INVESTIGATION INTO FLOOR BEARING STRENGTH OF INDIAN … · INVESTIGATION INTO FLOOR BEARING...

SAIMM, SANIRE and ISRM

6th

International Symposium on Ground Support in mining and civil engineering construction

D Kumar

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Page 345

INVESTIGATION INTO FLOOR BEARING STRENGTH OF INDIAN

COAL MEASURE STRATA BY FINITE

ELEMENT MODELING

D Kumar

Department of Mining Engineering, Indian School of Mines University, Dhanbad, India-

826004

Abstract

The investigation of the bearing strength of mine floor has become an integral part of the

study of mine stability. It is sometimes practical to conduct the in-situ plate loading tests;

however such tests are always expensive and can seldom encompass the whole range of

rock and environmental conditions pertinent to a foundation. Scale model tests offer

another approach by which the variability of site conditions and rock properties can be

studied to achieve an economical design. Experiments on artificial model rock masses

require lower capacity equipment and at the same time they yield better results. Intact

model rocks are more uniform and cheaper to produce compared with the cost of cutting

or sampling natural rocks.

Analysis of stability (mainly bearing strength and settlement) under a footing on regularly

bedded, jointed and layered model rock mass is conducted using 3D Non-linear FEM

analysis. The inputs required for the FEM modeling were imported from the laboratory

results of the measurements. The rock mass was modeled as elastic-plastic with Drucker-

Prager failure criteria for plane strain condition. The joints and the weak layers in the

floor rock mass were modeled in order to enable separation of zones in the models. The

footing settlements correspond to the maximum applied bearing pressure on floor strata

(for different sizes and shapes of footing plates and also under varying anisotropy

conditions of floor strata), as obtained from the experimental results and FEM

investigations, were compared and the maximum deviation was observed as 14 %

whereas the minimum was even less than 3 %. From FEM analysis it is interpreted that

the maximum stress concentration occurs at the tip of the footing plate all along the

boundary. The stress concentration extends to a maximum distance of 2 to 3 times

footing plate width in all direction of floor strata. It is further interpreted that the

maximum vertical settlement occurs near to the vicinity of the footing plate. From the

FEM analysis of jointed rock it is determined that there is a slight movement of the two

blocks separated by the joint. The joint plane acts as the rupture plane.


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Introduction

The two major criteria that control the design of spread footing foundations on weak floor

jointed and layered rock are the bearing capacity of the rock beneath the footing and

settlement of the foundation. As a consequence, bearing strength estimation and

settlement prediction are the two major concerns in the design process of shallow

foundations. The problem of estimating the bearing strength and the settlement of spread

footing foundations on weak floor jointed and layered rock mass is very complex due to

the uncertainty associated with the factors that affect these parameters. The geotechnical

literature has included many methods, both theoretical and experimental, to predict

settlement of shallow foundations on soils. Many settlement prediction methods have

focused on correlations with in-situ tests, such as the cone penetration tests (CPT),

standard penetration tests (SPT), dilatometer modulus tests (DMT), plate load tests,

pressure meter tests and screw plate load tests. These methods are based on the

reasonable assumption that soils are plastic, either purely cohesive or purely frictional

and generally homogeneous. Rocks, on the other hand, display brittle behavior, possess

both cohesion and friction and are usually far from homogeneous [1]. As a result, most of

the available methods are restricted by simplifying the problem, incorporating several

assumptions for the factors that affect the bearing capacity and the settlement of spread

footing foundations on weak and layered rock masses.

The determination of the ultimate bearing strength of spread footing foundations on rock

masses has traditionally been considered taking into account of previous experiences,

using empirical criteria or applying local or national codes [2-4]. It may be reasonable to

observe that because of minimal experimental evidence, suggested allowable design

pressures appear to be based on a guaranteed safe approach and consequently they are

generally very conservative.

The main objective of this research finding is confined to the stability analyses of jointed

and layered rock foundations by Finite Element Modeling (FEM) using multiple yield

models.

Non-linear FEM analyses of floor bearing characteristics (under similar conditions as in

the case of laboratory investigation) were carried out using the ANSYS 6.1 FEM

software package. The Drucker-Prager criterion for non metal plasticity was followed as

the failure criterion.

