1
Suitability of the Typology of Shallow Foundations on Hill-Slopes
Rana Acharyya
Research Scholar, Department of Civil Engineering, Indian Institute of Technology Guwahati, Assam, India.
Email: [email protected]. ORCID No.: 0000-0003-4428-532X
Arindam Dey
Associate Professor, Department of Civil Engineering, Indian Institute of Technology Guwahati, Assam, India. Email:
[email protected] No.: 0000-0001-7007-2729
Abstract
Several theories and methodologies are proposed over the years to assess the ultimate bearing capacity of isolated or 1
interfering shallow footings resting on horizontal or sloping grounds. Progressive urbanization on the hill-slopes 2
presents the problem of multiple footings of various typologies coexisting on the crest or slope face, leading to a 3
complex failure and interaction mechanism. It is essential to delineate the suitability of various typologies of shallow 4
footing located on the slope crest, and their influence on the overall slope stability and bearing capacity. This paper 5
highlights the interaction mechanism of such coexisting footings, as well as the applicability of interconnected footings 6
on the hill-slopes to attain higher bearing capacity. The influence of multiple footings of identical or different 7
typologies on the slope stability and ultimate bearing capacity was investigated. It is observed that interconnecting the 8
isolated footings located near the slope face to those located away from the slope face provides a tieback mechanism, 9
and is beneficial in reducing the bearing stresses as well as increasing the resistance to the outward deformation of 10
slope face. Based on the outcomes, it is recommended to adopt specific interconnected foundations on hill-slopes to 11
ensure higher safety and sustainability. 12
13
Keywords: Shallow foundation on slopes; Footing typology: Interaction mechanism; Bearing capacity; Slope 14
stability; Interconnected footings 15
2
1.0 Introduction 16
The ultimate bearing capacity is considered the most important parameter for designing foundations. The ultimate 17
bearing capacity is the maximum load that the footing can carry without failure. From the earliest times, several 18
researchers had proposed the bearing capacity expression, bearing capacity factors (Nc, Nq and Nγ) and failure 19
mechanism for isolated shallow footing resting on the horizontal ground [1-5]. Apart from isolated shallow footing 20
on horizontal ground, numerical studies were conducted to estimate the bearing capacity of interfering strip footings 21
on horizontal ground and the corresponding bearing capacity factors [6-12]. 22
23
Apart from footings resting on horizontal ground, many practical cases can be found where footings are resting on the 24
slope, especially in the hilly terrains. Electric transmission towers and telephone towers over the slope, bridge 25
abutments on the slope face and water storage tanks on the hill-slopes are few examples of foundations on slopes. In 26
the hilly regions, buildings are mostly placed on unreinforced hill-slopes. Owing to the different type of failure 27
mechanism developed beneath the foundations placed on such slopes, it is imperative to study their bearing capacity 28
and the deformation characteristics. In this respect, based on experimental and theoretical investigations, a handful of 29
researchers had provided the ultimate bearing capacity and bearing capacity factors for strip footings located on the 30
cohesionless slopes and subjected to centric and eccentric loading [13-18]. With the aid of centrifuge test, Gemperline 31
[19] had proposed bearing capacity expression for strip footing on sandy slope. By altering the geometrical and 32
geotechnical parameters, some of the researchers have conducted experimental and numerical investigations to 33
evaluate the ultimate bearing capacity and failure mechanism of square, strip and circular footings located near the 34
slope [20-26]. Very few researchers had numerically investigated the bearing capacity and failure mechanism of 35
shallow footing positioned on c-φ soil slope [27-29]. The bearing capacity and failure mechanism of special types of 36
footings, such as skirted or micro-piled strip footings, located near the crest of the slope, was also reported [30-31]. 37
Clark et al. [32] had conducted field tests to estimate the bearing capacity and stability of square footings resting on 38
slope. Numerical and experimental investigations were also carried out to determine the ultimate bearing capacity and 39
failure mechanism of shallow footings resting on reinforced slope [33-37]. It was comprehended from the past 40
researches that investigations were mainly targeted for estimating the bearing capacity and failure mechanism of 41
isolated shallow footings resting on or near the slope. It can be well imagined from the practical scenarios that response 42
of single isolated shallow footing would be inadequate in representing the actual foundation scenarios in inhabited 43
3
hill-slopes. The growing demand of infrastructure development has led to the existence of buildings on the crest or 44
face of the hill-slopes in close vicinity to each other, leading to complex interaction between the foundations located 45
at same or different elevations. Further, it is very common to find coexisting shallow foundations, of multiple 46
