When designing a foundation, the construction designer receives data on the physical and mechanical properties of the soil layers in the foundation. These data are provided by the engineering geological surveyor, usually in the form of a summary table that clearly states the borehole, the soil sample number, the sampling depth, and the physical and mechanical properties of each sample. When considering the data on a property of each soil layer, the design engineer needs to distinguish:
- Specific value: is the value of a mechanical or physical characteristic of the soil determined according to a specific test sample, that is, determined for a specific point of the soil layer.
- Standard value: is the value of a mechanical or physical characteristic of the soil layer common to the entire soil layer. The standard value cannot take the smallest or largest value, but will have a value in the range between those two values. Because this is an index representing the entire soil layer, in the Standards, technical instructions, and design consultants, this index is used as the standard index for the soil layer under consideration.
- Calculated value: is the value of a certain physical characteristic of a soil layer used in the calculation of foundation structure design as a physical constant.
1. Standard value
2. Calculation value
with $A^{tc}$ being the standard value of the physical characteristics under consideration, determined as in clause 1 above
$k_d$ is the soil safety factor.
Physical indicators of volumetric mass $\gamma$, of durability (unit cohesion $c$, internal friction angle $\varphi$ of soil and uniaxial compressive strength limit $R_n$ of hard rock): determine the soil safety factor $k_d$ according to the provisions in Appendix A of TCVN 9362:2012.
Other physical indicators take $k_d$=1, that is, the calculated value is equal to the standard value.
According to clause A.2.3 of the standard, the soil safety factor $k_d$ when determining the calculated value of unit cohesion c, internal friction angle φ, soil volumetric mass $\gamma$ and uniaxial compressive strength limit $R_n$ of hard rock is calculated according to the formula:
$$k_d=\frac{1}{1\pm\rho}$$
where $\rho$ is the index determining the accuracy of the average value of soil characteristics, in construction design calculated according to:
- for c and tgφ: $\rho=t_{\alpha}.\nu$
- for $R_n$ and $\gamma$: $\rho=\frac{t_{\alpha}.\nu}{\sqrt{n}}$
$t_{\alpha}$ is the coefficient taken according to table A.1 of the standard depending on the given confidence probability α and the number of degrees of freedom (n-1) when determining the calculated values for Rn and γ, (n-2) when determining the calculated values for c and φ.
ν is the coefficient of variation of the physical characteristics:
$$\nu=\frac{\sigma}{A^{tc}}$$
σ is the mean square error of the feature, calculated as follows:
- for c and tgφ:
$$\sigma_c=\sigma_{\tau}\sqrt{\frac{1}{\Delta}\sum_1^n{p_i^2}}$$
$$\sigma_{tg{\varphi}}=\sigma_{\tau}\sqrt{\frac{n}{\Delta}}$$
$$\sigma_{\tau}=\sqrt{\frac{1}{n-2}\sum_1^n{\left(p_i.tg{\varphi}^{tc}+c^{tc}-\tau_i\right)^2}}$$
- for Rn:
$$\sigma_{R_n}=\sqrt{\frac{1}{n-1}\sum_1^n{\left(R_n^{tc}-R_{ni}\right)^2}}$$
- for $\gamma$:
$$\sigma_{\gamma}=\sqrt{\frac{1}{n-1}\sum_1^n{\left(\gamma^{tc}-\gamma_i\right)^2}}$$
Thus, it can be seen that determining physical and mechanical indicators for Structural Engineering, including in foundation and geotechnical calculations, according to Vietnamese Codes is relatively complicated, requiring a large amount of calculations. It is not allowed to take average values for important indicators such as $c, φ, γ, R_n$
3. Number of tests n
The number of tests n to establish the standard value and the calculated value of the physical and mechanical properties of the soil depends on the level of homogeneity of the ground, the required accuracy of the calculation of the properties and the type of construction.
The minimum number of tests for a certain indicator for each geological unit of the construction is 6. When finding the calculated value of c, φ, it is necessary to determine no less than 6 values of τ for each normal pressure value p.
4. Evaluation of parameters
The sections presented above are ways to determine the calculated values of important parameters such as c, φ entirely from the test results. However, from the obtained numbers, the design consultant needs to consider and adjust based on the understanding of the advantages and disadvantages of each experimental method to determine those physical and mechanical indicators.
