A FAILURE ENVELOPE APPROACH FOR CONSOLIDATED … · 2020. 10. 7. · Published in ASCE Journal of...
Transcript of A FAILURE ENVELOPE APPROACH FOR CONSOLIDATED … · 2020. 10. 7. · Published in ASCE Journal of...
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Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
142(8), August http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
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A FAILURE ENVELOPE APPROACH FOR CONSOLIDATED 1
UNDRAINED CAPACITY OF SHALLOW FOUNDATIONS 2
Cristina VULPE (corresponding author) 3
Centre for Offshore Foundation Systems & ARC Centre of Excellence 4
M053 University of Western Australia 5
35 Stirling Highway, Crawley, Perth, WA 6009, Australia 6
Tel: +61 8 6488 7051, Fax: +61 8 6488 1044 7
Email: [email protected] 8
9
Susan GOURVENEC 10
Centre for Offshore Foundation Systems & ARC Centre of Excellence 11
M053 University of Western Australia 12
35 Stirling Highway, Crawley, Perth, WA 6009, Australia 13
Tel: +61 8 6488 3995, Fax: +61 8 6488 1044 14
Email: [email protected] 15
16
Billy LEMAN (formerly a student at The University of Western Australia) 17
Wellbore Intervention Engineer 18
Baker Hughes Incorporated 19
256 St Georges Terrace, Perth, WA 6000, Australia 20
Tel: +61 8 9455 0174 21
Cell: +61 406 773 974 22
Email: [email protected] 23
24
Kah Ngii FUNG (formerly a student at The University of Western Australia) 25
Design Assistant 26
CIMC Modular Building Systems (Australia) Pty Ltd 27
Level 10, 553 Hay Street, Perth, 6000 WA 28
Tel: +61 8 6214 3803 29
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Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
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Email: [email protected] 30
No. of words: 4921 (exc. Abstract and References) 31
No. of tables: 4 32
No. of figures: 20 33
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Abstract: 35
A generalized framework is applied to predict consolidated undrained VHM failure 36
envelopes for surface circular and strip foundations. The failure envelopes for 37
consolidated undrained conditions are shown to be scaled from those for unconsolidated 38
undrained conditions by the uniaxial consolidated undrained capacities, which are 39
predicted through a theoretical framework based on fundamental critical state soil 40
mechanics. The framework is applied to results from small strain finite element analyses 41
for a strip and circular foundation of selected foundation dimension and soil conditions 42
and the versatility of the framework is validated through a parametric study. The 43
generalised theoretical framework enables consolidated undrained VHM failure 44
envelopes to be determined for a practical range of foundation size and linearly 45
increasing soil shear strength profile, through the expressions presented in this paper. 46
Key words: consolidation, bearing capacity, combined loading, failure envelope 47
48
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Introduction 50
Shallow foundations are often subjected to combined vertical, horizontal and moment 51
(VHM) loading, particularly in a marine environment, derived from environmental or 52
operational loading. Significant research has been carried out on the undrained capacity 53
of shallow foundations under combined VHM loading (e.g. Martin & Houlsby 2001, 54
Bransby & Randolph 1998, Ukritchon et al. 1998, Taiebat & Carter 2000, Gourvenec & 55
Randolph 2003, Gourvenec 2007a, b, Bransby & Yun 2009, Gourvenec & Barnett 2011, 56
Vulpe et al. 2013, Vulpe et al. 2014, Feng et al. 2014). Limited insight has been offered 57
into the consolidated undrained response of shallow foundation systems, and most 58
studies have investigated the consolidation effect on undrained vertical bearing capacity 59
only (e.g. Zdravkovic et al. 2003, Lehane & Jardine 2003, Lehane & Gaudin 2005, 60
Chatterjee et al. 2012, Gourvenec et al. 2014, Vulpe & Gourvenec 2014, Fu et al. 2015) 61
and seldom combined capacity (Bransby 2002). 62
Undrained geotechnical resistance of a shallow foundation under any load path is 63
dependent on the undrained shear strength of the supporting soil and can be increased 64
by improvement of the undrained soil strength in the vicinity of a foundation. 65
Consolidation due to preloading (including the self-weight of the foundation and the 66
structure that it supports) causes the undrained shear strength of supporting soils to 67
increase non-uniformly with depth and lateral extent, consistent with the pressure bulb 68
developed from the applied foundation load. The soil immediately below the foundation 69
experiences the largest change in shear strength, diminishing to the in situ strength in 70
the far field. The degree of enhanced geotechnical resistance of a foundation is 71
governed by the degree of overlap between the zone of undrained soil strength 72
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improvement and the zone of soil involved in the kinematic mechanism accompanying 73
subsequent failure. 74
In the case of pure horizontal loading, failure occurs in the uppermost soil layer 75
coinciding with the zone of maximum shear strength increase – and considerable gain in 76
sliding resistance would therefore be expected. In the case of pure vertical loading, the 77
classical Prandtl or Hill failure mechanisms will extend laterally beyond the zone of 78
enhanced soil strength and therefore less relative increase in vertical bearing capacity 79
would be expected. A spectrum of kinematic mechanisms accompany failure under 80
combined VHM loading with maximum relative gains to be achieved in cases of 81
greatest overlap between the zone of maximum shear strength increase and the 82
governing failure mechanism. Since many structures are affected by multi-directional 83
loading, of duration to invoke an undrained soil response, the consolidated undrained 84
response under three-dimensional loading of shallow foundations is of considerable 85
practical interest. Particular applications include 1) reassessing the capacity of existing 86
foundations to withstand future or additional moment and horizontal loading, 2) 87
studying a foundation failure via back-calculation, and 3) reliance on consolidated 88
undrained strength for geotechnical shallow foundation design, for example for subsea 89
structures for which the foundation is set down, and the surrounding soil consolidates 90
under the foundation and structure self-weight for a period of time (often several 91
months or a year) in advance of operation at which stage multi-directional loading is 92
applied. 93
The study presented in this paper systematically investigated the effects of the relative 94
magnitude and duration of vertical preload on the undrained uniaxial vertical (V), 95
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horizontal (H) and moment (M) capacity and combined VHM capacity of circular and 96
strip surface foundations through finite element analyses (FEA). 97
Consolidated undrained capacities, Vcu, Hcu and Mcu, calculated in the FEA are 98
predicted through a recently developed generalised critical state framework for shallow 99
foundations (Gourvenec et al., 2014) while the normalised VHM interaction is shown to 100
scale with relative preload and degree of consolidation through the consolidated 101
undrained capacities. 102
The actual relative gains calculated by the FEA are particular to the foundation and soil 103
conditions considered – but the theoretical framework, with the stress and strength 104
factors provided in this paper, can be applied to a range of foundation dimensions and 105
soil properties (and therefore undrained shear strength profiles). The encapsulating 106
critical state framework extends the outcome of the results beyond the particular 107
foundation dimension and soil conditions considered in the FEA to a generalised 108
solution. 109
The value of this study lies in the demonstration that: 110
(i) consolidated undrained uniaxial capacities, Vcu, Hcu and Mcu can be predicted by the 111
generalized critical state framework presented; and 112
(ii) consolidated undrained VHM failure envelopes scale from the unconsolidated 113
undrained VHM failure envelope according to the consolidated uniaxial capacities 114