typologies, on the hill-slopes owing to the presence of different types of closely spaced infrastructure having varying 47
design definitions of the foundations. In this regard, it is important to understand how coexisting typologies of footings 48
can alter the bearing capacity and resistance to deformation when placed on the slopes. These understandings would 49
aid in framing guidelines about the safe construction of building foundations, which would subsequently aid in 50
lessening the foundation failures on slopes and its aftermath. 51
52
In the above context, this paper highlights two common foundation issues prevalent in hill-slopes. Firstly, it addresses 53
the case study of a 14 m high 220KV transmission tower jeopardized due to toe cutting of the hill-slope. The tower 54
was located on the crest of hill-slope and supported on isolated square footings. Based on evaluated factor of safety, 55
the enhancement in the stability and the bearing capacity of foundations on hillslopes by an alternative footing 56
typology is highlighted, so that the transmission tower is able to sustain higher levels of distress without succumbing 57
to failure. Secondly, studies are carried out considering coexistence of different types and sizes of footing on the crest 58
of a hill-slope, so that a recommendation can be framed about the possible safest foundation types that could be 59
adopted in the hilly areas for generating enhanced bearing capacities and higher resistance against deformation towards 60
the slope. 61
62
2.0 Numerical Modelling 63
It is perceived from earlier researches that Plaxis 3D can be successfully utilized to estimate the ultimate bearing 64
capacity of shallow footings located on or near the slope [22, 25, 29]. In the current study, the suitability of the footing 65
types were assessed with the aid of finite element (FE) package Plaxis 3D vAE.01. Plaxis 3D is generally considered 66
for three dimensional analysis of stability, deformation and ground water flow in geotechnical engineering, and has 67
the ability to solve several complex issues related to geotechnical engineering. Advanced constitutive models can be 68
incorporated to investigate anisotropic, non-linear and time-dependent performance of soil or rock. 69
70
71
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2.1 Description of FE Model 72
The details of the technical procedure adopted in the present research to develop the geometry of the model can be 73
found in the literature [28-29]. The geometry of the model was optimally defined, such that the ‘0.1q’ significant stress 74
isobar does not intersect the boundaries of the model domain, as shown in Fig. 1 (q is the applied stress over the 75
footing). 76
77
78
Fig.1 Typical geometry configuration (Not to scale) 79
80
In the geometry, the ‘standard fixity’ was considered, wherein the horizontal fixity was provided to vertical 81
boundaries, while the bottom boundary of the model was considered non-deformable in all directions. The slope face 82
was allowed free deformation, thus, no fixity was considered in the face boundary. The model domain is discretized 83
by 10-noded tetrahedral element (Fig. 2). Based on a convergence study, the optimal mesh refinement scheme was 84
adopted, as detailed by Acharyya et al. [28]. Local refinement was considered in the model where large stress 85
concentration is possible. 86
87
5
88
Fig. 2 Typical configuration of meshing and boundary conditions 89
90
The foundation soil was modelled with Mohr-Coulomb (M-C) model. The M-C model is defined with the aid of a 91
combination of shear strength parameters (cohesion c, angle of internal friction φ, and angle of dilatancy ψ) and 92
deformation parameters (elastic modulus E, and Poisson’s ratio v). In the present investigation, the magnitude of 93
dilatancy (ψ) was taken as 2/3rd of angle of internal friction (φ) as provided in the researchers [38-39]. It is worth 94
mentioning that Mohr-Coulomb (MC) model does not include stress path dependency of stiffness, post-peak softening, 95
material anisotropy and time-dependent viscoelastic creep of soils. These mechanisms are more realistic to affect the 96
slope movement under prolonged saturation, and an advanced constitutive model may be more suitable. However, in 97
the absence of any other test data, the influence of advanced constitutive models are beyond the scope of the present 98
study. 99
100
3.0 Validation of Numerical Procedure Adopted 101
It is noted from the literature that very few researches exist that addresses the response of isolated shallow footings 102
located on or near the slope. It is observed that, until date, no research was carried out, in the form of classical analytical 103
solution or through experimental investigation, regarding interfering shallow footings on or near the slope. Few 104
numerical studies were conducted [43-44] for interfering strip footings on crest of slope with the aid of finite element 105
analysis. It was reported that, beyond a critical center to center spacing between footings of S = 3B (B = Width of 106
footing), the interaction effect of footings disappears and the footings behave as isolated footing resting on crest of 107
slope. In this regard, to validate and gain confidence on the numerical procedure adopted in the present study, the 108