For the designer of foundation structures, the indicators of soil deformation (deformation modulus E), the indicators of soil strength (c, φ) are the most important indicators. The physical nature of the indicators c and φ is very complex, especially for cohesive soil (clay), people consider c and φ as parameters to calculate the shear strength of the soil without being able to associate it with a simple physical image of friction phenomenon, adhesion phenomenon as the name suggests. There are many factors affecting c and φ and there is no simple experimental method that can definitely determine c and φ with all the factors affecting them.
The task of the actual foundation design engineer is to assess and evaluate the experimental results of determining c and φ provided by the geological survey unit. From there, choose more reasonable and reliable values of c and φ to use for foundation design calculations, specifically to calculate the calculated pressure value R of the soil according to the formula of Standard TCVN 9362:2012:
$$R=\frac{m_1m_2}{k_{tc}}\left(A.b.\gamma_{II}+B.h.\gamma’_{II}+D.c_{II}-\gamma_{II}.h_o\right)$$
It should be noted that the c and φ data from the current geological survey reports are mostly determined from the rapid shear test. In theory, this is a shear test under conditions where water does not drain at all under the influence of compressive pressure or shear force. In practice, although the upper and lower surfaces of the soil sample were lined with impermeable fabric, the soil sample was still not watertight and water still partially drained. Depending on the type of soil and the operator’s operation, in practice, when cutting, the soil was more or less consolidated. With soil that does not contain much clay, although it is called rapid shear (UU), in reality it is close to the consolidated rapid shear (CU) diagram.
On the other hand, in the shear test, the value of the shear force acting on the soil sample increases very quickly, after a short time the soil sample is completely sheared, not very close to the actual working of the soil in the foundation under the construction because the load of the construction increases relatively slowly. Normally, the slow shear test method is more suitable for the actual working conditions of the foundation soil. Except for rare special cases: the foundation soil cannot drain, the construction load suddenly increases, then the fast shear test diagram can be considered appropriate.
It is worth noting that the values of c and φ obtained from fast and slow shear tests are significantly different. Fast shear tests and especially consolidated fast shear tests often give larger c values and smaller φ values than slow shear. Further verification can be done by comparing the values of c and φ calculated from the test results prepared by the geological survey unit with the standard values of different soil types as shown in Tables B.1 and B.2 of TCVN 9362:2012. The values in the table of this standard are essentially drawn on the basis of slow shear test data and re-statistically in standard form.
Thus, if the design consultant uses the values of c and φ according to the test data provided by the geological survey unit to determine the calculated pressure R of the foundation soil, the result will often be larger than R (because the value of c has the greatest influence on the value of R). Therefore, the construction designer must adjust the values of c and φ: choose a slightly larger value of φ and a slightly smaller value of c compared to the results of the quick shear test. The standard values given in the tables of TCVN are a good basis for comparison and correction.
The above presentations apply to normal soil, excluding muddy soil. Muddy soil requires separate studies.
5. Parameters on Deformation
The physical and mechanical index of deformation (Deformation module E) is the most important index for foundation design problems (calculation of foundation according to the second limit state: settlement calculation) and other geotechnical problems (retaining wall problems, diaphragm wall displacement). Choosing the right value of deformation module E that accurately reflects the working of soil layers in the foundation is a prerequisite for calculating and predicting accurately the deformation value of the foundation (settlement, displacement of excavation pits, etc.). Although the theory of soil mechanics has developed strongly, experimental methods have progressed a lot, the problem of determining the deformation module E value of soil in a simple, fast and accurate way is still a topic that often causes great controversy among design consultants and appraisal consultants.
Usually, there are currently 2 ways to determine the deformation module value of soil:
- The first method is based on compression tests in the laboratory. The laboratory uses a uniaxial compression machine to compress the non-expanding soil.
- The second method is to conduct a soil compression test in the field by loading a rigid plate placed on the ground and monitoring the settlement of the plate. From there, the deformation modulus of the soil is calculated.
