DESC:DESCRIPTION:
Field of the invention:
[0001] The present disclosure generally relates to the technical field of geotechnical engineering, and, in specific, relates to a method for determining the coefficient of elastic uniform compression (Cu) by accounting the effect of the embedment depth of the machine foundation.
Background of the invention:
[0002] Machines have become a vital element of human life as technology and industrialization have advanced. This has heightened the requirement for considerable research into several aspects of machine foundation design. The machine foundation soil system is equivalent to a spring mass system in machine foundation design, where soil is analogous to an elastic spring of stiffness 'k'. Soil stiffness is required in addition to bearing capacity and permissible settlement requirements in foundation design. Coefficient of elastic uniform compression (Cu) is one of the most important parameters in machine foundation design.

[0003] Many parameters such as the shape of the footing, the contact area of the foundation block, the modulus of elasticity of soil, the Poisson's ratio of soil, the type of soil, and the moisture content of the soil, influence the coefficient of elastic uniform compression. The foundations of industrial structures must be constructed to withstand both static and dynamic loads. As a result, foundation design must include soil stiffness in addition to bearing capacity. The equivalent soil spring stiffness is used to compute the natural frequency of the foundation soil system and the amplitude of vibration.

[0004] Soil stiffness is calculated for various modes of vibration using coefficients for elastic uniform compression, non-uniform compression, uniform shear, and non-uniform shear. Because established correlations are accessible, determining the above mentioned coefficients requires only the coefficient of elastic uniform compression (Cu). As a result, the coefficient of elastic uniform compression of soil (Cu) is the most essential parameter in the foundation design of structures subjected to dynamic loads. Cu is defined as the ratio of uniform compressive pressure (p) to corresponding elastic settlement (Se). The soil spring constant (k) for vertical excitation is calculated by multiplying the coefficient of elastic uniform compression Cu by the foundation base area (A).

[0005] Though the coefficient of elastic uniform compression (Cu) of soil can be estimated from the elastic constants of soil, cyclic plate load tests are commonly used to determine it due to the difficulty in accurately determining the elastic constants of soil. The value of Cu determined from the cyclic plate load test with square plates is commonly used to calculate the value of Cu for the actual footing via correlation. Cu is influenced by the shape of the footing, the contact area of the foundation block, the modulus of elasticity of soil, the Poisson's ratio of soil, the type of soil, and the moisture content of the soil. The effect of foundation shape on soil strength and stiffness variables, such as bearing capacity, elastic modulus, and modulus of subgrade reaction, is extensively documented.

[0006] However, the effect of embedment depth of footing on coefficient of elastic uniform compression of soil is rarely recorded in the literature, and established criteria for adjusting the values for embedment depth of footing are not known. As Cu is affected by the embedment depth of the footing; hence, the value of Cu calculated assuming the foundation being placed on the ground surface cannot be used reliably in the design of machine foundations

[0007] By addressing all the above mentioned problems, there is a need for a method that develops a generalized equation for determining the coefficient of elastic uniform compression (Cu) by considering the effect of the embedment depth of machine foundation in clayey silty sand. There is also a need for a method that performs small scale cyclic load tests in laboratory by placing circular and square plates at different embedment depths in clayey silty sand.
Objectives of the invention:
[0008] The primary objective of the present invention is to provide a method that develops a generalized equation for determining the coefficient of elastic uniform compression (Cu) by considering the effect of the embedment depth of machine foundation in clayey silty sand.

[0009] Another objective of the present invention is to provide a method that performs small scale cyclic load tests in laboratory for determining the coefficient of elastic uniform compression by placing circular and square plates at different embedment depths in clayey silty sand.
Summary of the invention:
[0010] The present disclosure proposes a method for determining the coefficient of elastic uniform compression (Cu) accounting for embedment depth effect. The following presents a simplified summary in order to provide a basic understanding of some aspects of the claimed subject matter. This summary is not an extensive overview. It is not intended to identify key/critical elements or to delineate the scope of the claimed subject matter. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is presented later.