Procedure

The present investigation has been carried out using the finite element program, ANSYS

6.1 [5] on an HP_UX Unix workstation running hp_ux11.0 OS. 3-D numerical models

were developed for different conditions of surface footing foundation using appropriate

rock mass properties. Rock masses were modeled as elastic-plastic with the Mohr-

Coulomb yield criterion and Hoek Brown criterion for plane strain conditions. Their

initial stress field was calculated from the weight of the mass due to gravity, without


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influence of the footing weight. Loading at the contact plane between the footing plate

and the rock surface has been represented as:

• Circular area load of diameter that of the footing plate, placed centrally over the

model floor strata in the case of circular surface footing.

• Square area load of length that of footing plate, placed centrally over the model

floor strata in the case of square surface footing.

The loads were uniformly distributed on the surface area of footing plate located over the

model floor strata. The loads were all symmetrically placed with respect to the vertical

axis. 3-D 10-Node Tetrahedral Structural Solid elements (solid 92) were considered in

this investigation for all types of modeling except joints. The analysis of floor bearing

strength of rock was carried out by adopting 3-D (three dimensional) analysis with

displacement approach. Depending on the availability of computing facilities, mesh size

and thus number of elements were decided on (for a block size of 17 cm long, 17cm wide

and 8 cm high) without losing accuracy.

The parameters that were analyzed for the purpose of stability analysis, are:

• Prediction of bearing strength of surface footings and settlement of the foundation

with regard to size effects:

• Introducing joints and weak layers (Fig. 1) in the model, to find the influence of

the following parameters on the ultimate bearing strength:

o Position of the layer (axis) :

� On the edge of the footing

� In the middle of the footing

o Inclination of the layer (β)

� β = 60o

, 40o

, 20o

, 0o

o Width of the layer (b)/width of the footing (B)

� b/B = 1/4, 2/4, 3/4

For these purposes the ground was modeled for different sizes and shapes of footing

plates resting on it under various loading conditions. The geometrical dimensions in the

numerical models were employed from the physical modeling tests conducted by the

author [6 -7]. In the present investigation, triangular elements and isoparametric elements

were used for nodal plates of different shapes on an isotropic foundation.

The joints between the layers and the mass were modeled in order to enable separation of

zones in the models. They were characterized by coulomb sliding and/or tensile

separation. The interface of the joint had the properties of friction, cohesion, normal (kn)

and shear (ks) stiffness, and tensile strength (σt). Figure 1 shows the analytical condition

and FEM mesh generation for the model floor strata with weak layer


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Fig. 1: Analytical condition and FEM mesh generation for the model floor strata

with weak layer

For the purpose of prediction of bearing strength of surface footings and settlement of the

foundation, the ground was modeled for different size and shapes of footing plates resting

on it under various loading conditions. The geometrical dimensions in the numerical

models were employed from the physical modeling tests conducted in the laboratory

using model plate loading tests on weak floor simulated strata.

Properties of rock mass required for the model are:

i) Modulus of Elasticity (E), GPa. ii) Poisson’s ratio (ν). iii) Cohesion (c), MPa. iv)

Angle of internal friction (φ), degrees. v) Unit weight of rock mass (γ), kg/m3

, and vi).

Shear Modulus (G), MPa.

The Table 1 depicts the parameter and the variables used for FEM analysis purposes.

Table 1 Parameters and the variables for FEM analysis

Physico-mechanical Properties: The physico-mechanical properties of the simulated floor

massive strata as determined from the laboratory investigation, has been used as the input

to FEM model maintaining the same geometry that of physical model.

Shape Square.

Dimension (LxW) 17cmX17cm.

Thickness (T) 4cm, 8cm, 12cm,16cm, 20cm

Strata condition Massive, jointed and layered

Uniaxial compressive strength 0.95 MPa

Density (γ) 1785 kg/m3

Modulus of Elasticity (Et) 0.134 GPa

Poisson’s ratio ( ν) 0.178

Cohesion (c ) 0.82 MPa

Angle of internal friction ( φ) 20o

Uniaxial tensile strength (σt) 0.143 MPa

Footing Plate : The Mild Steel ASTM – 154 plates of different sizes which were used as

surface footing for the plate bearing tests in the laboratory and in-situ, the same have

been modeled in FEM analysis. The footings have been modeled as an elastic material

without weight.

