Finite Element Analysis of Mixed-in-Place Columns (MIP ...

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Finite Element Analysis of Mixed-in-Place Columns (MIP) Supporting Excavations in Slopes Considering Tension

Softening

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2019-0093.R2

Manuscript Type: Article

Date Submitted by the Author: 18-Jun-2019

Complete List of Authors: Choosrithong, Kamchai; Graz University of Technology, Institute of Soil Mechanics, Foundation Engineering and Computational GeotechnicsSchweiger, Helmut; Graz University of Technology, Institute of Soil Mechanics, Foundation Engineering and Computational GeotechnicsMarte, Roman; Graz University of Technology, Institute of Soil Mechanics, Foundation Engineering and Computational Geotechnics

Keyword: finite element method, excavations in slopes, tension softening, brittle failure, Eurocode 7

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

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Canadian Geotechnical Journal

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1 Finite Element Analysis of Mixed-in-Place Columns (MIP) Supporting

2 Excavations in Slopes Considering Tension Softening

3

4 Kamchai Choosrithong Ph.D. Candidate, Institute of Soil Mechanics, Foundation

5 Engineering and Computational Geotechnics, Graz University of

6 Technology, Rechbauerstraße 12, 8010, Graz, Austria,

7 [email protected]

8

9 Helmut F. Schweiger Professor, Institute of Soil Mechanics, Foundation Engineering

10 and Computational Geotechnics, Graz University of


12 [email protected]

13

14 Roman Marte Professor, Institute of Soil Mechanics, Foundation Engineering

15 and Computational Geotechnics, Graz University of


17 [email protected]

18

19

20 Submitted to: Canadian Geotechnical Journal

21 Corresponding author:

22 Kamchai Choosrithong

23 Institute of Soil Mechanics, Foundation Engineering and Computational Geotechnics,

24 Graz University of Technology, Rechbauerstraße 12, 8010, Graz, Austria

25 Phone: +43 67762108400

26 e-mail: [email protected]

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27 Finite Element Analysis of Mixed-in-Place Columns (MIP) Supporting

28 Excavations in Slopes Considering Tension Softening

29 Kamchai Choosrithong, Helmut F. Schweiger & Roman Marte

30 Institute of Soil Mechanics, Foundation Engineering and Computational Geotechnics,

31 Graz University of Technology, Rechbauerstraße 12, 8010, Graz, Austria

32 Abstract

33 The use of mixed-in-place (MIP) columns can be considered as attractive alternative to sheet

34 pile, diaphragm or bored pile walls for supporting deep excavations, even when it comes to

35 difficult ground conditions. In this paper results from a numerical study based on a case history

36 are presented, where MIP-columns are used to support an excavation in a slope. The special

37 feature of this project is that tied-back anchors were not feasible as additional support measure

38 because it was not allowed to put any structural elements within the neighbouring ground. Thus

39 the MIP-columns were placed in such a way that they formed an arch including buttresses

40 capable to transfer the load acting on the backside of the wall into the ground. In this study an

41 advanced constitutive model for the MIP-columns is applied to capture the development of

42 possible cracking. Variations in geometry have been performed in order to investigate the

43 potential for optimization. Finally some analyses have been conducted to show that a design of

44 such structures compatible with EC7 requirements is perfectly feasible by means of the finite

45 element method.

46 Keywords: finite element method; excavations in slopes; tension softening; brittle failure;

47 cracks; Eurocode 7.

48 INTRODUCTION

49 The use of mixed-in-place (MIP) columns for supporting excavations is an attractive

50 alternative to more common retaining structures using sheet pile, diaphragm or bored pile walls,

51 even when it comes to difficult ground conditions (e.g., Briaud et al. 2000; Poh and Wong 2001;

52 Shao et al. 2005; Wang et al. 2013; Ignat et al. 2016). In this paper results from a numerical

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53 study based on a case history are presented, where MIP-columns are used to support an

54 excavation in a slope where placing tied-back anchors was not an option as additional support

55 measure because it was not allowed to put any structural elements within the neighbouring

56 ground. Thus the MIP-columns were placed in such a way that they formed an arch including

57 panels and buttresses capable to transfer the earth pressure acting on the backside of the wall

58 into the ground (Lüftenegger et al. 2013; Marte et al. 2017, 2019). In this paper emphasis is put

59 on the constitutive model describing the mechanical behaviour of the MIP-columns. Simple

60 elastic-perfectly plastic failure criteria (see e.g., O’Rourke and McGinn 2006; Ignat et al. 2015;

61 Wang et al. 2018; Comodromos et al. 2018; Liu et al. 2018) are often applied in practice for

62 this type of cemented materials although more advanced models have been presented in the

63 literature (e.g., Arroyo et al. 2012; Schütz et al. 2011). In general these columns are not

64 reinforced and their behaviour is rather brittle, although in some cases a steel bar is placed in

65 the centre of the column as a reinforcement immediately after construction before the added

66 cement is fully cured. It is therefore essential that a suitable criterion is introduced to take into

67 account the limited tensile strength of these materials and it is equally important to consider the

68 post peak behaviour, i.e., modelling strain softening in tension (and compression), in particular

69 when the structural performance is dominated by crack initiation. In recent years, much effort

70 has gone into studying the post-peak behaviour of cement treated soil such as jet grouting,

71 cement-treated soil and mixed-in-place columns considering tension softening. For example

72 Larsson et al. (2012) and Lee (2014) studied the mechanical behaviour of cement treated soil

73 in experiments and full-scale excavations by means of numerical analysis. These results showed

74 that their model captures the stress-strain relationship including the post peak behaviour.

