, it ends. The resulting stresses are called historical. If at the moment the current stresses in the soil coincide with the historical ones, then they say that it is normally compacted. In the case when the value of the former is less, the soil is overconsolidated (this is observed when the load decreases, for example, when the glacier melts).
- Primary, due to the migration of water in the pores with a decrease in their volume under the influence of the load. The amount of consolidation is determined by the graphs below (with a degree of consolidation in the range 0-100%).
- Secondary Compaction continues as a result of creep of solid particles (or skeleton) of the soil, which was not taken into account in the previous case. To determine precipitation, the soil consolidation coefficient of the secondary process is calculated.
The consolidation phenomenon differs from simple compression in that in the second case there is no change in the volume of water. Schematically, the difference between the two processes is presented in the figure below.
Key Assumptions
Solving the problems of filtration soil consolidation is based on the following assumptions:
- the soil is completely saturated, and the liquid medium is inextricable, that is, the decrease in soil porosity is proportional to the outflow of liquid;
- compaction occurs only by filtering the fluid and reducing the volume of skeletal pores;
- internal stresses instantly cause deformation; there are no viscous bonds;
- external pressure is initially completely transferred to water, structural strength is absent (sediment ends when mineral particles of the soil perceive internal stress);
- fluid filtration occurs according to Darcy's law.
This theory is used to determine the rate of development of sediment in water-saturated soils. When it approaches the limit values, an emergency occurs, the building construction collapses. At lower values, the deformation of the structure is compensated by the creep of the material and joints.
What soil properties affect the rate of consolidation?
The main characteristics of the soil, affecting the rate of precipitation, are:
- ability to pass water under pressure (permeability);
- structure (properties of the particles of which it consists);
- pressure created by the liquid on the pore walls;
- the ability of the skeleton to deform over time under the influence of a load;
- compressibility of mineral particles, water and air in the pores of the soil;
- loading scheme;
- geological structure;
- the predominance of a particular phase, the presence of air reduces the consolidation coefficient and the rate of equalization of excess pore pressure.
There are several calculation models with various assumptions that simplify the determination of the required indicators. The most common theory is filtration, according to which the soil is completely saturated with water (its main assumptions are indicated above). This model is used to calculate weak clay soils compacted over a large area.
The accuracy of the calculation and forecast depends on how close to reality it is possible to obtain the properties of soils. Hardly predictable changes such as leaks from water supply or discharge communications, changes in drainage in the adjacent area, and other processes also affect soil consolidation. An example of a calculation for determining filtration soil consolidation is discussed below.
Features of sandy and clay soils
In sandy soils with high water saturation, the extraction of water from the pores proceeds faster (correspondingly, the soil consolidation coefficient), since the gaps between solid particles are quite large. Shear deformations in sand and clastic rocks arise as a result of the mutual displacement of particles and the destruction of contacts between them.
In clays, volumetric deformation causes a dense repackaging of particles surrounded by a liquid shell. The speed of consolidation is determined mainly by the type of structural relationships and the magnitude of the load. The presence of water-colloidal bonds determines the elasticity of clay soils - their ability to recover after eliminating the load. Hardening after compaction is due to the fact that the resumption of these bonds occurs if the internal stress does not exceed the structural strength. Since the pores in clay soils are much smaller, consolidation is slower.
The most difficult to predict are structurally unstable soils, in which deformation occurs under the influence of additional external factors - thawing of frozen soils, decomposition of organic matter in peat and peat soils, flooding of loess, and an increase in salinity. So, in peat, filtration consolidation decays quickly, and sediment continues for a long period of time.
Basic Consolidation Equation
Calculation of soil consolidation is carried out according to the following basic equation:
where n ' is the fluid content per unit volume of soil;
t is the current time period;
s is the surface porosity;
p is the excess pressure in the pore water that appears due to consolidation;
p 1 - initial pressure before the consolidation process;
ΞΌ is the gas solubility coefficient;
e is the coefficient of porosity;
x and z are the coordinates for solving a flat problem (for an elementary volume of soil dx Γ dz Γ 1);
k x , k z are the filter coefficients through the left and right faces of the elementary cubic volume;
H is the pressure value;
i 0 is the initial pressure gradient.
For most types of soils, the process of pressure filtration of water is well described by the Darcy-Gersevanov dependence, which can be obtained from the main equation. It has the form:
where m is the ratio of the cross-sectional area of ββthe soil skeleton to the total area;
u s is the average relative velocity of the fluid in the pores;
v s - movement of the skeleton of the soil.