[0011] In order to overcome the above deficiencies of the prior art, the invention provides a method for determining the coefficient of elastic uniform compression (Cu) by accounting the effect of the embedment depth of the machine foundation.

[0012] In one embodiment, a generalized equation may be developed for the determination of the coefficient of elastic uniform compression (Cu) considering the effect of the embedment depth of machine foundation in clayey silty sand. The method for developing an equation to determine coefficient of elastic uniform compression (Cu) by considering the effect of embedment depth of machine foundation in the clayey silty sand.

[0013] At one step, plurality of specimens are prepared in a mould at one or more conditions for performing laboratory test upon loading the collected soil sample. The mould is a California bearing ratio (CBR) mould for laboratory evaluation. The laboratory test is to be performed at optimum moisture content (OMC) and maximum dry density (MDD).The prepared soil sample in the mould is loaded through a self-straining loading frame.

[0014] At one step, circular and square plates of same sizes and at different embedment depths (Df/B) are selected. The embedment depth ratios (Df/B) considered are 0, 0.5,1 and 1.5. The dial gauge unit readings are recorded until the rate of settlement is ceased under loading and unloading stages. The difference of settlement under loading and unloading stages determines the elastic settlement.

[0015] At one step, cyclic plate load test is then performed in the field on clayey silty sand (IS classification : SC-SM, Medium sand -17%, fine sand – 40%,fines – 26%, Wl – 21%, Ip - 6%) under various load intensities, the dial gauge unit readings are recorded until the rate of settlement is ceased under loading and unloading stages. The difference of settlement under loading and unloading stages determines the elastic settlement. The graph between load intensity and elastic settlement is analyzed, thereby determining the coefficient of elastic uniform compression (Cu) of soil through the slope of the linear portion of the plot.

[0016] At one step, the ratio of coefficient of elastic uniform compression Cu of square to circular loaded plungers at all the embedment depths are determined. The incremental results of the coefficient of elastic uniform compression (Cu) value are observed. The incremental results of the coefficient of elastic uniform compression (Cu) value increased by 14% in the clayey silty sand with increase in embedment depth ratio by 50%.

[0017] At one step, the equation is developed for coefficient of elastic uniform compression (Cu) from the results of cyclic plate load test for circular plunger or plate in the clayey silty sand at any embedment depth ratios. The earlier reported value of coefficient of elastic uniform compression (Cu) is 1.17 can be adopted to account for effect of shape of vibrating bases.

[0018] Further, objectives and advantages of the present invention will be apparent from a study of the following portion of the specification, the claims, and the attached drawings.

Detailed description of drawings:
[0019] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate an embodiment of the invention, and, together with the description, explain the principles of the invention.

[0020] FIG. 1 illustrates a flowchart of a method for developing an equation to determine coefficient of elastic uniform compression (Cu), in accordance to an exemplary embodiment of the invention.

[0021] FIG. 2 illustrates a graphical representation of a load intensity and elastic settlement plot of clayey silty sand with a circular plate for different (Df/B) ratios, in accordance to an exemplary embodiment of the invention.

[0022] FIG. 3 illustrates a graphical representation of a load intensity and elastic settlement plot of clayey silty sand with a square plate for different (Df/B) ratios, in accordance to an exemplary embodiment of the invention.

[0023] FIG. 4 illustrates a graphical representation of a load intensity and elastic settlement plot of clayey silty sand with a circular plunger for different (Df/B) ratios under unsoaked condition, in accordance to an exemplary embodiment of the invention.

[0024] FIG. 5 illustrates a graphical representation of a load intensity and elastic settlement plot of clayey silty sand with the circular plunger for different (Df/B) ratios under soaked condition, in accordance to an exemplary embodiment of the invention.

[0025] FIG. 6 illustrates a graphical representation of the variation of coefficient of elastic uniform compression Cu for different (Df/B) ratios of clayey silty sand using circular plunger, in accordance to an exemplary embodiment of the invention.

[0026] FIG. 7 illustrates a graphical representation of a load intensity and elastic settlement plot of clayey silty sand with a square plunger for different (Df/B) ratios under unsoaked condition, in accordance to an exemplary embodiment of the invention.