(which can be predicted through the theoretical framework outlined in (i)). 115
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Finite element model 116
The study is based on small strain finite element analyses carried out with the 117
commercial code Abaqus (Dassault Systèmes 2012). 118
Foundation geometry 119
Rigid circular and strip surface foundations with unit diameter (D) or breadth (B) were 120
analysed in the FEA, i.e. D = B was nominally taken as 1 m. The particular foundation 121
size selected for the FEA presented in the paper is arbitrary. A unit width foundation 122
was selected for illustration of the theoretical framework, which can be applied to any 123
foundation dimension through the dimensionless groups that the results are presented in. 124
This generality is demonstrated in the Results section. 125
Soil conditions and material parameters 126
Normally consolidated (NC) clay with linearly increasing shear strength with depth was 127
considered. Cam Clay parameters used in this study are based on element testing on 128
kaolin clay (Stewart 1992, Chen 2005) and are summarized in Table 1. The soil 129
behaviour is defined by a poro-elastic constitutive relationship pre-yield and by the 130
Modified Cam Clay critical state constitutive model post-yield. The specific gravity of 131
the soil is assumed constant and equal to 2.6, giving the buoyant unit weight as a 132
function of initial void ratio e0. 133
The coefficient of earth pressure at rest, after normal consolidation, is defined by 134
cs0 sin1K φ−= 1
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where ϕcs is the critical state internal friction angle. The in situ effective stresses vary 135
accordingly to the prescribed soil unit weight (Table 1). The initial size of the yield 136
envelope is prescribed as a function of the initial stresses in the soil 137
'0'
02cs
20'
c ppMqp += 2
where p0' and q0' are the in situ mean effective stress and deviatoric stress, respectively. 138
Mcs represents the slope of the critical state line and takes the form: 139
cs
cscs sin3
sin6Mφ−φ
= 3
The in situ density of the soil is taken into account through the initial void ratio, e0: 140
( ) 'c'010 plnplnee κ−λ−κ−= 4
with 141
( ) ( )2lnee cs1 κ−λ+= 5
The equivalent undrained shear strength of the normally consolidated clay layer is 142
calculated from the critical state parameters using the expression given by Potts & 143
Zdravkovic (1999): 144
( ) ( )λκ
−
++θθ=
σ
120
'v
u
2A1
3K21cosgs 6
where θ = -30° is the Lode angle for triaxial conditions to ensure equilibrium of the K0 145
consolidated initial stress state; σ'v is the in situ effective vertical stress; and 146
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( ) ( )
cs
cs
sinsin3
1cos
singφθ+θ
φ=θ
7
( )( )( )0
0
K2130gK13A+−
−=
8
For the initial set of analyses, an overburden pressure σ′vo equivalent to 1 m depth of 147
soil was imposed across the free surface to define a non-zero shear strength at the 148
mudline in the MCC model. The resulting undrained shear strength profile is linear with 149
depth of the form 150
zkss suumu += 9
where su represents the undrained shear strength at depth z, sum is the mudline strength 151
and ksu is the strength gradient. For the soil properties given in Table 1 and considered 152
in the initial set of FEA, sum = 4.79 kPa and ksu = 1.75 kPa/m. 153
The magnitude of the initial overburden pressure, and hence mudline strength, affects 154
the magnitude of unconsolidated undrained capacity and relative gain in consolidated 155
undrained capacity. However, the generalised framework presented to predict the 156
consolidated capacity gains incorporates the effect of initial overburden, such that the 157
methodology presented is applicable to a practical range of overburden (and foundation 158
breadth or diameter). This is demonstrated in the Results section. 159
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Finite element mesh 160
Three dimensional (3D) and plane strain finite element meshes were used to model the 161
circular and strip foundation conditions respectively. Due to symmetry along the 162
vertical centreline of the circular foundation, only half of the problem was modelled. A 163
schematic representation of the plane strain finite element model is illustrated in Figure 164
1 and an example mesh is shown in Figure 2. The circular foundation model was 165
constructed with boundary conditions and mesh discretisation in-plane identical to the 166
plane strain model. The mesh boundaries extend 10 times the foundation diameter or 167
breadth both horizontally and vertically from the centreline of the foundation in order to 168
ensure the foundation response is unaffected by the boundary. Horizontal displacement 169
was constrained on the vertical mesh boundaries and horizontal and vertical 170
displacements were constrained across the base of the mesh. The free surface of the 171
mesh, unoccupied by the foundation, was prescribed as a drainage boundary; the other 172
mesh boundaries and the foundation were modelled as impermeable. 173
The circular and strip foundations were represented as rigid bodies with a single 174
reference point (RP) located at the foundation centreline along the foundation-soil 175
interface. The foundation-soil interface was defined as fully bonded, i.e., rough in shear 176
and no separation permitted to represent that of shallowly skirted foundations, 177
commonly used offshore. In reality, a skirted foundation comprises a top plate equipped 178
with a peripheral skirt that penetrates into the seabed confining a soil plug. Negative 179
excess pore pressures generated between the underside of the top plate and the soil plug 180
enable tensile resistance (relative to ambient pressure) to be mobilised. It is common 181
practice to model skirted foundations as a surface foundation with a fully bonded 182
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foundation-soil interface (e.g. Tani & Craig 1995, Ukritchon et al. 1998, Bransby & 183
Randolph 1998, Gourvenec & Randolph 2003, Yun & Bransby 2007). The plane strain 184
and 3D finite element models were created with similar mesh discretisation in-plane 185
with an optimum number of elements of 6,500 for the plane strain model and 20,000 for 186
the 3D model. 187
Scope and loading methods 188
Initially, the unconsolidated undrained uniaxial vertical capacity, denoted Vuu, was 189
determined for each foundation geometry through a displacement-controlled uniaxial 190
vertical load path to failure. These analyses were carried out with the soil modelled as 191
both a Modified Cam Clay (MCC) material and Tresca material to ensure consistency of 192
results between constitutive models and with existing data. A series of MCC analyses 193
was then carried out to determine the consolidated undrained capacity. In each analysis, 194
the foundation was preloaded by a fraction of the unconsolidated undrained uniaxial 195
vertical capacity, denoted Vp/Vuu (each foundation geometry was preloaded relative to 196
the relevant undrained uniaxial vertical capacity, Vuu, and Vp was additional to the 197
overburden pressure acting). The soil was then permitted to consolidate under the 198
prescribed vertical preload before bringing the soil to undrained failure. 199
Relative preload, Vp/Vuu, was applied at intervals of 0.1 from 0.1 to 0.7 and partial or 200
full primary consolidation was permitted prior to undrained failure. Periods 201
corresponding 20, 50 and 80% of full primary consolidation, denoted T20, T50 and T80, 202
respectively, were considered. 203
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Following vertical preloading and consolidation for T20, T50, T80 and T99, the soil was 204
brought to undrained failure by means of displacement-controlled tests to determine the 205
uniaxial consolidated undrained capacities, denoted Vcu, Hcu and Mcu, or by constant-206
ratio displacement probes to obtain the consolidated undrained capacities in VHM 207
space. Pure uniaxial consolidated undrained capacity in each direction was obtained in 208
the absence of other loadings other than the applied preload (e.g. Vcu for H = 0 and M = 209