Volume forces model
In the model of volume forces proposed by Florin, the interaction of the phases of the soil (gas bubbles, liquid phase, solid particles) is taken into account. It is understood that shear stresses are perceived only by the skeleton of the soil. Normal effort is transmitted to all phases. The equation of consolidation taking into account linear creep has the form:
where a 0 , and 1 is the deformation that instantly arises at the moment of application of the load;
Ξ² is the coefficient of volumetric compressibility of the gas;
Ι£ and Ι£ 1 - creep parameters;
Ζ * is the sum of the stresses in the soil skeleton that would have arisen if the water had not impeded the change in pore size.
The coefficient of filtration soil consolidation is calculated by the formula:
In the engineering practice of building structures, different types of calculations are used in complexity. The basic equation of consolidation is reduced to a certain form depending on the conditions and tasks.
Simplified calculation
The main parameters that describe the stress state of the soil are:
- The consolidation coefficient characterizing the speed of compaction.
- The degree of soil consolidation. This concept is used to determine the draft from the moment the loading begins to any period of time.
- Initial consolidation period.
The main purpose of calculations according to the theory of filtration consolidation is to determine the amount of soil precipitation under the influence of a continuous load and the time during which it occurs. For this, two calculation methods are used - linear and nonlinear (for critical structures).
The filtration coefficient involved in the calculations is the rate of water filtration in the soil with a hydraulic gradient (slope). It is determined by one of 3 methods - a field test (pumping or filling), in laboratory conditions, by an indirect method (according to mechanical analysis and porosity).
Examples
An example of a calculation for determining soil filtration consolidation is given below.
Calculate the time of consolidation of the soil layer with a thickness of 4 m (400 cm) corresponding to 0.5 full draft. The ground loading pressure is 0.3 MPa, the relative compressibility coefficient is 0.015 cm 2 / kgf, the filtration coefficient is 1 β 10 -3 cm / s (vertical) and 2.8 β 10 -4 cm / s (horizontal).
Calculation without anisotropy. The full draft is calculated by the formula:
s = hm v p = 400 β 0.015 x 3 = 18 cm.
The specific gravity of water is 0.001 kgf / cm 3 . Given that 1 cm / s β 3 x 10 7 cm / year, we obtain the consolidation coefficient:
With v = (1 β 10 -8 β 3 β 10 7 ) / (0.015 β 0.001) = 20,000 cm 2 / year.
Then the time of soil consolidation is equal to:
t = 4 β 400 2 β 0.49 / (3.14 2 β 20 000) = 1.59 years.
where 0.49 is a constant factor (selected from reference data and depending on the degree of consolidation).
The effect of anisotropy
When constructing objects on macroporous loess soils, the correction factor for anisotropy is introduced into the calculations, since the isotropic method of solution provides underestimated rates of consolidation.
The anisotropy coefficient is calculated by the formula:
where n f is the degree of filtration anisotropy.
This parameter is entered into the numerator of the formula for calculating the consolidation coefficient. The obtained value allows you to make a decision on additional protective and preventive measures to strengthen the foundation of structures:
- general water reduction;
- design of surface runoff;
- fight against water leaks and others.
Laboratory tests
The consolidation coefficient is determined by calculation when testing soil samples. For this, special instruments are used - odometers. Drainage of fluid is carried out in horizontal, vertical and radial directions. Schematic diagram of the odometer is shown in the figure below.
A soil sample is installed in the lower part of the horizontal odometer chamber, in the center of which a hole is cut. A cylinder of porous solid material is inserted into it, through which water is supplied. Pore ββpressure sensors are fixed on the lower holder of the chamber and at the base. Water saturation is carried out during the day.
An axial vertical load is applied to the sample. At the same time, the pressure, force and displacement sensors are recorded. Based on the data obtained, compression curves are constructed. Studies show that the soil consolidation coefficient is much greater at a pressure whose value is less than the compaction stresses, and the filtration is higher in the radial direction.
In undisturbed soil structures, the compression curve has an initial section with a small angle of inclination. Such samples are also characterized by a sharp decrease in pore pressure coefficient. These properties are used to analyze soil structure disturbance. The degree of consolidation calculated in laboratory tests shows how much of the strain (in percent or fractions of a unit) takes place over a certain period of time.
The initial consolidation start point is obtained on the experimental curves by drawing a straight line on the graph that coincides with the initial section. Its intersection with the ordinate axis gives the desired value.