[0027] FIG. 8 illustrates a graphical representation of a load intensity and elastic settlement plot of clayey silty sand with the square plunger for different (Df/B) ratios under soaked condition, in accordance to an exemplary embodiment of the invention.

[0028] FIG. 9 illustrates a graphical representation of the variation of coefficient of elastic uniform compression Cu for different (Df/B) ratios of clayey silty sand using square plunger, in accordance to an exemplary embodiment of the invention.
Detailed invention disclosure:
[0029] Various embodiments of the present invention will be described in reference to the accompanying drawings. Wherever possible, same or similar reference numerals are used in the drawings and the description to refer to the same or like parts or steps.

[0030] The present disclosure has been made with a view towards solving the problem with the prior art described above, and it is an objective of the present invention to provide a method for determining the coefficient of elastic uniform compression (Cu) by accounting the effect of the embedment depth of the machine foundation.

[0031] According to one exemplary embodiment of the invention, FIG. 1 refers to a flowchart 100 of a method for developing an equation to determine coefficient of elastic uniform compression (Cu) by considering the effect of embedment depth of machine foundation in clayey silty sand. At step 102, plurality of specimens are prepared in a mould at one or more conditions for performing laboratory test upon loading the collected soil sample. The mould is a California bearing ratio (CBR) mould for laboratory evaluation. The laboratory test is to be performed at optimum moisture content (OMC) and maximum dry density (MDD). The prepared soil sample in the mould is loaded through a self-straining load frame.

[0032] At step 104, the circular and square plates of same sizes and at different embedment depth ratios (Df/B) are selected. The embedment depth ratios (Df/B) considered are 0, 0.5,1 and 1.5. At step 106, the dial gauge unit readings are recorded until the rate of settlement is ceased under loading and unloading stages. The difference of settlement under loading and unloading stages determines an elastic settlement.

[0033] At step 108, Cyclic plate load test is then performed in the field on clayey silty sand (IS classification: SC-SM ,Medium sand -17%, fine sand – 40%,fines – 26%, Wl – 21%, Ip - 6%)under various load intensities, the dial gauge unit readings are recorded until the rate of settlement is ceased under loading and unloading stages. The difference of settlement under loading and unloading stages determines the elastic settlement. The graph between load intensity and elastic settlement is analyzed, thereby determining the coefficient of elastic uniform compression (Cu) of soil through the slope of the linear portion of the plot.

[0034] At step 112, the ratio of coefficient of elastic uniform compression Cu of square to circular loaded plungers at all the embedment depths are determined. At step 114, the incremental results of the coefficient of elastic uniform compression (Cu) value are observed. The incremental results of the coefficient of elastic uniform compression (Cu) value increased by 14% in the clayey silty sand with increase in embedment depth ratio by 50%.

[0035] At step 116, the equation is developed for coefficient of elastic uniform compression (Cu) from the results of cyclic plate load test for circular plunger or plate in clayey silty sand at any embedment depth ratios. The earlier reported value of coefficient of elastic uniform compression (Cu) is 1.17 can be adopted to account for effect of shape of vibrating bases.

[0036] The cyclic plate load test has been conducted in field on square and circular plates of size 30cm in clayey silty sand at different embedment depth ratios. From the results it is observed that the coefficient of elastic uniform compression (Cu) for square footing is 1.14 times that of circular footing. As the depth of the embedment is increased by 50% the value of coefficient of elastic uniform compression (Cu) has been increased by 12% in both square and circular footings.