experimental investigation conducted by Mittal et al. [45] is considered. The researchers evaluated the ultimate bearing 109
6
capacity (qu) of strip footing resting on crest of unreinforced sand-slope. A strip footing of width 75 mm located on 110
crest of sand-slope of inclination 34° and a setback distance of 1.5B was considered in the experiment [45]. In the 111
numerical study, interfering strip footings of identical dimension are considered. The footing nearer to the slope face 112
was provided with a setback distance of 1.5B, while a spacing of S = 10B was provided between the interfering footings 113
to reduce the interference effect to the best possible extent, which makes the footing nearer the slope should behave 114
like an isolated strip footing. Identical model dimensions and soil properties were considered for the numerical 115
problem as that adopted in the experimental investigation [45]. Figure 3 depicts the load-settlement behavior of the 116
strip footing located on the slope crest, which exhibits an appreciable agreement between the findings, thereby 117
validating the numerical model adopted in the present study. 118
119
Fig. 3 Comparison of ultimate bearing capacity –settlement patterns obtained from the numerical model and 120
experimental study [45] 121
122
4.0 Case Study of Electrical Transmission Tower Located on Slope Crest 123
This case study refers to the destabilization of Electrical Transmission Tower No. 26 of the 220 kV 4CKT Sarusajai-124
Jawahar Nagar line, at Sarusajai, Guwahati, Assam. The 14 m high tower, which forms the major component of the 125
electrical supply line to Guwahati city, is supported by isolated square footings of width 2 m beneath each of its legs, 126
having its foundation at a depth of 2 m. The legs of the transmission tower are at a distance of 3 m from each other, 127
0
1
2
3
4
5
6
7
0 20 40 60 80
S (
mm
)
qu (kPa)
Mittal et al. (2009)
Plaxis 3D
B = 75 mm, b/B = 1.5, β = 34
7
forming a square periphery. The tower is located on a hill-slope where a wide bench, created by excavation, forms the 128
slope crest. Figure 4 provides a schematic sketch of the stated problem. 129
130
In order to support soil filling in the bench, an uncoursed random rubble-masonry guard wall was constructed. The 131
height of the rubble masonry wall is nearly 3.7 m from its foundation base. During the establishment of the tower in 132
its early days, the rubble masonry wall had sufficient earth cover in the sloping direction on its three sides. The 133
surrounding area had been devoid of human inhabitation. In the recent past, increasing human inhabitation in the 134
surrounding area had led to an intensive amount of the slope and toe cutting, thus removing the supporting soil in 135
masses (Fig. 3). Accompanied by removal of the soil from the outward portions of the slope containing the guard wall, 136
instability has resulted in significant outward movement of the guard wall. The stability of overall system declined 137
further in the monsoon season due to heavy rain as well as seepage and percolation induced saturation of the hill-138
slope. 139
140
141
Fig. 4 Schematic diagram of Sarusajai transmission tower problem (Not to scale) 142
143
The case study was investigated through FE modelling of foundations on slopes. In order to model the geometry of 144
the hill-slope, the plan and elevation details were collected, as reported in Fig. 3. Further, to model the geotechnical 145
characteristics, undisturbed as well as disturbed samples were collected from two numbers of boreholes of 15 m depth 146
from the corresponding ground surface. Soil stratification and subsurface identification were carried out, as well as 147
8
the shear strength and stiffness properties were ascertained through laboratory tests. Based on the information from 148
exploratory borehole investigation (Table 1), it was observed that the soil characteristics were mostly uniform along 149
the depth of borehole. As a result, homogeneous soil was considered for the numerical investigation and modelling of 150
the hill-slope. The soil properties are listed in Table 2. The dimensions and the material properties of the footing (made 151
of M30 grade of reinforced concrete) were collected, and accordingly modelled with non-porous linearly elastic model. 152
The properties of the footing, as adopted in the numerical model, is given in Table 3. A suitable magnitude of interface 153
strength reduction factor (Rinter) should be considered for modeling the interface characteristics. In the present study, 154
the footing was modelled as a rough footing by considering the same strength and deformation properties as considered 155
for the adjacent soil elements (Rinter = 1). It is assumed that there is no relative slip between soil and footing. The 156
properties of rubble masonry retaining wall, as provided in Table 3, is considered from relevant literature [40, 41]. 157
The loads and the moments developed at the base of tower (as transmitted to the footings) was calculated with the aid 158
of IS-802 (Part 1/Sec 1) [41]. The details of parameters, vertical load and moment is provided in the Table 4. 159
160
Table 1 Variation of shear strength parameters in the borehole 161