0, but Hcu for V = Vp and M = 0). Consolidated undrained failure envelopes were 210
determined by first applying the preload level as a direct force on the foundation, and 211
after consolidation, applying a constant-ratio displacement probe, u/Dθ, to failure 212
(where u represents the horizontal translation and θ represents the rotation applied to the 213
foundation reference point). 214
Sign convention and nomenclature 215
The sign convention for loads and displacements follows a right-handed axes and 216
clockwise rotations rule, as proposed by Butterfield et al. (1997). The notations adopted 217
for unconsolidated undrained and consolidated undrained capacities are summarized in 218
Table 2. 219
Results 220
Validation 221
Unconsolidated undrained ultimate limit states were defined with both the Tresca and 222
Modified Cam Clay constitutive models using the commercial finite element software, 223
Abaqus. For the Tresca analyses, the Menetrey-Willam deviatoric ellipse function is 224
used with the out-of-roundedness parameter, e, set to 1, giving a Von Mises circular 225
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flow potential surface in the deviatoric plane while the yield surface remains the regular 226
Tresca hexagon. For the MCC analyses, a Von Mises circular yield surface is used, by 227
setting the flow stress ratio, K = 1. 228
The finite element models were validated against theoretical solutions where available. 229
The undrained (unconsolidated) uniaxial vertical capacity predicted by the finite 230
element models using the Tresca criterion was validated against lower bound solutions 231
(Martin 2003) and agreed to within 2% for both the circular and strip foundation 232
geometries. The undrained unconsolidated horizontal capacity of the surface 233
foundations was compared with the theoretical solution (Huu/Asu0 = 1) and the 234
undrained unconsolidated moment capacity was compared with theoretical upper bound 235
solutions (Murff & Hamilton 1993, Randolph & Puzrin 2003). Both horizontal and 236
moment capacities of the strip foundations agreed with the theoretical solutions to 237
within 6% difference while the results diverged by 10% for the circular foundation due 238
to poor representation of a spherical scoop failure mechanism with hexahedral elements. 239
A mesh refinement study was undertaken to determine the optimum mesh discretisation 240
for both foundation types by gradually increasing the number of elements around the 241
foundation where the failure mechanism developed until further refinement did not 242
improve the result. 243
The dissipation response calculated in the FEA cannot be directly validated against the 244
classical elastic solution of time-settlement response (Booker & Small 1986) as the 245
coefficient of consolidation, cv, changes during the analysis with the elasto-plastic 246
critical state model, in contrast to the constant cv conditions of the elastic analysis. The 247
consolidation response from the tests is discussed in more detail below. 248
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Consolidation response 249
The dissipation response under preloading of the foundations is illustrated in Figures 4 250
and 5 as time histories of consolidation settlement, wc, normalised by foundation 251
dimension (diameter D or breadth B) and by the final consolidation settlement, wcf, 252
measured at the centreline of the foundation along the foundation-soil interface. The 253
immediate settlement following preloading is deducted from the total settlement to give 254
the consolidation settlement, wc. Time is expressed by the dimensionless factor 255
20v
DtcT = ; 2
0v
BtcT = 10
where t represents the consolidation time, D or B is the foundation diameter or breadth 256
and cv0 is the initial coefficient of consolidation: 257
( )w
'00
0vpe1kc
λγ+
= 11
where k is the permeability of the soil, λ is the slope of normal compression line and γw 258
= 9.81 kN/m3 is the unit weight of water. 259
Figure 4 shows that consolidation settlement increases with increasing relative preload 260
and is greater for the strip foundation compared with the circular foundation. Smaller 261
settlements (half the magnitude) were obtained under the same level of relative preload 262
in the same soil conditions for the circular foundation compared to the strip foundation 263
due to lateral load shedding under three-dimensional conditions. Figure 5 shows that 264
axisymmetric flow and strain around the circular foundation leads in general to a 265
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reduction in dissipation time of around one order of magnitude compared with plane 266
strain conditions. 267
The normalised time-settlement relationship for the circular foundation from the finite 268
element analyses, modelled with critical state coupled consolidation constitutive model, 269
agrees well with the classical elastic solution (Booker & Small 1986) initially, but as 270
consolidation progresses, the elasto-plastic soil consolidates at a faster rate owing to the 271
increasing stiffness of the soil as effective stresses increase. No elastic consolidation 272
solution is available for a strip foundation. 273
Effect of full primary consolidation on uniaxial V, H and M capacity 274
Figure 6 shows the gain in uniaxial capacity as the ratio of the consolidated undrained 275
capacity to the unconsolidated undrained capacity for vertical (vcu = Vcu/Vuu), horizontal 276
(hcu = Hcu/Huu) and moment (mcu = Mcu/Muu) loading. Results are shown for the circular 277
and strip foundations after vertical preloading and full primary consolidation. The term 278
uniaxial is usually reserved for loading in one direction with zero loading in any other 279
direction, e.g. uniaxial H loading in the absence of vertical load or moment. In this 280
paper, the term uniaxial is taken to define loading in only one direction over and above 281
the vertical preload, e.g. uniaxial H loading in the presence of the vertical preload but no 282
additional vertical load or moment. 283
The relative gain in capacity increases with the level of vertical preload under each load 284
path and potentially significant gains are achieved in each case. The highest relative 285
gain in capacity is observed under horizontal loading (following vertical preload and 286
consolidation). The lowest relative gain is observed under vertical loading (following 287
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vertical preload and consolidation). Shape effects were not observed in the relative gain 288
in capacity under vertical and horizontal loading, while a greater relative gain in 289
moment capacity was observed for the strip foundation than the circular foundation. The 290
observed trends in relative gain in capacity can be explained by considering the 291
interaction between the zone of shear strength increase and the kinematic mechanisms 292
accompanying failure. 293
Figure 7 compares the increase in shear strength due to full primary consolidation 294
beneath circular and strip foundations for levels of relative preload Vp/Vuu = 0.1, 0.4 and 295
0.7. The change in undrained shear strength is illustrated through contours of enhanced 296
soil strength relative to the in situ value, su,f/su,i defined as 297
λ−
= f0i,u
f,u eeexpss 12
where su,i and su,f are the in situ and final (i.e. post-consolidation) shear strength, e0 and 298
ef are the in situ and final void ratio and λ is the virgin compression index for kaolin 299
clay (Stewart 1992). 300
The extent of the zone of enhanced shear strength increases with level of relative 301
preload and is more extensive beneath the strip foundation than the circular foundation 302
due to the confinement of load shedding in-plane under plane strain conditions. 303
The relative gain in capacity of a foundation following a period of consolidation is 304
governed by the overlap between the zone of shear strength increase and failure 305
mechanism. Figure 8 shows contours of shear strength increase in the soil mass beneath 306
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the circular foundation under a preload Vp/Vuu = 0.4, overlaid by velocity vectors at 307
failure under uniaxial vertical load, horizontal load and moment. It is clear that the 308