[0037] The equation developed for coefficient of elastic uniform compression (Cu) from the results of cyclic plate load test for circular plunger or plate in clayey silty sand at any embedment depth ratios are
CufD = [1+0.35 (Df/B)] Cufo (1)
CufD = [1+0.3 (Df/B)] Cufo (2)

[0038] Coefficient of elastic uniform compression (Cu) for square plunger or plate in clayey silty sand at any embedment depth ratio is
CufD = [1+0.3 (Df/B)] Cufo (3)
CufD = [1+0.29 (Df/B)] Cufo (4)

[0039] Based on the above mentioned equations developed for coefficient of elastic uniform compression (Cu) at any embedment depth ratio for both circular and square footings in clayey silty sand following generalized equation (5) have been finalized.
CufD = [1+0.3 (Df/B)] Cufo (5)
Where
CufD - Coefficient of elastic uniform compression (Cu) at required embedment depth.
Cufo- Coefficient of elastic uniform compression (Cu) at zero embedment depth.
Df – Depth of vibrating base from the ground surface.
B – Width of vibrating base.

[0040] According to one exemplary embodiment of the invention, FIG. 2 refers to a graphical representation 200 of a load intensity and elastic settlement plot of clayey silty sand with circular plate for different (Df/B) ratios. The elastic settlement (Se) values are determined in (mm) of clayey silty sand for different (Df /B) ratios using circular plate.

[0041] In one embodiment here, the elastic settlement (Se) values in (mm) of clayey silty sand for different (Df /B) using circular plate as shown in Table 1.

[0042] Table 1:
q (kg/cm2) Elastic settlement, Se (mm)
(Df/B)=0 (Df/B)=0.5 (Df/B)=1 (Df/B)=1.5
0 0 0 0 0
0.5 0.15 0.14 0.14 0.09
1 0.35 0.27 0.26 0.22
1.5 0.52 0.42 0.37 0.35
2 0.7 0.56 0.5 0.46
2.5 0.82 0.69 0.62 0.56

[0043] According to one exemplary embodiment of the invention, FIG. 3 refers to a graphical representation 300 of a load intensity and elastic settlement plot of clayey silty sand with square plate for different (Df/B) ratios. The elastic settlement (Se) values are determined in (mm) of clayey silty sand for different (Df /B) ratios using square plate.

[0044] In one embodiment here, the elastic settlement (Se) values in (mm) of clayey silty sand for different (Df /B) using square plate as shown in Table 2.

[0045] Table 2:
q (kg/cm2) Elastic settlement, Se (mm)
(Df/B)=0 (Df/B)=0.5 (Df/B)=1 (Df/B)=1.5
0 0 0 0 0
0.4 0.13 0.14 0.12 0.11
0.8 0.29 0.26 0.22 0.2
1.2 0.42 0.39 0.33 0.31
1.6 0.56 0.53 0.45 0.45
2 0.7 0.65 0.53 0.5

[0046] In one embodiment herein, the coefficient of elastic uniform compression values for clayey silty sand at different (Df /B) ratios using circular plunger as shown in Table 3.

[0047] Table 3:
Df/B Cu (kg/cm3)
Square plate Circular plunger
0 30.7 26
0.5 32.8 31
1 37.4 35.7
1.5 43.9 41

[0048] According to one exemplary embodiment of the invention, FIG. 4 refers to a graphical representation 400 of a load intensity and elastic settlement plot of clayey silty sand with the circular plunger for different (Df/B) ratios under unsoaked condition. The elastic settlement (Se) values are determined in (mm) of clayey silty sand for different (Df /B) ratios using circular plunger under unsoaked condition.

[0049] In one embodiment here, the elastic settlement (Se) values in (mm) of clayey silty sand for different (Df /B) using circular plunger under unsoaked condition as shown in the Table 4.

[0050] Table 4:
q (kg/cm2) Elastic settlement, Se (mm)
(Df/B)=0 (Df/B)=0.5 (Df/B)=1 (Df/B)=1.5
0 0 0 0 0
0.5 0.05 0.06 0.03 0.02
1 0.1 0.12 0.05 0.05
1.5 0.15 0.24 0.09 0.09
2 0.18 0.32 0.14 0.1
2.5 0.22 0.36 0.16 0.14
3 0.26 0.42 0.2 0.16
3.5 0.33 0.47 0.22 0.19
4 0.37 0.51 0.26 0.21
4.5 0.44 0.55 0.29 0.24
5 0.48 0.6 0.32 0.27

[0051] According to one exemplary embodiment of the invention, FIG. 5 refers to a graphical representation 500 of a load intensity and elastic settlement plot of clayey silty sand with the circular plunger for different (Df/B) ratios under soaked condition. The elastic settlement (Se) values are determine in (mm) of clayey silty sand for different (Df /B) using circular plunger under soaked condition.