75 Qualitatively realistic crack patterns were predicted depending on the assumed value for the

76 fracture energy in tension ( ).𝐺𝑡

77 In this study a constitutive model for concrete-like material, originally developed by

78 Schädlich and Schweiger (2014) for modelling the time-dependent behaviour of shotcrete for

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79 tunnelling applications, was employed for the mixed-in-place columns. The model is

80 implemented in the finite element code Plaxis (Brinkgreve et al. 2018) which is used for all

81 analyses presented in this paper. The most important features of this model relevant for the

82 application discussed in this paper are presented later. The model has been successfully applied

83 to tunnelling problems, for modelling the behaviour of jet grout slabs in the context of deep

84 excavations (Schweiger et al. 2014, 2015, 2017) and to numerical simulation of anchor load

85 tests where the development of cracks in the grouted body was of interest (Fabris et al. 2018).

86 In this study, three-dimensional FE analyses are performed to investigate the behaviour

87 of an excavation situated in a slope, supported by MIP-columns. The influence of geometrical

88 factors (i.e., length and number of columns) is investigated as well as the influence of certain

89 material parameters. Emphasis is placed on the development of crack patterns in the columns

90 during excavation. Before discussing results in more detail the geometric layout of the problem

91 including ground conditions is provided together with a short description of the constitutive

92 model employed for modelling the MIP-columns.

93 NUMERICAL ANALYSIS

94 Geometry, ground conditions and construction phases

95 The basis for this numerical study is a case history described in Lüftenegger et al. (2013)

96 and Marte et al. (2017). However, for the purpose of the systematic study presented here the

97 original numerical model was simplified and only a representative section of the structure is

98 analysed. For this reason no comparison can be provided with in-situ measurements and

99 actually a comprehensive monitoring has not been performed for this project. This

100 simplification allowed for a very fine mesh, required in order to capture the development of

101 cracks in the column with progressing excavation. The inclination of the slope is 20° for all

102 layers. The mixed in place columns form an arch of 6-m span resting on supporting wall panels

103 oriented in the direction of the slope. The geological condition consists of three layers of soft

104 (upper), medium stiff (middle), and stiff to very stiff sandy silt (lower). The geometric layout,

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105 the finite element mesh (using 10-noded tetrahedrons), the simplified soil profile and the

106 structural layout are shown in Fig. 1. Figure 1a shows the entire model and Fig. 1b is the detail

107 of MIP structure. The analysis was performed as follows: starting from the in-situ slope

108 geometry wall installation was considered as wished-in-place, and excavation down to 7 m was

109 performed in 1 m steps.

110 The Hardening soil model with small strain stiffness as implemented in the finite

111 element code Plaxis (Brinkgreve et al. 2018) was employed to model the behaviour of the soil

112 layers. The parameters have been determined based on the soil investigation performed for the

113 actual project and have been taken from Lüftenegger et al. (2013) (Table 1). These are not

114 discussed further in this paper because the emphasis is on the behaviour of the MIP-columns.

115 All analyses were performed in drained conditions.

116 Constitutive model for MIP wall

117 The constitutive model employed for modelling the behaviour of the MIP-columns

118 (referred to as Concrete model in the following), originally developed to model shotcrete linings

119 in tunnelling, is explained in detail in Schädlich and Schweiger (2014) and only a brief summary

120 is given in the following for continuity. The model is capable to consider the increase of

121 stiffness and strength with time, strain hardening and softening in compression and tension, and

122 creep and shrinkage. As the emphasis in this study is on the evaluation of the development of

123 cracks in the MIP-columns with progressing excavation, the time dependent behaviour is

124 switched off because the columns can be considered as cured when excavation started.

125 Plastic strains are calculated according to strain hardening/softening elastoplasticity.

126 The model employs a Mohr-Coulomb yield surface for deviatoric loading and a Rankine 𝐹𝑐

127 yield surface in the tensile regime (Fig. 2). Constant values of = 30° and = 0° are 𝐹𝑡 𝜑𝑚𝑎𝑥 𝜓𝑚𝑎𝑥

128 employed in this study.

129 Strain hardening in compression follows a quadratic function up to peak strength , 𝑓𝑐

130 with subsequent bi-linear softening, governed by a normalised hardening/softening parameter

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131 , where = minor plastic strain, and = minor plastic strain at peak in uniaxial 𝐻𝑐 = 𝜀𝑝3/𝜀𝑝

𝑐𝑝 𝜀𝑝3 𝜀𝑝

𝑐𝑝

132 compression (Fig. 3a). Full mobilization of coincides with = 1, after which linear 𝑓𝑐 𝐻𝑐

133 softening take places corresponding to fracture energy in compression , failure strength is 𝐺𝑐

134 reached at . The softening rate is governed by the fracture energy , which is used within 𝐻𝑐𝑓 𝐺𝑐

135 a smeared crack approach to ensure mesh independent results.

136 The model behaviour in tension is linear elastic until the tensile strength is reached. 𝑓𝑡

137 Linear strain softening follows, governed by the normalised tension softening parameter 𝐻𝑡 =

138 , where = major principal plastic strain, and = plastic ultimate strain in uniaxial 𝜀𝑝1/𝜀𝑝

𝑡𝑢 𝜀𝑝1 𝜀𝑝

𝑡𝑢

139 tension (Fig. 3b).