horizontal failure mechanism is almost entirely confined in the zone of maximum 309
strength increase, close to the foundation-soil interface, and is associated with the 310
greatest relative gain in capacity. The moment failure mechanism is confined within the 311
zone of strength increase, but penetrates into the soil mass into zones of lesser strength 312
enhancement, which is reflected in a lower relative gain in capacity. The vertical failure 313
mechanism is seen to extend into the soil mass, benefitting least from the consolidation 314
process, and also laterally beyond the region of shear strength increase, and is 315
associated with the lowest relative gain in capacity. 316
The reason for the similar observed relative gain in capacity under vertical loading for 317
both strip and circular foundations is illustrated in Figure 9. The failure mechanisms for 318
both strip and circular foundations cut through zones of soil of equal increase in shear 319
strength. Although the size of the failure mechanisms varies with foundation shape, the 320
size of the zone of enhanced strength varies similarly. The greater observed relative gain 321
in moment capacity for the strip foundation compared with the circular foundation is 322
explained by Figure 10 that compares the zone of shear strength increase and extent of 323
the failure mechanisms in the two cases. The failure mechanism for the strip foundation 324
occurs in soil with higher shear strength increase while the circular foundation failure 325
mechanism reaches into soil with lesser strength enhancement. In this case, the extent of 326
the zone of sheared soil is similar for both foundation shapes but the zone of increased 327
shear strength is dependent on foundation geometry. 328
Critical state framework 329
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The relative gain in undrained capacity following consolidation is interpreted through 330
fundamental critical state soil mechanics (CSSM) (Schofield & Wroth 1968). A CSSM 331
framework for predicting gain in undrained vertical capacity of surface strip and circular 332
foundations for a range of over consolidation ratios was set out by Gourvenec et al. 333
(2014). That method is applied and extended here to predict gains in undrained uniaxial 334
but multi-directional capacity of surface strip and circular foundations. 335
The mobilised soil below the pre-loaded foundation is considered as a single ‘operative’ 336
element, which for initially normally consolidated conditions, the increment in operative 337
stress due to the preload can be estimated as 338
AV
fvf' pppl σσ ==σ∆ 13 339
where vp is the preload stress given by the applied vertical preload Vp divided by the 340
area of the foundation A, and the stress factor fσ accounts for the non-uniform 341
distribution of the stress in the affected zone of soil. Gourvenec et al. (2014) present 342
more general expressions for over-consolidated conditions. 343
The resulting increase in the operative strength of the soil involved in the subsequent 344
failure mechanism is then calculated as 345
( )
=σ∆=∆ σ A
VRff'Rfs psuplsuu 14 346
where the shear strength factor fsu scales the gain in strength from that caused by ∆σ′pl 347
to that mobilised throughout the subsequent failure, and R is the normally-consolidated 348
strength ratio of the soil, su/σ'v = 0.279 for the MCC parameters given in Table 1. 349
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Separate scaling factors, fσ and fsu, allow the response in over-consolidated conditions to 350
be captured (Gourvenec et al. 2014), but in the present normally-consolidated 351
conditions there is effectively a single scaling parameter, fσfsu. 352
Capacity is then assumed to scale with the change in operative strength, so that 353
cVuu
psu
u
u
uu
cu
uu
cu
uu
cu NVV
Rff1ss1
MM,
HH,
VV
+=
∆+= σ 15
where NcV is the unconsolidated undrained vertical bearing capacity factor defined as 354
Vuu/Asu0 and the factor fσfsu is fitted to give the best agreement with the observed gains 355
from the FEA for each load path direction. Derived factors fσfsu for uniaxial vertical, 356
horizontal and moment capacity for strip and circular foundation geometry are 357
summarised in Table 3. 358
Extension to partially consolidated undrained uniaxial capacity 359
Determining the gain in capacity over time, not solely after full dissipation of excess 360
pore water pressure, is of practical interest since often sufficient time is not available to 361
achieve full primary consolidation. Figure 11 illustrates the evolution of the proportion 362
of maximum potential gain in undrained vertical and horizontal capacity as a function of 363
consolidation time. A simple equation linking the consolidation time, represented by the 364
non-dimensional time factor T, and the proportion of maximum potential gain (i.e. 365
following full primary consolidation) is proposed: 366
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n
50
uucu
uup,cu
uucu
uup,cu
uucu
uup,cu
TTm1
1MMMM
,HHHH
,VVVV
+
=−−
−−
−−
16
from which the partial relative gains in undrained uniaxial capacity, Vcu,p, Hcu,p and 367
Mcu,p may be determined. The non-dimensional time factor for 50% consolidation T50 is 368
0.21 and 1.50 for circular and strip foundations, respectively. Fitting coefficients n = -369
1.20 and m are given in Table 4 for each loading direction. Figure 11 indicates good 370
agreement between the FEA results for a variety of discrete levels of preload, Vp/Vuu, 371
and the relative gains in undrained uniaxial capacity derived from Equation (16). 372
Parametric study for scale effects and soil properties 373
To demonstrate the generality of the theoretical method outlined above, a parametric 374
study varying the foundation size and soil properties was conducted. 375
Figure 12 compares finite element analyses results and predictions from the theoretical 376
method for circular foundations with diameter D = 1 m and 10 m for constant κsu = 377
ksuD/sum modelled with the MCC parameters given in Table 1. The critical state 378
framework shows that the relative gain in capacity in all uniaxial directions is 379
independent of the actual foundation size provided the dimensionless group κsu = 380
ksuD/sum is constant. The relative gain in capacity is governed only by the stress and 381
strength factor fσfsu, normally consolidated in situ strength ratio R and undrained 382
vertical bearing capacity factor NcV. Given that the soil conditions and dimensionless 383
soil strength heterogeneity are identical in both cases, R and NcV are constant, Figure 12 384
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shows that the derived fσfsu factor captures the change in gain in strength irrespective of 385
foundation size. 386
Figure 13 demonstrates the applicability of the critical state framework with unique fσfsu 387
values to capture relative gains in foundation capacity for a range of MCC input 388
parameters. FEA were carried out where critical state parameter values κ/λ and Mcs 389
were altered, while keeping all other parameters from Table 1 identical. Although the 390
value of R changes for varying κ/λ and Mcs, the critical state framework accurately 391
captures the changing gains in capacity using the same fσfsu values from Table 3. 392
Figure 14 demonstrates the applicability of the critical state framework with unique fσfsu 393
values to capture the relative gains in foundation capacity for different values of 394
overburden stress σ′vo to define the initial stress state and mudline strength intercept. 395
The theoretical framework has been shown to accurately predict gains for a practical 396
range of overburden (which is expressed dimensionlessly via the variation in κsu = 397
ksuD/sum) with unique values of fσfsu for a given foundation geometry and load path. 398
The cases shown in Figure 14 capture the practical range of κsu for which surface 399
foundations are used. For higher κsu the low mudline strength means that foundation 400
skirts are required in order to achieve a practical bearing capacity. The critical state 401
framework is equally applicable to foundations with shallow skirts, as demonstrated by 402