[0052] In one embodiment herein, the elastic settlement (Se) values in (mm) of clayey silty sand for different (Df /B) using circular plunger under soaked condition as shown in Table 5.

[0053] Table 5:
q (kg/cm2) Elastic settlement, Se (mm)
(Df/B)=0 (Df/B)=0.5 (Df/B)=1 (Df/B)=1.5
0 0 0 0 0
0.5 0.04 0.04 0.06 0.03
1 0.09 0.07 0.08 0.08
1.5 0.17 0.14 0.14 0.15
2 0.2 0.19 0.18 0.2
2.5 0.28 0.25 0.22 0.24
3 0.34 0.29 0.26 0.28
3.5 0.39 0.34 0.31 0.33
4 0.44 0.38 0.36 0.37
4.5 0.51 0.43 0.4 0.41
5 0.56 0.48 0.44 0.45

[0054] According to one exemplary embodiment of the invention, FIG. 6 refers to a graphical representation 600 of the variation of the coefficient of elastic uniform compression Cu for different (Df/B) ratios of clayey silty sand using circular plunger.

[0055] In one embodiment herein, the coefficient of elastic uniform compression values for clayey silty sand at different (Df /B) ratios using circular plunger as shown in Table 6.

[0056] Table 6:
Df/B Cu (kg/cm3)
Unsoaked condition Soaked condition
0 92.3 76
0.5 110 93
1 130 105
1.5 150 116.67

[0057] According to one exemplary embodiment of the invention, FIG. 7 refers to a graphical representation 700 of a load intensity and elastic settlement plot of clayey silty sand with a square plunger for different (Df/B) ratios under unsoaked condition. The elastic settlement (Se) values are determine in (mm) of clayey silty sand for different (Df /B) using circular plunger under unsoaked condition.

[0058] In one embodiment herein, the elastic settlement (Se) values in (mm) of Clayey silty sand for different Df /B using square plunger under unsoaked condition as shown in Table 7.

[0059] Table 7:
q (kg/cm2) Elastic settlement, Se (mm)
(Df/B)=0 (Df/B)=0.5 (Df/B)=1 (Df/B)=1.5
0 0 0 0 0
0.5 0.04 0.03 0.06 0.03
1 0.07 0.04 0.08 0.05
1.5 0.12 0.1 0.14 0.08
2 0.16 0.13 0.19 0.12
2.5 0.2 0.16 0.22 0.14
3 0.25 0.2 0.26 0.17
3.5 0.3 0.23 0.28 0.19
4 0.34 0.27 0.31 0.22
4.5 0.38 0.31 0.34 0.25
5 0.43 0.36 0.37 0.27

[0060] According to one exemplary embodiment of the invention, FIG. 8 refers to a graphical representation 800 of a load intensity and elastic settlement plot of Clayey silty sand with the square plunger for different (Df/B) ratios under soaked condition. The elastic settlement (Se) values are determine in (mm) of Clayey silty sand for different (Df /B) using circular plunger under soaked condition.

[0061] In one embodiment herein, the elastic settlement (Se) values in (mm) of Clayey silty sand for different Df /B using the square plunger under soaked condition as shown in Table 8.

[0062] Table 8:
q (kg/cm2) Elastic settlement, Se (mm)
(Df/B)=0 (Df/B)=0.5 (Df/B)=1 (Df/B)=1.5
0 0 0 0 0
0.5 0.06 0.06 0.05 0.06
1 0.12 0.11 0.13 0.1
1.5 0.18 0.21 0.18 0.14
2 0.24 0.24 0.23 0.2
2.5 0.28 0.31 0.29 0.24
3 0.35 0.36 0.34 0.31
3.5 0.4 0.42 0.39 0.35
4 0.46 0.47 0.44 0.39
4.5 0.51 0.52 0.48 0.44
5 0.56 0.58 0.53 0.48

[0063] According to one exemplary embodiment of the invention, FIG. 9 refers to a graphical representation 900 of the variation of coefficient of elastic uniform compression Cu for different (Df/B) ratios of clayey silty sand using the square plunger.

