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: r.acharyya@iitg.ac.in. ORCID No.: 0000-0003-4428-532X

Arindam Dey

Associate Professor, Department of Civil Engineering, Indian Institute of Technology Guwahati, Assam, India. Email:

arindamdeyiitg16@gmail.com.ORCID 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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