140 (1) 𝑓𝑡𝑦 = 𝑓𝑡 ∙ (1 + (𝑓𝑡𝑢𝑛 ―1) ∙ 𝐻𝑡)

141 is derived from the fracture energy in tension, and the characteristic length of the finite 𝜀𝑝𝑡𝑢 𝐺𝑡

142 element, , which provides the necessary regularization to avoid mesh dependency of the 𝐿𝑒𝑞

143 numerical results. is calculated from the size of the finite element, , and the number of 𝐿𝑒𝑞 𝐴𝑒𝑙

144 stress points per element, (Pölling 2000).𝑛𝐺𝑃

145 (2) 𝜀𝑝𝑡𝑢 =

2 ∙ 𝐺𝑡 (1 + 𝑓𝑡𝑢𝑛) ∙ 𝑓𝑡 ∙ 𝐿𝑒𝑞

146 (3) 𝐿𝑒𝑞 = 2𝐴𝑒𝑙

3 ∙ 𝑛𝐺𝑃

147 Once the residual strength, , is reached, no further softening takes place. 𝑓𝑡𝑢 = 𝑓𝑡𝑢𝑛 ∙ 𝑓𝑡

148 Therefore, equal to 0 means that value of the tensile stress is below or equal to , 𝐻𝑡 𝐹𝑡 0 < 𝐻𝑡

149 describes the softening zone, and indicates the residual level.< 1 𝐻𝑡 > 1

150 The material parameters used in this study are listed in Table 2. As for this project no

151 experimental data have been available for the MIP-columns and therefore reasonable strength

152 and stiffness parameters based on experience have been assumed. However, Dik (2017) studied

153 the behaviour of steel beam reinforced cement treated soil by means of finite element

154 investigations and compared the results to real-scale three points bending test, as reported by

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155 Denies et al. (2014, 2015). The results showed that the variation of tensile fracture energy

156 follows approximately linearly with tensile strength as depicted in Fig. 4. One of the most

157 important parameters for this type of analysis is the fracture energy in tension and compression,

158 and respectively, whereas is of major importance. The values of tensile fracture energy 𝐺𝑡 𝐺𝑐 𝐺𝑡

159 are small, even for high cement-soil ratio, because this value is affected by the maximum

160 aggregate size and usually ranges from 7 to 45 N/m as summarized in Table 3 (Namikawa and

161 Koseki 2006; Tariq and Maki 2014). For comparison values for cement-treated Singapore

162 marine clay are also listed in Table 3 (Lee 2014). The value chosen for the reference analysis

163 in this study is 10 N/m, but it is varied to highlight the influence of this parameter. As indicated

164 in Fig. 1 some columns have been reinforced by a steel bar placed in the centre of the columns

165 along the entire length of individual columns. In order to account for this in a simplified manner

166 the tensile strength of these columns has been increased (see Table 2) and the reinforcing bar is

167 not modelled as structural element. In addition, the value for fracture energy is not increased 𝐺𝑡

168 because firstly it would have been difficult to choose a correct value and secondly it is argued

169 that with increasing tensile strength the post peak behaviour becomes less crucial. It should be

170 emphasized that the purpose of this study is to investigate the behaviour of MIP-columns when

171 used as supporting elements for excavations in some detail and not to analyse the case history,

172 which serves as a basis for these analyses, itself and therefore it is not important that the

173 properties of the MIP-columns are based on experience and are not strictly corresponding to

174 the properties of the columns constructed for the actual project.

175 For comparison reasons some analyses have been performed employing the elastic-

176 perfectly plastic Mohr-Coulomb constitutive model for the MIP-columns.

177 Constitutive model validation

178 The three-point bending test is a typical method to determine the behaviour of bending

179 induced tensile stress and fracture of cement-treated soil as in concrete (see Table 3). A two-

180 dimensional FE-analysis was conducted to investigate the influence of on the strain-𝐺𝑡

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181 softening behaviour of cement-treated sand based on experiments by Namikawa and Koseki

182 (2006). The finite element meshes, input parameters and results are shown in Fig. 5a. The

183 analysis is performed by applying displacement controlled.

184 It follows from Fig. 5a that the load-displacement behaviour agrees very well with the

185 experiment and the crack evolves correctly from the tip of the notch (Fig. 5a).

186 As mentioned earlier the finite element investigations presented in this paper are based

187 on a real project but no experimental data have been available for the MIP-columns and

188 therefore reasonable strength and stiffness parameters based on experience have been assumed.

189 To show the capability of model for simulating reinforced cement-treated soil, a real-scale

190 bending test (Denies et al. 2014, 2015) has been chosen in order to validate the modelling

191 assumption made for the steel reinforced cement-treated soil. For this test the reinforcement is

192 modelled as structural element on one hand (discrete modelling) and the smeared approach on

193 the other hand. The parameters are summarized in Table 4. A steel beam (HEA 240) was taken

194 as reinforcement for a cement-sand mixture. Figure 5b shows schematically the test setup and

195 the finite element mesh. Again, the prescribed displacement is used for simulating bending

196 test.

197 The result shows that modelling the reinforcement explicitly (adopting a fully bonded

198 interface) using the Concrete model accurately predicts the flexural bending moment capacity,

199 whereas the MC model ( = 30° and = 550 kPa, tension cut-off = 250 kPa) overestimates 𝜑′ 𝑐′

200 the bending strength approximately by 10% (Fig. 5b). If the smeared modelling approach is

201 adopted the elastic-perfectly plastic MC model significantly overestimates the bending moment

202 whereas the Concrete model still yields very reasonable results. The compressive strength and

203 tensile strength of the beam in the smeared approach are calculated based on the condition that

204 the steel is yielding and the ultimate compressive strain in the cement-treated soil is reached in

205 the compression zone.