the additional results and prediction line shown in Figure 14a. These results are from 403
independent FEA of consolidated bearing capacity reported by Fu et al. (2015), using 404
similar soil parameters to the present study and a circular foundation with skirts to a 405
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depth of 20% of the diameter. The theoretical framework yields predictions that lie 406
within 3% of the Fu et al. (2015) numerical results. 407
Effect of consolidation on combined capacity 408
Failure envelopes in horizontal and moment load space for discrete levels of relative 409
vertical preload (Vp/Vuu = [0.1, 0.7]) followed by full primary consolidation are 410
compared with the unconsolidated undrained case in Figure 15. The failure envelopes 411
are presented in terms of loads normalised by the respective unconsolidated undrained 412
capacity, Huu and Muu, i.e. h = H/Huu vs. m = M/Muu. 413
The effect of increasing vertical load without consolidation results in contraction of the 414
failure envelope (as seen in Figure 15 a and b), indicating a reduction in capacity. In 415
contrast, increasing vertical load coupled with consolidation leads to expansion of the 416
failure envelope (Figure 15c and d), indicating increasing capacity. 417
The results also show that the shape of the normalised H-M failure envelope for a given 418
vertical load is similar for the consolidated and unconsolidated cases, as shown in 419
Figure 16 for discrete levels of preload Vp/Vuu = 0.3 and 0.6. This observation enables 420
consolidated undrained failure envelopes to be constructed by simple scaling of the 421
unconsolidated undrained failure envelope by the consolidated undrained uniaxial 422
horizontal and moment capacity, Hcu and Mcu (following partial or full primary 423
consolidation). 424
The similitude of the failure envelopes for consolidated undrained conditions to those 425
for unconsolidated undrained conditions is reflected in the similitude of failure 426
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mechanisms under combined loads with and without consolidation as illustrated in 427
Figure 17 for a selected H/M load path. 428
Approximating expressions for VHM envelopes 429
Undrained (unconsolidated) capacity 430
An approximating expression based on a rotated ellipse is suitable for predicting the 431
unconsolidated undrained failure envelopes of shallow foundations: 432
01mh
hm2mm
hh
**** =−µ+
+
βα
17
where h = H/Huu and m = M/Muu define the normalised unconsolidated undrained 433
horizontal load and moment mobilisation. 434
The form of the expression was originally proposed for prediction of (unconsolidated) 435
undrained capacity of shallow strip and circular foundations under general loading 436
(Gourvenec & Barnett 2011). An additional fitting parameter, µ, which controls the 437
eccentricity of the ellipse, has been incorporated into the original expression to improve 438
the fit. 439
*h and *m represent the normalized unconsolidated horizontal and moment capacities 440
as a function of relative vertical preload Vp/Vuu for which conservative approximating 441
expressions have been previously derived (Gourvenec & Barnett 2011, Vulpe et al. 442
2014): 443
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69.4
uu
p*
VV
1h
−=
12.2
uu
p*
VV
1m
−=
18
for circular foundations and 444
59.3
uu
p*
VV
1h
−=
41.3
uu
p*
VV
1m
−=
19
for strip foundations. 445
Gourvenec & Barnett (2011) proposed polynomials for fitting the vh (m = 0) and vm (h 446
= 0) interactions, i.e. h* and m* here, of strip foundations. The original data has been 447
refitted with a power law for a better fit and for consistency with the expressions 448
adopted for the circular foundation geometry. 449
Fitting parameters α, β and μ capture the change in size and shape of the unconsolidated 450
undrained failure envelopes as a function of relative preload Vp/Vuu. Unique fitting 451
parameters α, β and μ for circular and strip foundations can be described by linear 452
functions of relative preload: 453
30.4VV
20.2uu
p +−=α 20
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90.1VV
62.0uu
p +−=β 21
35.0VV
48.0uu
p −=µ 22
The unconsolidated undrained failure envelopes for circular and strip foundations, are 454
shown as two-dimensional slices in the HM plane of three-dimensional VHM failure 455
envelopes in dimensionless space *h/h - *m/m in Figure 18 compared with the 456
approximating expression. The curves resulting from the approximating expression 457
show good agreement with the FEA results and capture the changing shape of the 458
failure envelopes with varying level of preload. 459
Consolidated undrained capacity 460
As indicated in Figure 15 and Figure 16, an approximation of the consolidated 461
undrained failure envelope can be achieved by scaling the normalised unconsolidated 462
undrained VHM failure envelope (Eqn 17) by the corresponding consolidated undrained 463
uniaxial horizontal and moment capacities, cuh and cum , for each level of preload (from 464
Eqn 15) and various consolidation times (from Eqn 16). Figure 19 and Figure 20 465
compare the FEA results against the approximating approach described here and show 466
good agreement. 467
Example application 468
Taking a hypothetical but realistic example of a subsea structure supported by a 5 m 469
diameter circular surface foundation, imposing a self-weight preload Vp/Vuu = 0.5 to a 470
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typical deep offshore seabed with coefficient of consolidation, cv = 10 m2/yr, the results 471
presented in this study show a maximum potential gain of 45 % in the undrained 472
vertical capacity and 92 % in the undrained sliding capacity, i.e. for full primary 473
consolidation (Figure 6). A half year time lag between foundation set down and 474
operation would lead to 77 % of the maximum gain in vertical capacity and 84 % of the 475
maximum gain in sliding capacity, i.e. an overall increase in undrained vertical capacity 476
of 1.35Vuu and in horizontal sliding capacity of 1.78Huu. The same foundation under the 477
same loading resting on a seabed with an order of magnitude greater coefficient of 478
consolidation would achieve the same gains in an order of magnitude less time (~18 479
days). These time frames are realistic for offshore field operations and offer significant 480
improvements in undrained capacity, which can be translated into smaller foundation 481
footprints. 482
Concluding remarks 483
A generalised critical state framework in conjunction with the failure envelope approach 484
has been applied to quantify the effect of vertical preloading and consolidation on the 485
undrained VHM capacity of circular and strip surface foundations on normally 486
consolidated clay. The outcomes of this study are summarized as follows: 487
• Three-dimensional flow and strain led to higher consolidation rates and smaller 488
consolidation settlements of the circular foundation compared to the strip 489
foundation under vertical preload. 490
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• Greatest relative gain in capacity was observed under pure horizontal load, 491
relative gain in moment capacity was intermediate and the lowest gain was 492
associated with pure vertical capacity. 493
• Relative gains in capacity have been explained in terms of the overlap of zones 494
of shear strength increase and the kinematic mechanism accompanying failure. 495
• The magnitude of relative gain under uniaxial vertical, horizontal and moment 496
loading has been described within a generalised critical state framework that is 497
applicable to a practical range of foundation dimensions and overburden 498
pressures. 499
• Relative gains in uniaxial capacity under uniaxial vertical, horizontal and 500
moment loading following partial consolidation have been estimated as a 501
function of non-dimensional consolidation time and an approximating 502
expression is presented. 503
• The full or partially-consolidated undrained VHM failure envelope for circular 504
or strip foundations represents an expansion of the unconsolidated undrained 505
VHM failure envelope at a given relative preload and degree of consolidation. 506
The consolidated undrained VHM failure envelope can be determined by scaling 507