Bore Hole Description of strata Depth (m) c (kN/m2) φ (°)
BH1
Reddish Sandy clay
3.0
4.5
6.0
7.5
9.0
10.5
13.5
15.0
10
10
10
10
10
9
10
10
24
24
25
25
25
25
25
25
BH2
Reddish sandy clay colour
3.0
4.5
6.0
7.5
9.0
10.5
13.5
15.0
10
10
10
10
10
9
10
10
24
25
25
25
25
25
25
26
162
163
164
165
166
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Table 2 Soil Properties as used in the FE modeling 167
Type of soil Unit weight (γ)
(kN/m3)
Modulus of elasticity
(E)(MPa)
Cohesion
(c) (kPa) φ(°)
Foundation soil 17 10 10 25
168
169
Table 3 Properties of footing and rubble masonry as used in FE modeling of the case study 170
Material type Type of material behavior Unit weight (γ) (kN/m3) Modulus of elasticity (E)(GPa)
Concrete Linear elastic and non-porous 25 27
Rubble masonry Linear elastic and non-porous 22.75 12
171
172
Table 4 Parameters considered for calculating the load and moment of tower 173
Parameters Magnitudes
Risk Coefficient (K1) 1.0
Terrain Roughness Coefficient (K2) 1.0
Design wind speed (Vd) 50 m/s
Design Wind Pressure (Pd) 1500 N/m2
Drag coefficient (Cdt) 3.6
Total net surface area (Ae) 3.15 m2
Gust response factor (GT) 1.92
Vertical load on each footings 63 kN
Moment acting on each footing 60 kN-m
174
175
4.1 Safety and Stability Analysis 176
‘Phi-c reduction technique’ was utilized to compute the global safety factor. In the adopted technique, the shear 177
strength parameters, φ and c, are successively reduced until failure of the structure occurs. The dilatancy angle ψ is, 178
in principle, not affected by phi-c reduction procedure. However, the dilatancy angle, in general, is never larger than 179
the friction angle. Thus, when the friction angle φ has been reduced to such extent that it becomes equal to the given 180
10
dilatancy angle ψ, any further reduction of friction angle leads to identical reduction of dilatancy angle. The strength 181
of interfaces, if used, is reduced in the same way. Optionally, the strength of structural objects like plate and anchors 182
can also be reduced in the safety calculation. The total multiplier ∑Msf is used to define the value of soil strength 183
parameters at a given stage in the analysis, and is determined from Eq. 1. Safety factor (SF) can be obtained as per 184
Eq. 2. 185
,
,
tan Tensile strength
tan Tensile strength
input input u input input
sf
reduced reduced u reduced reduced
c sM
c s
(1) 186
sf failure
SF M (2) 187
4.2 Discussions and Interpretations 188
In the current investigation, the overall stability of the tower on the crest of slope was inspected through safety analysis. 189
In the present analysis, the safety factors (SF) were determined for different stages of construction. The stages are as 190
follows. 191
Safety factor for virgin slope under both dry and wet (or, saturated) conditions 192
Safety factor after construction of transmission tower and rubble masonry wall on the crest and slope face, 193
respectively (for both dry and wet conditions) 194
Safety factor after toe cutting (for both dry and wet conditions) 195
In the present analyses, the dry and wet conditions are simulated by the saturation level of the soil. In dry condition, 196
the pore-water pressures are not considered in the soil slope, and a total stress analysis is considered; whereas, in the 197
wet conditions, the slope soil is considered to be fully saturated, and accordingly, an effective stress analysis is 198
conducted. 199
The foremost intention for conducting the stability analysis under various conditions was to make a forensic study to 200
infer the condition that led to the impending failure of the slope, and correspondingly validate the FE model with the 201
field information. For analyzing the stability of the transmission tower, the safety analysis started with the virgin slope 202
and sequentially to the toe cutting. In the analysis, firstly, the dry virgin slope was modelled (Fig. 5a) and the global 203
safety factor was determined. Thereafter, the isolated square footings of transmission tower, with incumbent loads and 204
moments, and rubble masonry wall were activated, and the corresponding safety factor was estimated (Fig. 5b). 205
Finally, the toe cutting was simulated and the safety factor was assessed (Fig. 5c). The above said procedures were 206
11
followed for wet conditions as well to illustrate the reduction of stability under the rainfall-saturated conditions, and 207
the corresponding safety factors were assessed. 208
209
210
(a) Virgin slope 211
212
(b) Transmission tower and boulder wall on slope (Arrangement F1) 213
214
(c) Toe cutting 215
Fig. 5 Different stages of numerical investigation as applied for the case study 216
217
12
Figure 6 portrays the safety factors (SF) obtained for different stages of numerical analysis. It can be seen that the SF 218
for dry and wet virgin slopes are 1.57 and 1.51, respectively. Further, after the construction of tower and rubble 219
masonry wall, the SFs are reduced to 1.39 and 1.26 for dry and wet slopes, respectively. Finally, due to toe cutting, 220
the SFs are further reduced to 1.18 and 1.11 for dry and wet slopes, respectively. 221
222
223
Fig. 6 Safety factors for various stages of analysis considering dry and saturated slopes 224
225
Based on the results, it can be stated that the virgin slope was stable under both dry and rainfall saturated conditions. 226