[0064] In one embodiment herein, the coefficient of elastic uniform compression values for clayey silty sand at different (Df /B) ratios using square plunger as shown in Table 9.

[0065] Table 9:
Df/B Cu (kg/cm3)
Unsoaked condition Soaked condition
0 107.142 90.9
0.5 130 100
1 150 111.11
1.5 166.67 125

[0066] In one embodiment herein, the cyclic plate load test has been conducted in field on square and circular plates of size 30cm in clayey silty sand at different embedment depth ratios. After extensive studies on granular soils, the value of Cu has been observed more in laboratory tests when compared with field results and then the equation was formulated.

[0067] From the results it is observed that the coefficient of elastic uniform compression (Cu) for square footing is 1.14 times that of circular footing. As the depth of the embedment is increased by 50% the value of coefficient of elastic uniform compression (Cu) has been increased by 12% in both square and circular footings.

[0068] Numerous advantages of the present disclosure may be apparent from the discussion above. In accordance with the present disclosure a method for determining the coefficient of elastic uniform compression (Cu) accounting for depth effect is disclosed. The proposed invention provides a method that develops a generalized equation for determining the coefficient of elastic uniform compression (Cu) by considering the effect of the embedment depth of machine foundation in clayey silty sand. The proposed invention also provides a method that to perform small scale cyclic plate load test in the laboratory by placing circular and square plates at different embedment depths in clayey silty sand for determining the coefficient of elastic uniform compression (Cu).

[0069] It is apparent that numerous modifications and alterations can be made to the processes described in the foregoing examples without departing from the principles underlying the invention, and all such modifications and alterations are intended to be embraced by this application.
,CLAIMS:CLAIMS:
I/We Claim:
1. A method for determining a coefficient of elastic uniform compression (Cu), comprising:
preparing plurality of specimens in a mould prepared at OMC and MDD conditions;
selecting circular and square plates of same sizes at different embedment depth ratios (Df/B);
recording readings of a dial gauge unit until the rate of settlement is ceased under loading and unloading stages;
performing a cyclic plate load test in a field on Clayey silty sand (IS classification : SC-SM, Medium sand -17%, fine sand – 40%,fines – 26%, Wl – 21%, Ip - 6%), thereby obtaining the data;
generating a graph between a load intensity and the elastic settlement based on the obtained data of the Clayey silty sand and the elastic settlement, thereby determining the coefficient of elastic uniform compression (Cu) of soil through the slope of the linear portion of the plot;
determining the ratio of coefficient of elastic uniform compression (Cu) of square to circular loaded plungers at all the embedment depths (varies between 1.14 and 1.18);
observing the incremental results of the coefficient of elastic uniform compression (Cu) value; and
developing the equation for the coefficient of elastic uniform compression (Cu) from the results of the cyclic plate load test for circular plunger or plate in the clayey silty sand at various embedment depth ratios.
2. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the mould is a California bearing ratio (CBR) mould for laboratory evaluation.
3. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the samples are prepared at OMC and MDD conditions.
4. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the collected sand is loaded through a self-straining load frame.
5. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the one or more embedment depths (Df/B) include 0, 0.5,1 and 1.5.
6. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the difference of settlement under loading and unloading stages determines the elastic settlement.
7. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the cyclic plate load test is conducted on soil at site(IS classification : SC-SM, Medium sand -17%, fine sand – 40%,fines – 26%, Wl – 21%, Ip - 6%).
8. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the incremental results of the coefficient of elastic uniform compression (Cu) value is increased by 14% in the Clayey silty sand with increase in embedment depth ratio by 50%.
9. The method for determining the coefficient of elastic uniform compression (Cu) as claimed in claim 1, wherein the earlier reported value of coefficient of elastic uniform compression (Cu) of at least 1.17 is adopted to account for effect of shape of vibrating bases.