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206 Based on these results it seems justified to adopt the smeared approach for taking into

207 account the reinforcement, present only in a limited number of columns, for this investigation.

208 RESULTS

209 Reference geometry

210 Table 5 summarizes the investigated parameter combinations. The material sets include

211 different values for the tensile strength ( ) and different values for the tensile fracture energy 𝑓𝑡

212 ( ). The analyses for set A account for a higher tensile strength in the reinforced columns and 𝐺𝑡

213 a variation in . The analyses for set B represent cases when the columns are not reinforced. 𝐺𝑡

214 The changes of tensile stresses and the progressive development of crack patterns are shown in

215 Fig. 6 for case of High , Low . The distributions of tensile stresses along the reinforced 𝑓𝑡 𝐺𝑡

216 column (location indicated in Fig. 6a) indicated in a stepwise drop to residual from stage 6 to 7

217 (i.e., excavation depth of 6 m from top the wall elevation down to final excavation stage at 7

218 m). In the final excavation stage (Stage 7), the tension crack (i.e., > 1.0) occurs at the 𝐻𝑡

219 reinforced columns around excavation level (indicated by zero wall elevation) as illustrated in

220 Fig. 6b.

221 Figure 7a shows the lateral deflection of a column at the backside of the wall (location

222 indicated in the figure) for three different analyses, namely employing the Concrete model (for

223 all columns) but with different values for the fracture energy for the reinforced columns 𝐺𝑡

224 (High , Low and High , High ) and the Mohr-Coulomb model. It follows that similar 𝑓𝑡 𝐺𝑡 𝑓𝑡 𝐺𝑡

225 results are obtained with Mohr-Coulomb and the Concrete model when is large (behaviour 𝐺𝑡

226 is more ductile). This is to be expected because if the softening behaviour is not pronounced

227 the two models are similar when a tension-cut off is activated in the Mohr-Coulomb model.

228 When softening becomes more pronounced differences become larger because in the Mohr-

229 Coulomb model the tensile stresses remain at the tension-cut off value and are not reduced to a

230 residual value. When is small (0.01, behaviour is more brittle) a kink in the deflection curve 𝐺𝑡

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231 is observed indicating that cracking has occurred in the column. This is confirmed in Fig. 7b

232 where a profile of tensile stresses along the column is plotted. The drop to zero in stress in the

233 excavation from stage 6 to 7 for the analysis with = 0.01 kN/m is obvious (High , Low 𝐺𝑡 𝑓𝑡 𝐺𝑡

234 ). It is apparent that these cracks increase the maximum displacement at the top of the wall, the

235 overall stability however is still guaranteed. Although the mesh is very fine in this area some

236 stress oscillations are observed but it is argued that this does not affect the overall behaviour.

237 Figure 8 shows a contour plot of the principal stress, whereas only tensile stresses 𝜎3

238 are shown. Again it is clearly observed that the stress distribution is similar for Mohr-Coulomb

239 and the Concrete model with a high value for but is different for the Concrete model with a 𝐺𝑡

240 low value, where cracking is indicated by zero tensile stresses, approximately at excavation 𝐺𝑡

241 level. These cracks do not have a serious effect on the excavation side (Fig. 9) where

242 compression softening does not occur ( < 1.0) although the contour plot of indicates a 𝐻𝑐 𝐻𝑐

243 strain concentration at excavation level. It should be mentioned that compression softening is

244 governed by the value of but this parameter has not been varied in this study. The resulting 𝐺𝑐

245 tensile stresses along the column at the arch section of the wall are plotted in Fig. 10 and it

246 follows that the different assumptions made for for the reinforced columns do not have a 𝐺𝑡

247 significant influence on the stresses in these columns, at least not for the given geometrical

248 configuration.

249 Figures 11 and 12 show the effect of the reinforcement in the two columns on the

250 backside of the wall. In Fig. 11 the lateral deflection is compared for different tensile strength

251 and it follows that there is only a marginal increase in lateral deflection of the column at the

252 backside of the wall. However the stress in the columns are significantly different as is shown

253 in Fig. 12 where comparison between the case of High , Low and Low , Low is made 𝑓𝑡 𝐺𝑡 𝑓𝑡 𝐺𝑡

254 for excavation stages 5 to 7. The missing reinforcement leads to a downward shift of the tensile

255 stresses.

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256 Influence of geometry

257 As mentioned in the previous section the behaviour of MIP-columns is dominated by

258 the tensile strength of the soil-cement mixed and by the bending resistance, in particular when

259 the columns are not reinforced (i.e., brittle behaviour). In order to investigate the potential for

260 optimization of the layout of the MIP-columns a study was performed varying the geometry of

261 the support structure. The reference geometry (wall type 1) is the one depicted in Fig. 1 and

262 wall types 2 to 5 are shown in Fig. 13. It should be mentioned that wall type 1, adopted for the

263 case history, is based on a conventional design without using numerical methods. It is the

264 purpose of this study to explore by means of advanced numerical models whether a possible

265 reduction of the volume of MIP-columns is possible without compromising the stability of the

266 structure. Thus the length of the columns has been reduced in a first step, then the panel length

267 has been reduced and finally both measures have been taken together. As examples for these

268 considerations wall types 2 to 5 are analysed whereas the extreme case is wall type 5 where the

269 wall depth and the supporting wall length are significantly reduced.