Footing plate size 2.5 cm, 5.0 cm, 7.5 cm, 10.0 cm, 12.5 cm


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Footing plate shape Circular, square, rectangular

Footing plate / strata thickness (ratio) 0.3125,0.625,0.9375, 1.25, and 1.5625

Modulus of Elasticity (E) 199.5 GPa


Density (γ) 7861.4 Kg/m3

Joint properties : The mica sheet with the following properties was used to simulate the

joint in the laboratory investigation as well FEM analysis

Joint surface Rough

Joint aperture, mm 0.2

Joint spacing Remote

Joint filling Soft

Friction coefficient 0.3

Normal Stiffness (Kn) 200 GPa/m

Shear Stiffness (Ks) 2 GPa/m

Layer Properties: The physico-mechanical properties of the mixture Fly ash: cement:

water (1: 0.250: 0.530) earlier determined in the laboratory and used as a "weak" layer

for the experimental investigation, is introduced in FEM model too.

Uniaxial compressive strength(σc), 0.125

Bulk density (γ) 1421 kg/m3

Layer thickness (b) 1.25cm , 2.5cm , 3.75cm , 5cm

Modulus of Elasticity (Et) 0.05 GPa


Cohesion (c ) 0.120 MPa

Angle of Internal friction ( φ) 8o

The bearing strength as determined from the model plate loading test on simulated floor

strata in the laboratory was considered as the surface pressure to be applied on the footing

plate resting over the model floor strata. For the purpose of comparison of the results

obtained from the ANSYS program and the model plate loading tests for the

determination of floor bearing strength in the laboratory, the FEM analyses were carried

out on same dimensions and the magnitude of loading corresponding to the plate loading

tests as carried out in the laboratory.

The loads were applied in steps with respect to time under ramped loading conditions.

The Drucker-Prager criterion for non metal plasticity was used as the failure criterion.

The numbers of load sub-steps were varied between 10 – 40 depending on the maximum

intensity of the bearing strength and time. The full Newton-Raphson method was used for

the non-linear converging solution.

Analysis

The FEM analysis has been carried out for circular, square, and rectangular footings of

various sizes as mentioned in the Table1. The results have been presented in the form of


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illustrations showing floor strata deformation behavior, extent of footing settlement (in

meters) along the boundary, and stress (Pa) distribution (mainly von Mises) in the model

strata for circular, square and rectangular footing plates with varying plate sizes (keeping

the B/T ratio constant at 0.625).

The von Mises stresses (equivalent stresses) are based on the normal and shear stresses.

They are combined into the single stress value. This stress value is always positive. It is

generally used to evaluate yield failure stress. The von Mises stresses are calculated in

terms of Principal stresses σ1, σ2, and σ3:

( ) ( ) ( )[ ]2

13

2

32

2

21

5.0 σσσσσσσ −+−+−=eqv

(1)

The magnitude of footing settlements in the case of central footing for the maximum

bearing pressure (bearing strength), corresponding with the experimental value as applied

to floor strata in the FEM analysis, are given in Tables 2 & 3. The footing settlements as

obtained from FEM analysis have been compared with the experimental results and the

percentage deviation is shown in the above mentioned tables. The maximum deviation is

observed as 14 % whereas the minimum is about 3 %.

Table 2 Comparison among laboratory and FEM result of the footing settlement

(central square footing in the presence of weak layer).

Central footing Edge footing

Settlement (mm) Settlement (mm)

Weak layer

thickness (cm)

Lab FEM

%

deviation Lab FEM

% deviation

1.25 1.78 1.937 8.8 1.62 1.396 13.8

2.50 1.846 1.741 7.2 1.73 1.527 11.7

3.75 1.511 1.418 6.2 1.80 1.714 4.7

5.00 0.806 0.752 6.7 1.11 0.978 11.9

Table 3 Comparison among laboratory and FEM result of the footing settlement

(central circular footing in the presence of joint).

Central footing Edge footing

Settlement (mm) Settlement (mm)

Joint orientation

(degree)

Lab FEM

%

deviation Lab FEM

% deviation

0 1.18 1.070 9.3 1.21 1.153 5.7

20 1.20 1.158 3.5 1.74 1.630 6.3

40 1.16 1.111 4.3 1.28 1.215 2.3

60 1.01 0.965 4.5 1.08 1.034 4.3

80 0.89 0.876 1.4 1.07 0.961 10.2

Figure 2 shows the deformation characteristics of floor strata in case of a square footing

plate of 5 cm with a B/T ratio of 0.625. The bearing pressure of magnitude 8.20 MPa was

applied in 20 equal sub-steps.