Comparison of the results of 2 types of tests on the same experimental soil shows that the deformation modulus value determined by the field compression test is always larger than the deformation modulus value derived from the laboratory compression test. There are many reasons for this difference. Some of the main reasons are that when the soil sample is taken out of the soil layer, it has been completely deloaded and the structural connection of the soil is weakened. During the process of taking the sample, transporting, preserving and until the test, the soil is subjected to many destructive mechanical impacts, its structure is more or less damaged, the load-increasing characteristics and drainage conditions of the 2 tests are different… It is recognized that the deformation modulus value determined by the field compression test is more reliable because it is closer to the actual working conditions of the foundation and the construction. In Vietnam, there have been some studies comparing these two tests by statistically analyzing many experimental results of determining E by the two methods. It was concluded that for each different type of soil, the values of the two methods differed by about 2-3 times. Thus, to have the deformation modulus value as in the field compression test, it is necessary to multiply the deformation modulus value according to the results of the laboratory compression test by a certain adjustment factor m (this is not true for soft and mushy clay).
TCVN 9362:2012 provides standard values of the deformation modulus E of different types of soil in the form of table B.3 (appendix B of the standard). This is the statistical result of many field compression tests conducted in practice for each type of soil, similar to the standard values of c and φ.
In reality, design engineers only have the results of laboratory compression tests, but very rarely have field compression tests for civil works. Thus, it is necessary to take the deformation modulus value E from the laboratory experiment and compare it with the standard E values stated in Table B.3 of the standard (look up the table according to the physical and mechanical indicators of the void ratio e and the viscosity index Is of the soil layer under consideration). We will know how many times smaller the E values calculated from the laboratory compression test are. Then we will decide to choose an appropriate adjustment factor m to multiply into the E value according to the laboratory experiment to get the calculated E value to be included in the structural design problems.
The adjustment factor can be used:
$$m=\frac{2,72}{e}$$
as suggested by Professor Vu Cong Ngu in the document “Design and calculation of shallow foundations” with the condition of application for soil layers with viscosity $I_s$ = 0 – 1, void ratio e = 0.4 – 1.
As for the strength parameters (c and φ), the above correction judgments for the E value according to the results of laboratory tests are mainly suitable for normal soils. Particularly for muddy soils, it is often seen that the calculated settlement value is smaller than the actual settlement value, a separate study is needed to be able to choose their E values to reflect closely the actual working in the ground.
6. Determining the index for Sands
Void coefficient e:
Soil density γ:
With the sandy soil layer located below the groundwater level, in a saturated state, G=1.
Δ – grain density, given in the geological survey results
A parameter often used in the design of retaining wall structures is the saturated density determined by the formula:
$$\gamma_{sat}=\frac{\Delta+e}{1+e}\gamma_n$$
The density of water is taken as $\gamma_n=10kN/m^3$
Internal friction angle φ:
$$\varphi=\sqrt{12N_{SPT}}+a$$
There are some values of a as suggested by Dunham, Osaki, Peck, Terzaghi according to figure E.2 of the Standard.
It is necessary to refer to table E.1 of this standard and compare with the values of table B.1 of TCVN 9362:2012 to consider choosing the value for structural design calculation.
Note that the internal friction angle φ must not be confused with the angle of repose of sand (in dry and wet state) given in the geological survey report.
Deformation module E:
Determine according to clause E.1.2 of TCVN 9351:2012 as follows:
$$E=\frac{a+c\left(N_{SPT}+6\right)}{10} (MPa)$$
in which the coefficients a = 40 when $N_{SPT}$≥ 15, a = 0 when $N_{SPT}$<15, the coefficient c depends on different soil types as indicated in the standard.
It is necessary to compare with the values of table B.1 of TCVN 9362:2012 to consider choosing the calculation value.
To serve the construction design work, it is necessary to automate the above calculation work by computer. We have shared the spreadsheet in Excel format here.
See more Physical and mechanical characteristics of the foundation soil for Plaxis, Geo5
References:
TCVN 9362:2012: “Standard for Design of foundations of houses and works”
TCVN 9351:2012: “Construction soil – Field testing method – Standard penetration test (SPT)”
“Design and calculation of shallow foundations” – Prof. Vu Cong Ngu – University of Construction – 1998
Reference:
TCVN 9362: 2012: “Standard design and construction”TCVN 9351: 2012: “Construction land – Field experimental method – Standard experiment (SPT)””Design and calculation of agricultural foundation” – GS. Dancer – Construction University – 1998