270 As expected horizontal wall deformations increase when changing the support structure

271 (Fig. 14) but the analysis shows that it is possible to achieve equilibrium even with the worst

272 case scenario (wall type 5). Figure 15 illustrates calculated tensile stresses at the reinforced

273 column from excavation stage 5 to 7. At excavation stage 5 the maximum tensile strength is not

274 reached for all geometries (Fig. 15a) but when excavation progresses cracking starts to develop

275 in some of the configurations (Fig. 15b) and for excavation stage 7 cracking is evident for all

276 geometries (compare also Fig. 7 for reference geometry). The resulting tensile stresses along

277 the column at the arch section of the wall are not influenced by the changes in wall geometry

278 as illustrated in Fig. 16.

279 As mentioned above even for wall type 5 equilibrium can be achieved in the finite

280 element analysis. However, from a design point of view this is not sufficient because input

281 parameters are characteristic parameters and therefore no safety margin is introduced. With

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282 respect to EC7 a partial factor on material parameters has to be introduced when employing

283 Design Approach 3 (DA3), which is commonly adopted for this type of problems. Although

284 “structural elements”, and in this context the MIP-columns can be considered as such, are not

285 explicitly dealt with in EC7 in combination with DA3 it seems logical to introduce a partial

286 factor not only to soil strength but also to the strength parameters of the MIP-columns. If, with

287 reduced strength parameters, equilibrium can be achieved in the finite element calculation it

288 can be argued that design requirements according to EC7 are fulfilled. A similar approach has

289 been adopted by Schweiger et al. (2017) for the design of shallow tunnels supported by a

290 shotcrete lining. In the following section it is shown that it is a feasible approach also for the

291 problem discussed in this paper.

292 Application of Eurocode 7

293 Only the two extreme cases, namely wall type 1 and 5 (see Fig. 13) are considered for

294 the design analysis. Calculations were carried out according to Eurocode 7 Design Approach 3

295 (DA3). Consequently the characteristic strength parameters of soil layers ( and ) and 𝑡𝑎𝑛𝜑′ 𝑐′

296 MIP-columns ( and ) are reduced by a partial factor of 1.25, whereas different combinations 𝑓𝑐 𝑓𝑡

297 (see Table 6) have been investigated due to the fact that EC7 is not clear on how to deal with

298 structural elements, in particular if they cannot be considered to behave as linear elastic material

299 as is the case for the MIP-columns. It is noted that the normalised residual strength in

300 compression and tension were adopted to be the same as for the characteristic strength

301 parameters ( = 0.1 and = 0.05, see Table 2), i.e., only the peak tensile strength has been 𝑓𝑐𝑢𝑛 𝑓𝑡𝑢𝑛

302 factored but because they are normalised a factoring is implicitly assumed. However, the -𝐺𝑡

303 value has been taken the same as for the characteristic strength. Of course this is a simplification

304 which can be discussed because it modifies the softening branch of the stress-strain behaviour

305 but it is argued that it can be considered as a first approach and does not question the general

306 validity of this study. Furthermore it is by no means clear what partial factor should be applied

307 to because there is no experience available and EC7 in general only factors strength. 𝐺𝑡

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308 As mentioned before, failure in the analysis is defined by means of non-convergence

309 of the iteration procedure, i.e., if a state of equilibrium could not be established with the factored

310 strength parameters of soil and/or the structural elements failure is indicated. If equilibrium is

311 achieved with factored strength parameters the requirements of EC7 are fulfilled and no explicit

312 calculation of the safety factor is required. Therefore the strength reduction procedure

313 (Brinkgreve et al. 2018) is not employed in this study.

314 Figures 17 and 18 show the development of tensile stresses in the reinforced column

315 and a column in the centre of the arch (location indicated in figure) for wall type 1 and 5, for

316 the case when the partial factor is only applied to soil strength but not to the MIP-columns

317 (denoted W1-S and W5-S). It can be observed from Fig.17 that for wall type 1, the tensile

318 stresses start to reduce indicating tension softening in excavation stage 4 for the reinforced

319 column (Fig. 17a), and in subsequent excavation stages also for the arch section (Fig. 17b).

320 However, the decreasing of tensile stresses occurs simultaneously in both columns (i.e., in

321 excavation stage 5) for wall type 5 which is illustrated in Fig. 18. In addition, the analysis cannot

322 be completed to the final excavation stage and therefore the design would not be valid according

323 to EC7. Equilibrium and stability are not obtained in the finite-element calculation at stage 6

324 for wall type 5 (Fig. 18). Figure 19 shows the crack development at the end of excavation for

325 wall type 1 (Fig. 19a) and at the stage where failure occurs for wall type 5 (Fig. 19b). The failure

326 also affects the behaviour on the excavation side where compression softening is indicated for

327 the case of low , indicated by the softening parameter .𝐺𝑡 𝐻𝑐

328 Figure 20 shows the calculated tensile stresses according to EC7-DA3 for wall type 1.

329 Figures 20a-20c show the development of tensile stresses in the reinforced column. For the case

330 when the partial factor is only applied to the MIP-columns (denoted Wall1-W) the calculated

331 tensile stresses are lower than for all cases where the soil strength is reduced for excavation

332 stage 3 (where S denotes soil). This can be expected because the earth pressure acting on the

333 wall is smaller in this case (Fig. 20a). However at later stages of excavation cracking occurs

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334 also under these assumptions (Fig. 20c). Table 6 summarizes at which excavation stage the

335 analysis for wall type 5 fails together with the calculated wall displacements which significantly

336 increase, also indicating unstable behaviour. At the end of excavation, it is evident that for the

337 case when the partial factor is applied to soil and the MIP-columns and = 1.0 kN/m for 𝐺𝑡

338 reinforced columns (denoted as Wall1-SWGt) tensile stresses are redistributed along the

339 reinforced column at the backside (Fig. 20c) leading to an acceptable tensile stress state along

340 the column at the arch section (Fig. 20d). The stress distribution for wall type 5 when the partial

341 factor is applied to soil strength and the MIP-columns (W5-SW) is compared to wall type 1 as

342 illustrated in Fig. 21. The difference in geometry, the reduced material strength and

343 consequently the increased earth pressure result in unstable behaviour before reaching the final

344 excavation level (Fig. 21b). Figure 21d shows the drop of tensile stresses due to cracking at

345 stage 5 for case W5-SW at which failure is indicated at arch section (see Table 6).