the unconsolidated undrained envelope by the respective uniaxial consolidated 508
undrained horizontal and moment capacities, which can be predicted by the 509
critical state framework. 510
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The study presented in this paper highlights the potential benefit of increases in the 511
undrained soil strength from preloading and a period of consolidation when designing 512
shallow foundations against multi-directional loading following. The generalised 513
method provides a simple basis to estimate these potentially significant gains in 514
capacity, which are most significant under load paths associated with near-surface 515
kinematic mechanisms, such as those dominated by sliding. 516
Acknowledgements 517
This work forms part of the activities of the Centre for Offshore Foundation Systems 518
(COFS). Established in 1997 under the Australian Research Council’s Special Research 519
Centres Program. Supported as a node of the Australian Research Council’s Centre of 520
Excellence for Geotechnical Science and Engineering, and through the Fugro Chair in 521
Geotechnics, the Lloyd’s Register Foundation Chair and Centre of Excellence in 522
Offshore Foundations and the Shell EMI Chair in Offshore Engineering. The second 523
author is supported through ARC grant CE110001009. The work presented in this paper 524
is supported through ARC grant DP140100684. This support is gratefully 525
acknowledged.526
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REFERENCES 527
Booker, J.R. and Small, J.C (1986). The behaviour of an impermeable flexible raft on a deep layer of 528
consolidating soil. International Journal for Numerical and Analytical Methods in Geomechanics, 529
10: 311 – 327. 530
Bransby, M.F. (2002). The undrained inclined load capacity of shallow foundations after consolidation 531
under vertical loads. Proc. 8th Numerical Models in Geomechanics (NUMOG), Rome, 431-437. 532
Bransby, M.F. and Randolph, M.F. (1998). Combined loading of skirted foundations. Géotechnique, 533
48(5): 637-655. 534
Bransby, M.F. and Yun, G.J. (2009). The undrained capacity of skirted strip foundations under combined 535
loading. Géotechnique, 59(2): 115-125. 536
Butterfield, R. and Banerjee, P.K. (1971). A rigid disc embedded in an elastic half space. Geotechnical 537
Engineering, 2(1): 35-52. 538
Butterfield, R., Houlsby, G.T. and Gottardi, G. (1997). Standardised sign conventions and notation for 539
generally loaded foundations. Géotechnique, 47(4): 1051–1052. 540
Chatterjee, S., Yan, Y., Randolph, M.F. and White, D.J. (2012). Elastoplastic consolidation beneath 541
shallowly embedded offshore pipelines. Géotechnique Letters 2: 73-79. 542
Chen, W. (2005). Uniaxial behaviour of suction caissons in soft deposits in deepwater. PhD thesis, 543
University of Western Australia. 544
Dassault Systèmes (2012). Abaqus analysis user’s manual. Simulia Corp. Providence, RI, USA. 545
Davis, E.H. and Poulos, H.G. (1972). Rate of settlement under two- and three-dimensional conditions. 546
Géotechnique, 22(1): 95 - 114. 547
http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
-
Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
142(8), August http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
30
Feng, X., Randolph, M. F., Gourvenec, S. and Wallerand, R. (2014) Design approach for rectangular 548
mudmats under fully three dimensional loading, Géotechnique 64(1): 51-63. 549
Fu, D., Gaudin, C., Tian, C., Bienen, B. and Cassidy, M.J. (2015). Effects of preloading with 550
consolidation on undrained bearing capacity of skirted circular footings. Géotechnique, 65(3): 231-551
246. 552
Gourvenec, S. (2007a). Failure envelopes for offshore shallow foundations under general loading. 553
Géotechnique, 57(3): 715–728. 554
Gourvenec, S. (2007b) Shape effects on the capacity of rectangular footings under general loading. 555
Géotechnique, 57(8): 637-646. 556
Gourvenec, S. and Barnett, S. (2011). Undrained failure envelope for skirted foundations under general 557
loading. Géotechnique, 61(3): 263–270. 558
Gourvenec, S.M. and Mana, D.S.K. (2011). Undrained vertical bearing capacity factors for shallow 559
foundations. Géotechnique Letters, 1(4): 101 – 108. 560
Gourvenec, S. and Randolph, M.F. (2003). Effect of strength non-homogeneity on the shape and failure 561
envelopes for combined loading of strip and circular foundations on clay. Géotechnique, 53(6): 562
575-586. 563
Gourvenec, S. and Randolph, M.F. (2009). Effect of foundation embedment and soil properties on 564
consolidation response, Proc. Int. Conf. Soil Mechanics and Geotechnical Engineering (ICSMGE), 565
Alexandria, Egypt. 638-641. 566
Gourvenec, S. and Randolph, M.F. (2010) Consolidation beneath skirted foundations due to sustained 567
loading. International Journal of Geomechanics, 10(1): 22 - 29. 568
Gourvenec, S.M., Vulpe, C. and Murthy, T.G. (2014). A method for predicting the consolidated 569
undrained bearing capacity of shallow foundations. Géotechnique, 64(3): 215 – 225. 570
http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
-
Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
142(8), August http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
31
Lehane, B.M. and Gaudin, C. (2005). Effects of drained pre-loading on the performance of shallow 571
foundations on over consolidated clay. Proc. Offshore Mechanics and Arctic Engineering 572
(OMAE), OMAE2005-67559. 573
Lehane, B.M. and Jardine, R.J. (2003). Effects of long-term preloading on the performance of a footing 574
on clay. Géotechnique, 53(8): 689 - 695. 575
Martin, C.M. and Houlsby, G.T. (2001). Combined loading of spudcan foundations on clay: numerical 576
modelling. Géotechnique, 51(8): 687–699. 577
Martin, C.M. (2003). New software for rigorous bearing capacity calculations. Proc. British Geotech. 578
Assoc. Int. Conf. on Foundations, Dundee, 581-592. 579
Murff, J.D. and Hamilton, J.M. (1993). P-ultimate for undrained analysis of laterally loaded piles. J. Geot. 580
Eng. Div., ASCE 119(1): 91-107. 581
Potts, D.M. and Zdravkovic, L. (1999). Finite element analysis in geotechnical engineering – theory. 582
London, UK: Thomas Telford. 583
Randolph, M. F and Puzrin, A. M (2003). Upper bound limit analysis of circular foundations on clay 584
under general loading. Géotechnique, 53(9): 785-796. 585
Schofield, A.N. and Wroth, C.P. (1968). Critical state soil mechanics. London, UK: McGraw-Hill. 586
Stewart, D.P. (1992). Lateral loading of pile bridge abutments due to embankment construction. PhD 587
thesis, University of Western Australia. 588
Taiebat, H.A. and Carter, J.P. (2000). Numerical studies of the bearing capacity of shallow foundations 589
on cohesive soil subjected to combined loading. Géotechnique, 50(4): 409–418. 590
Tani, K. and Craig, W.H. (1995). Bearing capacity of circular foundations on soft clay of strength 591
increasing with depth. Soils and Foundations, 33(4): 21-35. 592
http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
-
Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
142(8), August http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
32
Ukritchon, B., Whittle, A.J. and Sloan, S.W. (1998). Undrained limit analysis for combined loading of 593
strip footings on clay. J. Geot. and Geoenv. Eng., ASCE 124(3): 265-276. 594
Vulpe, C., Bienen, B. and Gaudin, C. (2013). Predicting the undrained capacity of skirted spudcans under 595
combined loading. Ocean Engineering, 74: 178-188. 596
Vulpe, C. and Gourvenec, S. (2014). Effect of preloading on the response of a shallow skirted foundation. 597
Proceedings of the 33rd International Conference on Ocean, Offshore and Arctic Engineering 598
(OMAE2014), San Francisco, USA, OMAE2014-23440. 599
Vulpe, C., Gourvenec, S. and Power, M. (2014). A generalised failure envelope for undrained capacity of 600
circular shallow foundations under general loading. Géotechnique Letters, 4: 187 – 196 601
(http://dx.doi.org/10.1680/geolett.14.00010). 602
Wroth, C.P. (1984). The interpretation of in-situ soil tests. 24th Rankine Lecture, Géotechnique, 34(4): 603
449 - 489. 604
Yun, G. and Bransby, M.F. (2007). The undrained vertical bearing capacity of skirted foundations. Soils 605
Foundations 47(3): 493-506. 606