Similarly, it can be observed that although the presence of tower and rubble-masonry wall reduced the safety factors, 227
the reduction was not sufficient to lead to impending failure under both dry and saturated conditions. Further, it can 228
be noticed that toe cutting led to further reduction in the safety factors, highlighting the same to be a causal factor for 229
impending failure as the reduced SF reached nearly 1.1. It can be observed that even with toe cutting, the dry slope 230
exhibited a SF of approximately 1.18, while the saturated slope showed a SF of 1.1, highlighting impending failure of 231
the wet hill-slope. These observations reinforce the physical observation of the impending failure at the site where 232
major distress and outward movement leading to the cracking of rubble masonry was noted after the monsoon season 233
of 2014. 234
235
236
1.00
1.10
1.20
1.30
1.40
1.50
1.60
0.00 0.10 0.20 0.30 0.40
∑M
sf
Total displacement (U) (m)
Dry virgin slope
Wet virgin slope
Tower on dry slope
Tower on wet slope
Toe cutting for dry
slope
Toe cutting for wet
slope
13
4.2.1 Influence of Alternative Footing Typology on Stability 237
Apart from the original arrangement of 2×2 square footing (Arrangement F1) as used for the transmission tower, the 238
study is further extended to investigate the influence of footings of different shapes and arrangements on the possible 239
enhancement in the stability and the corresponding safety factors. Further numerical investigations were done for the 240
following arrangements (a) Rectangular footings perpendicular to slope face, obtained by connecting the 241
corresponding square footings (Arrangement F2 as in Fig. 7a), and (b) Grid footing formed by connecting all the 242
individual square footings (Arrangement F3 as in Fig. 7b). For all the alternative arrangements, the same stages of 243
analysis were followed as considered for isolated square footings, and the corresponding safety factor has been 244
determined. The loads and moments mobilized from the transmission tower were considered identical to that utilized 245
for isolated square footings. It is worth mentioning that the area of footing configurations is not same for the various 246
cases (F1, F2 and F3) as considered in the analysis. Although it is understood that the actual effect of footing shape 247
will be properly highlighted when the area of the footing remains the same, the study was not meant to investigate the 248
influence of shape of the footing on the FoS. The main intention of the present study was to identify the extent of 249
improvement in FoS when the isolated footings located on the crest of the slope are interconnected by various possible 250
configurations. Hence, in the present study, the area of the footing for various configurations are not maintained to be 251
the same. Further, it is to be noted that the actual construction sequence of various footing configurations was not 252
modelled through the numerical procedure adopted and is beyond the scope of the present study. 253
254
Figure 8 portrays the safety factors of the fully saturated hill-slope, subjected to toe cutting, while supporting the 255
transmission tower with alternative footing typologies. In the current investigation, only fully saturated condition was 256
considered, as such condition has yielded the least SF (in the previous analysis) and adjudged to be the critical 257
condition (Fig. 6). It can be observed that for both the arrangements of F2 and F3, the overall stability increased. When 258
there was no toe cutting, the SF of the slope supporting the transmission tower with footing typology F2 and F3 is 259
observed to be 1.35 and 1.48, respectively. Due to toe cutting, the SF values decreased to 1.19 and 1.24, respectively, 260
for footing typology F2 and F3. It can be noted that any of the above SFs are higher than that obtained for the case 261
when the transmission tower is supported on isolated square footings (F1); for such case, the SF was obtained as 1.26 262
and 1.11, respectively, before and after toe cutting. This confirms that the presence of interconnection between the 263
footings lead to enhanced stability of the foundations on slopes. 264
14
265
266
(a) Rectangular footings perpendicular to slope face (Arrangement F2) 267
268
(b) Grid footing formed by connecting isolated square footings (Arrangement F3) 269
Fig. 7 Different footing arrangement and typologies as adopted for case study 270
271
15
272
Fig. 8 Stability of the fully saturated hill-slope subjected to toe cutting and supporting the transmission tower having 273
various alternative footing typologies 274
275
Figure 9 exhibits that, even when toe cutting is not considered in the saturated hill-slope, various typologies of footing 276
exhibits varying magnitudes of total displacement towards the slope face. It can be observed that when the footings 277
located near the slope are connected to the ones located away from the slope, the latter produces a tieback mechanism, 278
thus restricting the outward movement of the former ones towards the slope. In this process, the resistance to 279
deformation increases, thus enhancing the stability of the hill-slope against failure and preventing consequent failure 280