346 From the numerical studies performed the conclusion can be drawn that EC7-DA3 is

347 applicable to assess the design of such structures in accordance with Eurocode 7. However, it

348 should be kept in mind that the behaviour of soil-structure interaction problems such as deep

349 excavations is governed also by stiffness and not only by strength, but EC7 does not consider

350 factoring stiffness and therefore it has also not been investigated here. Furthermore, non-linear

351 material behavior of support structures, in particular in the context of numerical analyses, is not

352 covered in EC7. Based on the results of this study it is claimed that the proposed approach is a

353 step forward towards a more rational design of complex geotechnical structures by exploiting

354 the full capabilities of advanced numerical modelling taking into account highly nonlinear

355 material behaviour and still be in line with EC7. However, it is acknowledged that more

356 sensitivity studies are required before consistent and robust recommendations for practical

357 engineering could be formulated (e.g., Lees and Walter 2018).

358 CONCLUSIONS

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359 An extensive parametric study was carried out to investigate the behaviour of mixed in

360 place columns (MIP) for supporting an excavation in a slope by means of FE-analyses.

361 Emphasis was put on the behaviour of the supporting structure after reaching the tensile strength

362 of the column material. An advanced constitutive model for concrete was applied for modelling

363 the mechanical behaviour of the MIP structure, in order to capture the initiation of cracks and

364 the crack development with progressing excavation. It could be shown that significantly

365 different stress distributions in the MIP wall are obtained as compared to applying a simple

366 Mohr-Coulomb failure criterion with tension cut-off for the wall.

367 In order to investigate the potential for savings a parametric study was performed

368 changing the geometry of the supporting structure. Column length and supporting panel length

369 were reduced and several combinations have been investigated. It was found that a reduction

370 of column length and supporting panel length would still lead to equilibrium but from a design

371 point of view this would not be sufficient because no safety margin is introduced when

372 performing the analysis using characteristic strength parameters. Therefore additional analyses

373 were performed according to EC7 utilizing Design Approach 3 where partial factors on soil

374 strength and, in this particular case, also on the strength of the MIP-columns are applied. It

375 could be shown, that for the reference geometry equilibrium could still be achieved, but for the

376 extreme case investigated this is no longer the case. Thus it can be concluded that this type of

377 analysis is well suited for designing this type of geotechnical structures in accordance with EC7.

378 ACKNOWLEDGEMENTS

379 The first author would like to acknowledge the financial support with Ernst Mach Grant,

380 ASEA-UNINET provided by the Austrian Federal Ministry of Science, Research and Economy

381 (BMWFW) for doctoral degree study.

382 REFERENCES

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479 effects of horizontal twin-jet grouting in Shanghai soft soil deposits. Canadian

480 Geotechnical Journal, 50(3): 288–297. doi:10.1139/cgj-2012-0199.

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LIST OF TABLES

Table 1. Input parameter for soil layers.

Table 2. Input parameter for MIP wall.

Table 3. Tensile fracture energy for cement treated soil from three-point bending notched

beam test.

Table 4. Input parameter for investigation of reinforcement modelling.

Table 5. Tensile strength and tensile fracture energy parameters for analysis of reference

geometry.

Table 6. Analyses performed according to EC7-DA3.

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TABLES

Table 1. Input parameter for soil layers.

Parameter Soil layer

Description UnitSoft Sandy Silt(Upper)

Medium Stiff Sandy Silt(Middle)

Stiff to Very Stiff Sandy Silt(Lower)

Unsaturated soil unit weight 𝛾𝑢𝑛𝑠𝑎𝑡 [kN/m3] 20 20.5 21Deviatoric modulus 𝐸𝑟𝑒𝑓

50 [kPa] 10 000 25 000 45 000Reference pressure 𝜎𝑟𝑒𝑓 [kPa] 100 100 100Oedometric modulus 𝐸𝑟𝑒𝑓

𝑜𝑒𝑑 [kPa] 10 000 25 000 45 000Unloading-reloading modulus 𝐸𝑟𝑒𝑓

𝑢𝑟 [kPa] 30 000 75 000 135 000Cohesion 𝑐′ [kPa] 0 1 5Friction angle 𝜑′ [°] 25 27.5 30Dilatancy angle 𝜓 [°] 0 0 0Unloading-reloading Poisson’s ratio 𝜈𝑢𝑟 [-] 0.2 0.2 0.2Stress-dependency coefficient for stiffness 𝑚 [-] 0.5 0.5 0.5Coefficient of earth pressure at rest in primary one-dimensional compression

𝐾𝑛𝑐0 [-] 0.58 0.54 0.5

Stiffness at very small strains 𝐺𝑟𝑒𝑓0 [kPa] 62 500 156 250 281 250

Shear strain at 70%𝐺𝑟𝑒𝑓0 𝛾0.7 [-] 1.5E-4 1.5E-4 1.5E-4

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Table 2. Input parameter for MIP wall.