Zdravkovic, L. Potts, D.M. and Jackson, C. (2003). Numerical study of the effect of preloading on 607
undrained bearing capacity. Int. J. Geomechanics ASCE, September, 1 – 10. 608
609
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LIST OF TABLES 610
Table 1. Soil properties used in finite element analyses. 611
Table 2. Definition of notations for loads and displacements. 612
Table 3. Stress and strength factor fσfsu for fully consolidated gain in uniaxial capacity 613
for surface circular and strip foundations. 614
Table 4. Fitting coefficient m for determining the gain in capacity following partial 615
consolidation for surface circular and strip foundations. 616
617
618
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TABLES 619
Parameter input for FEA Magnitude
Index and engineering parameters Saturated Bulk Unit Weight (kN/m3) Specific gravity (Gs) Permeability (m/s)
Elastic parameters (as a porous elastic material)
Recompression Index (κ) Poisson’s Ratio (ν') Tensile Limit
Clay plasticity parameters
Virgin compression Index (λ) Stress Ratio at Critical State (Mcs) Wet Yield Surface Size* Flow Stress Ratio** Intercept (e1, at p'=1 on CSL)
17.18 2.6 1.3 E-010 0.044 0.25 0 0.205 0.89 1 1 2.14
*The wet yield surface size is a parameter defining the size of the yield surface on the “wet” side of critical state, β. (β = 1 means that the yield surface is a symmetric ellipse). **The flow stress ratio represents the ratio of flow stress in triaxial tension to the flow stress in triaxial compression
Table 1. Soil properties used in finite element analyses. 620
621
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622
Vertical Horizontal Rotational
Displacement w u θ
Load Vp (preload) H M
Uniaxial (unconsolidated) undrained capacity
Vuu Huu Muu
Unconsolidated undrained bearing capacity factor
NcV = Vuu/Asu0 NcH = Huu/Asu0 NcM = Muu/ADsu0
Normalized load v = Vp/Vuu h = H/Huu m = M/Muu
Pure uniaxial consolidated undrained capacity
cuV cuH cuM
Normalized pure uniaxial consolidated undrained capacity
uucucu V/Vv = uucucu H/Hh = uucucu M/Mm =
Table 2. Definition of notations for loads and displacements. 623
fσfsu
Loading direction circular strip V 0.43 0.49 H 0.88 1.00 M 0.57 0.73
624
Table 3. Stress and strength factor fσfsu for fully consolidated gain in uniaxial capacity for surface 625
circular and strip foundations. 626
Loading direction m V 0.32 H 0.20 M 0.50
Table 4. Fitting coefficient m for determining the gain in capacity following partial consolidation 627
for surface circular and strip foundations. 628
629
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LIST OF FIGURES 630
Figure 1. Schematic representation of the strip foundation model. 631
Figure 2. Example of finite element mesh for plane strain analysis. 632
Figure 3. Sign convention and notation nomenclature used in the study. 633
Figure 4. Non-dimensional time-settlement response for strip and circular foundations from FEA results. 634
Figure 5. Normalized time-settlement response of strip and circular foundations from FEA results 635
compared to theoretical elastic solution with constant cv. 636
Figure 6. Gain in uniaxial capacity for strip and circular foundations as a function of relative preload 637
Vp/Vuu. 638
Figure 7. Contours of relative shear strength gain after full primary consolidation; circular and strip 639
foundations. 640
Figure 8. Failure mechanisms under pure horizontal, moment and vertical loading following preloading 641
and consolidation for the discrete level of preload Vp/Vuu = 0.4 (circular foundation) (Contour lines 642
represent the relative change in shear strength). 643
Figure 9. Comparison of failure mechanisms of circular and strip foundations under pure vertical loading 644
following preloading and consolidation for a discrete level of preload Vp/Vuu = 0.4 (Contour lines 645
represent the relative change in shear strength). 646
Figure 10. Comparison of failure mechanisms of circular and strip foundations under pure moment 647
loading following preloading and consolidation for a discrete level of preload Vp/Vuu = 0.4 (Contour lines 648
represent the relative change in shear strength). 649
Figure 11. Gain in uniaxial capacity as a function of non-dimensional time factor T: comparison between 650
FEA and Equation (16). 651
Figure 12. Sensitivity study showing applicability of theoretical framework to variations in foundation 652
size of circular foundations for constant soil heterogeneity index κsu. 653
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Figure 13. Sensitivity study showing applicability of theoretical framework to varying MCC input for 654
circular foundations 655
Figure 14. Sensitivity study showing applicability of theoretical framework to varying overburden for 656
constant foundation size for circular foundations. 657
Figure 15. (a, b) Unconsolidated and (c, d) consolidated undrained failure envelopes as a function of 658
relative preload for full primary consolidation (T99) 659
Figure 16. Comparison of shape of normalized failure envelopes for unconsolidated and fully 660
consolidated undrained capacity of a circular foundation: a) Vp/Vuu = 0.3, b) Vp/Vuu = 0.6. 661
Figure 17. Failure mechanisms under undrained load paths to failure in HM space (u/Dθ = 1) for circular 662
foundation. 663
Figure 18. Unconsolidated undrained normalized failure envelope for varying relative preload; FEA 664
results and approximating expression (a) circular foundation and (b) strip foundation. 665
Figure 19. Consolidated undrained normalized failure envelope for varying relative preload after full 666
primary consolidation; FEA results and approximating expression (a) circular foundation and (b) strip 667
foundation. 668
Figure 20. Consolidated undrained normalized failure envelope for a discrete relative preload Vp/Vuu = 669
0.3 and varying consolidation times; FEA results and approximating expression (a) circular foundation 670
and (b) strip foundation. 671
672
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38
FIGURES 673
B
10 B
10 B
Drainage boundary Drainage boundary
Not to scale
674
Figure 21. Schematic representation of the strip foundation model. 675
676
677
Figure 22. Example of finite element mesh for plane strain analysis. 678
679
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39
680
681
Figure 23. Sign convention and notation nomenclature used in the study. 682
683
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.001 0.01 0.1 1 10 100
Prel
oad,
Vp/V
uu
0.1
0.7
Dim
ensi
onle
ss c
onso
lidat
ion
settl
emen
t, w
c/D o
r w
c/B
circular
strip
Time factor, T = cv0t/D2 or T = cv0t/B2
684
Figure 24. Non-dimensional time-settlement response for strip and circular foundations from FEA results. 685
686
687
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40
688
00.10.20.30.40.50.60.70.80.9
1
0.001 0.01 0.1 1 10 100
circular strip
Time factor, T = cv0t/D2 or T = cv0t/B2
Deg
ree o
f con
solid
atio
n,w
c/wcf
Elastic solution, circular foundation, constant cv(Booker & Small 1986)
689
Figure 25. Normalized time-settlement response of strip and circular foundations from FEA results 690
compared to theoretical elastic solution with constant cv. 691
692
1
1.2
1.4
1.6
1.8
2
2.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Gai
n in
uni
xial
cap
acity
follo
win
g fu
ll pr
imar
y co
nsol
idat
ion
vcu = Vcu/Vuu
circular
strip
Relative preload, Vp/Vuu
mcu = Mcu/Muu
hcu = Hcu/Huu
FE results
693
Figure 26. Gain in uniaxial capacity for strip and circular foundations as a function of relative preload 694
Vp/Vuu. 695
696
697
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41
698
Figure 27. Contours of relative shear strength gain after full primary consolidation; circular and strip 699
foundations. 700
701
Figure 28. Failure mechanisms under pure horizontal, moment and vertical loading following preloading 702
and consolidation for the discrete level of preload Vp/Vuu = 0.4 (circular foundation) (Contour lines 703
represent the relative change in shear strength). 704
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42
705
Figure 29. Comparison of failure mechanisms of circular and strip foundations under pure vertical loading 706
following preloading and consolidation for a discrete level of preload Vp/Vuu = 0.4 (Contour lines 707