of the supported structure. Similar observations in total outward displacement is noted when the toe cutting is carried 281
out, as illustrated in Fig. 10. Hence, based on the understanding of reduced outward displacements, it is recommended 282
to interconnect the footings placed near to the slope to those away from the slope, to ensure higher stability to the 283
foundations supported on slopes. 284
285
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
0.00 0.10 0.20 0.30 0.40
∑M
sf
Total displacement (U) (m)
Tower on wet slope
F1
Tower on wet slope
F2
Tower on wet slope
F3
Toe cutting for wet
slope F1
Toe cutting for wet
slope F2
Toe cutting for wet
slope F3
16
(a) 286
(b) 287
(c) 288
Fig. 9 Total displacement towards the slope face, generated in a typical section of slope passing through the base of 289
the footing, originating due to various footing typologies in absence of toe cutting of hill-slope (a) F1 (b) F2 (c) F3 290
17
(a) 291
(b) 292
(c) 293
Fig. 10 Total displacement towards the slope face, generated in a typical section of slope passing through the base of 294
the footing, originating due to various footing typologies in presence of toe cutting of hill-slope (a) F1 (b) F2 (c) F3 295
296
18
Figure 11 exhibits the total vertical stress generated at a typical section through the base of the footings supporting the 297
electric transmission tower, resting on the hill-slope without any toe cutting. It can be observed that isolated footing 298
arrangement F1 produces the maximum vertical stress owing to the smallest contact area of the individual footings. 299
The rectangular arrangement F2 and the grid arrangement F3 produce the reduced vertical stress owing to higher 300
contact area and larger dissipation of the superstructure load. Similar observation is made when the hill-slope is 301
subjected to toe-cutting; however, for the sake of brevity, the same is not presented here. Thus, it is recommended to 302
interconnect the footings so that the stresses transferred from the superstructure to the foundation soils also are 303
reduced. 304
305
As a consequence of toe cutting, Fig. 12 exhibits the total lateral stress towards the slope face, generated at a typical 306
section passing through the base of the footings supporting the electric transmission tower. It can be observed that F1 307
exhibits the maximum area of large outward horizontal stress towards the slope face, while F3 exhibits it as the least 308
stresses generated. Although the magnitude of maximum lateral stress generated for F2 is the higher than F1, as 309
observed earlier, the area of the section exhibiting higher stresses for F2 is lower as compared to F1. The observations 310
based on vertical and horizontal stresses well conform to the observations made earlier with respect to the 311
displacements. Based on the current findings, it is recommended to use interconnected footings for foundations on 312
slopes, which leads to simultaneous reduction of stress transferred to the foundation as well as generates lesser outward 313
deformation toward the slope face. 314
315
Figures 13 and 14 depict the incremental displacement mechanism developed beneath the footings of the transmission 316
tower resting on fully saturated slope. The developed mechanism is hereby illustrated for two footing typologies F1 317
and F2, considering both pre- and post-toe cutting scenarios. When the pre- toe-cutting scenario is considered (Fig. 318
13a and Fig. 14a), it can be observed that in comparison to F1, a larger bearing zone is created beneath F2, and a larger 319
volume of foundation soil is involved in producing the resistance to failure. 320
19
(a) 321
(b) 322
(c) 323
Fig. 11 Total vertical stresses generated in a typical section of slope passing through the base of the footing, originating 324
due to various footing typologies in absence of toe cutting of hill-slope (a) F1 (b) F2 (c) F3 325
326
20
(a) 327
(b) 328
(c) 329
Fig. 12 Total vertical stresses generated in a typical section of slope passing through the base of the footing, originating 330
due to various footing typologies in presence of toe cutting of hill-slope (a) F1 (b) F2 (c) F3 331
332
21
The mobilization of the shear resistance of this larger volume of soil leads to the enhancement in the bearing capacity. 333
Similar observation can be made for the post- toe-cutting scenario (Fig. 13b and Fig. 14b), wherein a larger soil mass 334
forms the passive resistance zone, thus leading to greater resistance against the slope failure. Further, from the 335
incremental displacement mechanisms, it can be ensured that for the present case study, the failure has taken place 336
mainly because of the toe cutting, and hence, the failure primarily confirms a slope stability failure rather than a 337
foundation failure. 338
339
340
(a) Incremental displacement before toe cut for isolated square footings 341
342
(b) Incremental displacement after toe cut for isolated square footings 343
Fig. 13 Typical failure mechanism of the hill-slope supporting an electric transmission tower resting on isolated square 344
footing (Arrangement F1) (a) Before toe cutting (b) After toe cutting 345
346
22
347
(a) Incremental displacement before toe cut for rectangular footing 348
349
(b) Incremental displacement after toe cut for rectangular footing 350