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Fig. 2: Nodal displacements U in vertical direction - Z for footing size of 5.0 cm with

B/T ratio of 0.625 (Square footing)

Figure 3 shows the equivalent stress concentration along the X (length) direction of the

floor strata in the case of a square central footing for different plate sizes. From this

figure it can be interpreted that the maximum stress concentration occurs at the tip of the

footing plate all along the boundary. The stress concentration extends to a maximum

distance of 2 to 3 times the footing plate width in all directions.


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Fig. 3: Equivalent stresses along the entire length of model strata for square footing

of various sizes with fixed B/T ratio of 0.625

Figure 4 shows the deformation behaviors of the floor strata for different sizes of square

central footing plates with fixed footing size/strata thickness (B/T) ratio. From all these

results, it can be interpreted that maximum vertical settlement occurs near the vicinity of

the footing plate.


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Fig. 4: Footing settlement along the entire length of model strata for various sizes of

square footing with fixed B/T ratio of 0.625

Figure 5 shows the deformation behavior of floor strata in the presence of weak layers of

varying thickness. The square footing plate of 5 cm was used as the central surface

footing. A bearing pressure of magnitude 5.44 MPa was applied in 20 equal sub-steps. It

can be interpreted from the figure that the maximum settlement occurs near the vicinity

of the footing plate.


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Fig. 5: Deformation behaviors of model strata in the presence of weak layer of 1.25

cm for square footing plate of 5.0 cm centrally located

Figure 6 shows the variation in the footing settlement along the X-direction (length) of

floor strata in the presence of weak layers of varying thickness. The square footing plate

of 5 cm was used as central surface footing. From all of these it can be interpreted that

maximum settlement occurs near the vicinity of the footing plate.


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Fig. 6: Footing settlement in the presence of joint located at an angle 0o

from the

direction of applied load i.e. vertical (central circular footing).

Conclusion

The following conclusions can be drawn from the above investigations, based on the

analysis of the results.

1. Tensile cracks are initiated at the rim of the footing forcing a depression beneath

the footing leading to a stable crack growth as load increases.

2. With increased loads, the depression may eventually crush the floor with unstable

crack growth and with fracture reaching the surface.

3. The maximum stress concentration occurs at the tip of the footing plate all along

the boundary. The stress concentration extends to a distance 2 to 3 times the

footing plate width in all directions.

4. The maximum normalized footing settlement occurs near the vicinity of the

footing plate.

5. The footing settlement correspond with the maximum bearing strength as

obtained from the bearing strength tests on simulated floor strata in the laboratory

and using FEM analysis shows the minimum and maximum deviation of about 3

% and 14 % respectively.


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References

1. Johnston. I. W. Soft Rock Engineering. SME Handbook, J.A. Hudson (ed.); 1992,

Vol. I. p. 367-391

2. Serrano A, Olalla C. Ultimate bearing capacity of an anisotropic discontinuous

rock mass, part II: determination procedure. Int. J. Rock Mech. Min Sci. Vol. 35

(3); 1998. p. 325-348

3. ANSYS Release 6.1. ANSYS Structural Analysis Guide. ANSYS Inc. 001612;

2002

4. Kumar D, Das S. K. Experimental investigations into floor bearing strength of

jointed and layered rock mass. Proceedings of the 5th international conference on

analysis of discontinuous deformation (ICADD), Wuhan, P.R.China, Ben-Gurion

University of the Negev Beer Sheva, Israel; 2002. p. 87-93.

5. Kumar D, Das S. K. Estimation of weak floor strata properties and their influence

on floor bearing strength through physical modeling technique. Journal of the

Institution of Engineers (India), Vol. 82; 2002. p. 48-51.

6. Kumar D, Das S. K. Experimental investigation into floor bearing strength of

weak floor jointed rock mass,. Proceedings of the second international conference

on new development in rock mechanics and rock engineering (NDRM),

Shenyang, P. R. China; (2002). P. 167-172.

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