Parameter Concrete modelDescription Unit Wall Reinforced columnsUnit weight 𝛾 [kN/m3] 22 22Young’s modulus of cured MIP 𝐸28 [kPa] 300 000 300 000Poisson’s ratio 𝜈 [-] 0.15 0.15Uniaxial compressive strength 𝑓𝑐,28 [kPa] 1 200 1 200Uniaxial tensile strength 𝑓𝑡,28 [kPa] 125 600Dilatancy angle 𝜓𝑚𝑎𝑥 [°] 0 0Normalised initially mobilised strength 𝑓𝑐0𝑛 [-] 0.15 0.15Normalised failure strength (compression) 𝑓𝑐𝑓𝑛 [-] 0.95 0.95Normalised residual strength (compression) 𝑓𝑐𝑢𝑛 [-] 0.1 0.1Uniaxial plastic failure strain 𝜀𝑝

𝑐𝑝 [-] -0.0035 -0.0035Compressive fracture energy 𝐺𝑐,28 [kN/m] 30 30Normalised residual tensile strength 𝑓𝑡𝑢𝑛 [-] 0.05 0.05Tensile fracture energy 𝐺𝑡,28 [kN/m] 0.01 0.01Maximum friction angle 𝜑𝑚𝑎𝑥 [°] 30 30Note: Input parameter for MC model: = 22 kN/m3, = 300 000 kPa, = 0.15, = 350 kPa, = 30°, tension cut-off = 125 𝛾 𝐸 𝜈 𝑐′ 𝜑′

and 600 kPa for general and reinforced columns, respectively.

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Table 3. Tensile fracture energy for cement treated soil from three-point bending notched beam test.

Cement treated soil Gt (N/m) ft (kPa)* Cement-Soil content (%)

Water-Cement ratio

Size of specimen (W/D/L, unit in cm)

Reference

Sandy loam 9.5†-23.6† 200-1000 3-10 0.6-1.2 60/120/430 Dik (2017)

Singapore marine clay 2.6-4.4 120 25-35 0.6 5/5/20 Lee (2014)

Toyoura sand 9.3-12 380 15 1.9 4/4/16 Namikawa and Koseki (2006)

Uniformly graded sand 7.4-46 400-2600 30 1.0-1.9 10/10/40 Tariq and Maki (2014)

Note: W = width; D = depth; and L = span length.

*Splitting tensile strength test.

†Back analysis of real-scale 3-point bending test on steel beam (HEA 240) reinforced cement treated soil.

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Table 4. Input parameter for investigation of reinforcement modelling.

Parameter Concrete modelDescription Unit Discrete model Smeared modelUnit weight 𝛾 [kN/m3] 20 20Young’s modulus of cured MIP 𝐸28 [MPa] 2 000* 2 000Poisson’s ratio 𝜈 [-] 0.2 0.2Uniaxial compressive strength 𝑓𝑐,28 [kPa] 2 000* 12 000Uniaxial tensile strength 𝑓𝑡,28 [kPa] 200* 4 200Dilatancy angle 𝜓𝑚𝑎𝑥 [°] 0 0Normalised initially mobilised strength 𝑓𝑐0𝑛 [-] 0.15 0.15Normalised failure strength (compression) 𝑓𝑐𝑓𝑛 [-] 0.95 0.95Normalised residual strength (compression) 𝑓𝑐𝑢𝑛 [-] 0.1 0.1Uniaxial plastic failure strain 𝜀𝑝

𝑐𝑝 [-] -0.002 -0.002Compressive fracture energy 𝐺𝑐,28 [kN/m] 30 30Normalised residual tensile strength 𝑓𝑡𝑢𝑛 [-] 0.05 0.05Tensile fracture energy 𝐺𝑡,28 [kN/m] 0.016* 0.1Maximum friction angle 𝜑𝑚𝑎𝑥 [°] 30 30Note: Input parameters for reinforced steel beam (HEA 240): E = 200 GPa, = 0.29, Yield stress = 235 MPa.𝜈*Selected parameter values are based on back-analysis of Dik (2017) for steel reinforced cement-treated sand reported by Denies et al. (2014, 2015).

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Table 5. Tensile strength and tensile fracture energy parameters for analysis of reference geometry.

Set Cases General columns Reinforced columns Remarks

ft (kPa) Gt (kN/m) ft (kPa) Gt (kN/m)

A High ft, Low Gt 125 0.01 600 0.01

High ft, High Gt 125 0.01 600 1 Reference analysis

MC model 125 - 600 - MC model

B Low ft, Low Gt 125 0.01 125 0.01

Note: The input parameter for the MC model is described in Table 2.

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Table 6. Analyses performed according to EC7-DA3.

Wall Cases Partial factors General columns Reinforced columns ResultsSoil ( )𝑡𝑎𝑛𝜑′,𝑐 Wall ( )𝑓𝑐,𝑓𝑡 ft (kPa) Gt (kN/m) ft (kPa) Gt (kN/m) Uy (mm)*

1 W1-S 1.25 - 125 0.01 600 0.01 15.8 ConvergeW1-W - 1.25 100 0.01 480 0.01 7.5 ConvergeW1-SW 1.25 1.25 100 0.01 480 0.01 16.5 ConvergeW1-SWGt 1.25 1.25 100 0.01 480 1.0 8.3 Converge

5 W5-S 1.25 - 125 0.01 600 0.01 107 Failed at stage 6W5-W - 1.25 100 0.01 480 0.01 57 Failed at stage 7W5-SW 1.25 1.25 100 0.01 480 0.01 36 Failed at stage 5W5-SWGt 1.25 1.25 100 0.01 480 1.0 32 Failed at stage 7

*Lateral wall displacement at top of the reinforced column.