Fig. 14 Typical failure mechanism of the hill-slope supporting an electric transmission tower resting on rectangular 351
footing (Arrangement F2) (a) Before toe cutting (b) After toe cutting 352
353
5.0 Load Carrying Capacity of Different Footing Arrangements for Common Residential Buildings on Hill-354
Slopes 355
Based on the explanations and discussions of the mechanisms associated with the case study as elaborated earlier, the 356
current section illustrates the different footing arrangements that can be chosen as alternatives for common residential 357
buildings constructed on hills-lopes so that a higher bearing capacity can be ensured. Several footing typologies are 358
investigated, specifically 22 and 33 arrangements of the square footings, and customized arrangements created out 359
of their interconnections. For each of the different combinations, the bearing load was estimated. In the current 360
simulation, a constant setback distance (b) of 0.5B, embedment depth (Df) of 0.5B, and spacing between footings (S) 361
of 1.5B, were considered (B is the width of square footing). For the simulation, c-φ soil is considered as foundation, 362
the parameters (c = 10 kPa, φ = 25º, γ =17 kN/m3 and E = 10 MPa,) of which are adopted from the available literature 363
[22]. The footing properties are already provided in Table 3. 364
23
5.1 22 Arrangement of Square Footing and Its Various Interconnections 365
In this study, 22 square footings, each of size 2 m x 2 m, is interconnected in various patterns to create various 366
combinations of combined footings (Fig. 14) and the estimation of corresponding bearing capacity through the FE 367
analysis. The footings are considered to rest on the crest of a hill slope of height 5 m. Several slope inclinations have 368
been considered in the analysis. In all the simulations, centric vertical loading has been considered, and the footing 369
systems have been led to failure. 370
371
372
(a) 2 2 isolated square footings on slope crest (Arrangement 2S-I) 373
374
375
(b) Rectangular footings formed by connecting square footings parallel to the slope face (Arrangement 2S-R1) 376
24
377
(c) Rectangular footings formed by connecting square footings perpendicular to the slope face (Arrangement 2S-R2) 378
379
(d) Crossed rectangular footings formed by connecting square footings located opposite to each other (Arrangement 380
2S-C) 381
382
383
(e) Grid footings formed by connecting all the square footings (Arrangement 2S-G) 384
Fig. 15 Various footing typologies comprising of 22 square footings and their various combinations 385
25
386
Table 4 portrays the load bearing capacity of different 22 arrangements of the square footings and their various 387
interconnected forms. The load carrying capacity of different arrangements were checked for different slope angles 388
(β). The slope angle was varied from 10° to 40°. It is observed that the grid footing made by connecting all the square 389
footings (2S-G) possess maximum load carrying capacity than any other arrangements. It is perceived from Table 3 390
that rectangular footings perpendicular to slope face (2S-R2) shows higher load carrying capacity than isolated square 391
footings or the rectangular footings located parallel to slope face (2S-R1). This is attributed to the fact that when 392
rectangular footings are arranged parallel to slope face (2S-R1), higher length of footing interacts with the slope face 393
leading to a bigger active zone of outwards lateral displacement towards the slope face. Such phenomenon reduces 394
the bearing capacity of 2S-R1 arrangement in comparison to the case when rectangular footings are located 395
perpendicular to the slope face (2S-R2). For the latter case, much lesser soil volume participates in the formation of 396
sliding zone towards the slope face. Further, the perpendicularly placed rectangular footing drives its resistance from 397
the far end of the same, thus exhibiting a higher bearing capacity. It is seen from Table 5 that the load carrying 398
capacity of cross-connected rectangular (2S-C) footing and footing connecting isolated square footings (2S-G) are 399
more than isolated square footings and rectangular footings. It confirms the fact that as the footing area increases; the 400
load on the footing will spread over the larger area in the subsoil, thereby increasing the bearing capacity. 401
402
403
Table 5 Load carrying capacity of various arrangements of 22 square footings 404
Footing typologies obtained from
22 arrangement
Slope inclination (βº)
10º 20º 30º 40º
Load carrying capacity (MN)
2S-I 10.05 8.13 6.09 4.06
2S-R1 12.6 9.48 6.68 4.41
2S-R2 14.39 13.65 12.38 10.10
2S-C 20.23 17.94 14.79 10.96
2S-G 24.32 21.33 17.46 12.39
405
26
406
5.2 3 3 Arrangement of Square Footing and Its Various Interconnections 407
Similar to the earlier arrangements, in this section, 33 square footings, each of size 2 m 2 m, has been interconnected 408
in various patterns to create various combinations of combined footings (Fig. 16) and investigated for their bearing 409
capacity. As earlier, the footings are considered to rest on the crest of a hill slope of height 5 m. Several slope 410
inclinations have been considered in the analysis. In 33 arrangements, different combinations have been taken into 411