represent the relative change in shear strength). 708
709
710
Figure 30. Comparison of failure mechanisms of circular and strip foundations under pure moment 711
loading following preloading and consolidation for a discrete level of preload Vp/Vuu = 0.4 (Contour lines 712
represent the relative change in shear strength). 713
714
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43
0
0.2
0.4
0.6
0.8
1
0.001 0.01 0.1 1 10
0.10.30.50.7
Time factor, T = cv0t/D2
Prop
ortio
n of
the
max
imum
pot
entia
l gai
n in
ca
paci
ty, (
Vcu
,p-V
uu)/(
Vcu
-Vuu
)
Vp/Vuu
circular
Equation (16)
a)
0
0.2
0.4
0.6
0.8
1
0.001 0.01 0.1 1 10 100
0.10.30.50.7
Time factor, T = cv0t/D2
Prop
ortio
n of
the
max
imum
pot
entia
l gai
n in
ca
paci
ty, (
Vcu
,p-V
uu)/(
Vcu
-Vuu
) Vp/Vuu
strip
Equation (16)
b)
0
0.2
0.4
0.6
0.8
1
0.001 0.01 0.1 1 10
0.10.30.50.7
Time factor, T = cv0t/D2
Prop
ortio
n of
the
max
imum
pote
ntia
l gai
n in
ca
paci
ty, (
Hcu
,p-H
uu)/(
Hcu
-Huu
) Vp/Vuu
circular
Equation (16)
c)
0
0.2
0.4
0.6
0.8
1
0.001 0.01 0.1 1 10 100
0.10.30.50.7
Time factor, T = cv0t/D2
Prop
ortio
n of
the
max
imum
pot
entia
lgai
n in
ca
paci
ty, (
Hcu
,p-H
uu)/(
Hcu
-Huu
) Vp/Vuu
strip
Equation (16)
d)
Figure 31. Gain in uniaxial capacity as a function of non-dimensional time factor T: comparison 715
between FEA and Equation (16). 716
717
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1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
D = 1 m, σ′vo = 17.18 kPa
D = 10 m, σ′vo = 171.8 kPa
theoretical prediction
Gai
n in
uni
aixi
al ca
paci
ty fo
llow
ing
full
prim
ary
cons
olid
atio
n
Relative preload, Vp/Vuu
κsu = 0.36D = 1 m, σ′vo = 17.18 kPa
D = 10 m, σ′vo = 171.8 kPa
Vcu/Vuu
Mcu/Muu
Hcu/Huu
718
Figure 32. Sensitivity study showing applicability of theoretical framework to variations in foundation 719
size of circular foundations for constant soil heterogeneity index κsu. 720
721
1
1.2
1.4
1.6
1.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
M = 0.89, κ/λ = 0.215κ/λ = 0.107κ/λ = 0.429M = 1M = 1.1theoretical prediction
Gai
n in
uni
aixi
al v
ertic
al c
apac
ity fo
llow
ing
full
prim
ary
cons
olid
atio
n, V
cu/V
uu
Relative preload, Vp/Vuu
theoretical prediction
a) vertical
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45
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
M = 0.89, κ/λ = 0.215κ/λ = 0.107κ/λ = 0.429M = 1M = 1.1theoretical prediction
Gai
n in
uni
aixi
al h
oriz
onta
l cap
acity
fo
llow
ing
full
prim
ary
cons
olid
atio
n, H
cu/H
uu
Relative preload, Vp/Vuu
theoretical prediction
b) horizontal
1
1.2
1.4
1.6
1.8
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
theoretical predictionM = 0.89, κ/λ = 0.215κ/λ = 0.107κ/λ = 0.429M = 1M = 1.1
Gai
n in
uni
aixi
al m
omen
t cap
acity
follo
win
g fu
ll pr
imar
y co
nsol
idat
ion,
Mcu
/Muu
Relative preload, Vp/Vuu
theoretical prediction
c) moment
Figure 33. Sensitivity study showing applicability of theoretical framework to varying MCC input for 722
circular foundations 723
724
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46
1
1.2
1.4
1.6
1.8
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
theoretical predictionq = 2.15 kPaq = 4.3 kPaq = 8.59 kPaq = 17.18 kPaq = 171.8 kPaFu et al. (2015)
Gai
n in
uni
aixi
al v
ertic
al c
apac
ity fo
llow
ing
full
prim
ary
cons
olid
atio
n, V
cu/V
uu
Relative preload, Vp/Vuu
σ′vo = 2.15 kPaσ′vo = 4.3 kPaσ′vo = 8.59 kPaσ′vo = 17.18 kPaσ′vo = 171.8 kPa
a) vertical
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
theoretical predictionq = 2.15 kPaq = 4.3 kPaq = 8.59 kPaq = 17.18 kPaq = 171.8 kPa
Gai
n in
uni
aixi
al h
oriz
onta
l cap
acity
fo
llow
ing
full
prim
ary
cons
olid
atio
n, H
cu/H
uu
Relative preload, Vp/Vuu
σ′vo = 2.15 kPaσ′vo = 4.3 kPaσ′vo = 8.59 kPaσ′vo = 17.18 kPaσ′vo = 171.8 kPa
b) horizontal
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47
1
1.2
1.4
1.6
1.8
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
theoretical predictionq = 2.15 kPaq = 4.3 kPaq = 8.59 kPaq = 17.18 kPaq = 171.8 kPa
Gai
n in
uni
aixi
al m
omen
t cap
acity
follo
win
g fu
ll pr
imar
y co
nsol
idat
ion,
Mcu
/Muu
Relative preload, Vp/Vuu
σ′vo = 2.15 kPaσ′vo = 4.3 kPaσ′vo = 8.59 kPaσ′vo = 17.18 kPaσ′vo = 171.8 kPa
c) moment
Figure 34. Sensitivity study showing applicability of theoretical framework to varying overburden for 725
constant foundation size for circular foundations. 726
727
728
729
730
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48
731
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Nor
mal
ized
und
rain
ed m
omen
t,m
= M
/Muu
Normalized undrained horizontal load,h = H/Huu
Vp/Vuu = [0.1,0.7]
circular
unconsolidatedundrained
a)
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5Nor
mal
ized
und
rain
ed m
omen
t,m
= M
/Muu
Normalized undrained horizontal load,h = H/Huu
Vp/Vuu = [0.1,0.7]
strip
unconsolidated undrained
b)
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
Normalized undrained horizontal load,h = H/Huu
Nor
mal
ized
und
rain
ed m
omen
t,m
= M
/Muu
Vp/Vuu = [0.1,0.7]circular
consolidated undrained
c)
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5Nor
mal
ized
und
rain
ed m
omen
t,m
= M
/Muu
Normalized undrained horizontal load,h = H/Huu
Vp/Vuu = [0.1,0.7]strip
consolidatedundrained
d)
Figure 35. (a, b) Unconsolidated and (c, d) consolidated undrained failure envelopes as a function of 732
relative preload for full primary consolidation (T99) 733
734
735
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49
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5Normalized undrained horizontal load,
h = H/Huu
Nor
mal
ized
und
rain
ed m
omen
t,m
= M
/Muu
Vp/Vuu = 0.3
consolidated undrained (cu)
unconsolidated undrained (uu)
a)
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5Normalized undrained horizontal load,
h = H/Huu
Nor
mal
ized
und
rain
ed m
omen
t,m
= M
/Muu
Vp/Vuu = 0.6
consolidated undrained (cu)
unconsolidated undrained (uu)
b)
Figure 36. Comparison of shape of normalized failure envelopes for unconsolidated and fully 736
consolidated undrained capacity of a circular foundation: a) Vp/Vuu = 0.3, b) Vp/Vuu = 0.6. 737
738
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50
739
740
Figure 37. Failure mechanisms under undrained load paths to failure in HM space (u/Dθ = 1) for circular 741
foundation. 742
743
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51
744
0
0.2
0.4
0.6
0.8
1
1.2
-1 -0.5 0 0.5 1
m/m
*
h/h*
Vp/Vuu = 0.1, 0.3, 0.5, 0.7
curve fit
FEA
circular
a)
0
0.2
0.4
0.6
0.8
1
1.2
-1 -0.5 0 0.5 1
m/m
*
h/h*
curve fit
Vp/Vuu = 0.1, 0.3, 0.5, 0.7
FEA
strip
b)
Figure 38. Unconsolidated undrained normalized failure envelope for varying relative preload; FEA 745
results and approximating expression (a) circular foundation and (b) strip foundation. 746
747
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
m/m
*
h/h*
Vp/Vuu = 0.1, 0.3, 0.5, 0.7curve fit FEA
circular
a)
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
m/m
*
h/h*
Vp/Vuu = 0.1, 0.3, 0.5, 0.7
curve fit FEA
strip
b)
Figure 39. Consolidated undrained normalized failure envelope for varying relative preload after full 748
primary consolidation; FEA results and approximating expression (a) circular foundation and (b) strip 749
foundation. 750
751
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52
752
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-1.5 -1 -0.5 0 0.5 1 1.5
m/m
*
h/h*
T20, T50, T80
curve fit FEA
circularVp/Vuu = 0.3
a)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-1.5 -1 -0.5 0 0.5 1 1.5
m/m
*
h/h*
T20, T50, T80stripVp/Vuu = 0.3
curve fit FEA
b)
Figure 40. Consolidated undrained normalized failure envelope for a discrete relative preload Vp/Vuu = 753
0.3 and varying consolidation times; FEA results and approximating expression (a) circular foundation 754
and (b) strip foundation. 755
756
757
758
759
http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0001498
IntroductionFinite element modelFoundation geometrySoil conditions and material parametersFinite element meshScope and loading methodsSign convention and nomenclature
ResultsValidationConsolidation responseEffect of full primary consolidation on uniaxial V, H and M capacityEffect of consolidation on combined capacity
Approximating expressions for VHM envelopesConcluding remarksAcknowledgements