account in the numerical study, specifically square footings, strip footings, connected square footings, as well as 412
rectangular, strip and raft footings. In all the simulations, centric vertical loading has been considered, and the footing 413
systems have been led to failure. 414
415
416
(a) 33 isolated square footings on slope crest (Arrangement 3S-I) 417
418
419
(b) Strip footings formed by connecting square footings perpendicular to the slope face (Arrangement 3S-S) 420
27
421
(c) Grid footings formed by connecting square footings (Arrangement 3S-G) 422
423
(d) Raft footing formed by connecting all square footings (Arrangement 3S-R) 424
425
(e) Mixed interconnection to develop combined arrangement of raft and strip footings parallel and perpendicular to 426
slope face (Arrangement 3S-S1-S2-R) 427
28
428
(f) Mixed interconnection to develop combined arrangement of raft and strip footings perpendicular to slope face 429
(Arrangement 3S-S2-R) 430
Fig. 16 Various footing typologies comprising of 33 square footings and their various combinations 431
432
Table 6 depicts the load bearing capacity of different 33 arrangements of the square footings and their various 433
interconnected forms. It is observed that raft (3S-R) footing having maximum load carrying capacity than all other 434
arrangements used in the simulation. Increase of load bearing capacity confirms the fact that a greater footing width 435
involves a larger soil domain to support the incumbent load. It is observed that the load carrying capacity of strip 436
footings (3S-S) is more than isolated square footing (3S-I). It is perceived that the load bearing capacity marginally 437
varies for Arrangement 3S-S, Arrangement 3S-S1-S2-R and Arrangement 3S-S2-R. It has been revealed that the load 438
carrying capacity of footing connected all square footing is more than isolated square footings (3S-I), or for 439
arrangements 3S-S1-S2-R and 3S-S2-R. 440
441
442
443
444
445
446
447
448
29
Table 6 Load carrying capacity of various arrangements of 33 square footings 449
Footing typologies obtained from
33 arrangement
Slope inclination (βº)
10º 20º 30º 40º
Load carrying capacity (MN)
3S-I 11.87 9.59 7.07 4.58
3S-S 17.77 16.81 15.46 13.41
3S-S1-S2-R 17.81 17.57 16.69 14.02
3S-S2-R 19.13 18.46 17.42 15.60
3S-G 47.85 42.57 35.12 24.04
3S-R 65.48 52.91 38.90 28.24
450
451
6.0 Conclusions 452
In the present investigation, a case study is taken into account to analyze the stability of an electric transmission tower 453
resting on crest of sloping ground, supported on isolated square footings. A forensic study is conducted with the aid 454
of FE simulations to identify the root cause of impending failure of the structure, which was recognized as the toe 455
cutting of the hill-slope. Further, different alternative footing typologies were used to check the possibility in 456
enhancing the bearing and deformation resistance of the system. It was observed that in comparison to the isolated 457
square footings, the safety factor enhanced by notable magnitudes for considering interconnected rectangular footing 458
and grid footings. It was understood that the presence of interconnecting the footings placed near the slope crest with 459
those located away from the slope crest would provide a tieback mechanism and generate more restraint against free 460
outward and lateral deformation towards the slope face. Further, the increased area of the footing due to the 461
interconnection, the increase in the footing area reduces the stress transferred to the foundations, thus also aiding in 462
increase of the bearing capacity of the foundations on slopes. Further, in order to investigate the influence of 463
coexistence of the multiple footing typologies on the load carrying capacity, as commonly experienced in closely 464
spaced habitations in the hill-slopes, the study is enhanced to consider various arrangements of 2×2 and 3×3 square 465
footings and their interconnections. In 2×2 arrangement, with respect to the isolated footings resting on the slope crest, 466
the average load carrying capacity increased for various interconnected forms of footings, in which the grid connection 467
30
exhibited maximum enhancement. The average load carrying capacity for rectangular footings perpendicular to slope 468
face is observed to be higher than the rectangular footings parallel to the slope. For the 3×3 arrangements, it is noted 469
that raft footing exhibits maximum bearing capacity than any other arrangements. 470
471
Based on the understanding developed, it is prescribed to interconnect footings to enhance their load carrying capacity 472
and resistance against deformation towards slope. Interconnecting shallow footings resting near the crest of a slope 473
with those located away from the slopes provides an effective means of enhancing the bearing resistance of the shallow 474
foundation grid for buildings located on hilly terrains. Footings located away from the crest act as additional ties to 475
those located near the crest, and prevents the latter from free deformation towards the slope face, thus enhancing the 476
overall bearing resistance of the foundation. It is recommended to provide such interconnections, perpendicular to the 477
slope face, for more sustainable foundations on slopes. 478
479
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