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FIGURE CAPTIONS

Fig. 1. (a) Schematic view of wall geometry and (b) wall configuration with details.

Fig. 2. Yield surfaces and failure envelope (Schädlich and Schweiger 2014).

Fig. 3. Normalised stress-strain curve: (a) in compression and (b) in tension (modified from

Schädlich and Schweiger 2014).

Fig. 4. Variation of tensile fracture energy with tensile strength.

Fig. 5. Constitutive model validation: (a) three-point bending test and (b) bending test of steel

reinforced cement-treated soil.

Fig. 6. (a) Changes of tensile stresses and (b) the progressive development of crack patterns

for case of High ft, Low Gt.

Fig. 7. Reference geometry: (a) lateral wall deflection and (b) calculated tensile stresses at

backside.

Fig. 8. Contour lines of principal tensile stresses ( ) of MIP wall.𝜎3

Fig. 9. Contour lines of parameter for case of High ft, Low Gt ( > 1.0 indicates 𝐻𝑐 𝐻𝑐

compression softening).

Fig. 10. Calculated tensile stresses at arch section.

Fig. 11. Effect of tensile strength of reinforced column on lateral wall deflection.

Fig. 12. Calculated tensile stresses for High ft, Low Gt and Low ft, Low Gt: (a) stage 5; (b)

stage 6 and (c) stage 7.

Fig. 13. Wall types in different geometries.

Fig. 14. Lateral wall deflection for different types of walls.

Fig. 15. Calculated tensile stresses for different types of walls at reinforced column: (a) stage

5; (b) stage 6 and (c) stage 7.

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Fig. 16. Calculated tensile stresses for different types of walls at arch section: (a) stage 5; (b)

stage 6 and (c) stage 7.

Fig. 17. Calculated tensile stresses for W1-S: (a) reinforced column and (b) arch section.


Fig. 19. Crack pattern and compression softening: (a) W1-S and (b) W5-S (failed at stage 6).

Fig. 20. Calculated tensile stresses of wall type 1 according to EC7-DA3: (a) stage 3; (b)

stage 5; (c) stage 7 and (d) stage 7 at arch section.

Fig. 21. Comparison of calculated tensile stresses for wall type 1 and 5: (a) stage 3; (b) stage

5; (c) stage 7 and (d) stage 7 at arch section.

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Fig. 1. (a) Schematic view of wall geometry.

179x140mm (300 x 300 DPI)

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Fig. 1. (b) wall configuration with details.

211x132mm (600 x 600 DPI)

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Fig. 2. Yield surfaces and failure envelope (Schädlich and Schweiger 2014).

144x87mm (600 x 600 DPI)

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Fig. 3. Normalised stress-strain curve: (a) in compression and (b) in tension (modified from Schädlich and Schweiger 2014).

279x108mm (600 x 600 DPI)

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Fig. 4. Variation of tensile fracture energy with tensile strength.

272x208mm (300 x 300 DPI)

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Fig. 5. Constitutive model validation: (a) three-point bending test.

288x201mm (300 x 300 DPI)

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Fig. 5. Constitutive model validation: (b) bending test of steel reinforced cement-treated soil.

292x204mm (300 x 300 DPI)

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Fig. 6. (a) Changes of tensile stresses and (b) the progressive development of crack patterns for case of High ft, Low Gt.

385x288mm (300 x 300 DPI)

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Fig. 7. Reference geometry: (a) lateral wall deflection and (b) calculated tensile stresses at backside.

388x298mm (300 x 300 DPI)

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Fig. 8. Contour lines of principal tensile stresses (σ3) of MIP wall.

349x194mm (300 x 300 DPI)

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Fig. 9. Contour lines of Hc parameter for case of High ft, Low Gt (Hc > 1.0 indicates compression softening).

170x161mm (300 x 300 DPI)

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Fig. 10. Calculated tensile stresses at arch section.

201x288mm (300 x 300 DPI)

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Fig. 11. Effect of tensile strength of reinforced column on lateral wall deflection.

201x288mm (300 x 300 DPI)

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Fig. 12. Calculated tensile stresses for High ft, Low Gt and Low ft, Low Gt: (a) stage 5; (b) stage 6 and (c) stage 7.

564x288mm (300 x 300 DPI)

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Fig. 13. Wall types in different geometries.

140x181mm (600 x 600 DPI)

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Fig. 14. Lateral wall deflection for different types of walls.

201x288mm (300 x 300 DPI)

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Fig. 15. Calculated tensile stresses for different types of walls at reinforced column: (a) stage 5; (b) stage 6 and (c) stage 7.

558x288mm (300 x 300 DPI)

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Fig. 16. Calculated tensile stresses for different types of walls at arch section: (a) stage 5; (b) stage 6 and (c) stage 7.

558x288mm (300 x 300 DPI)

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388x288mm (300 x 300 DPI)

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388x288mm (300 x 300 DPI)

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Fig. 19. Crack pattern and compression softening: (a) W1-S and (b) W5-S (failed at stage 6).

320x208mm (300 x 300 DPI)

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Fig. 20. Calculated tensile stresses of wall type 1 according to EC7-DA3: (a) stage 3; (b) stage 5; (c) stage 7 and (d) stage 7 at arch section.

391x576mm (300 x 300 DPI)

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Fig. 21. Comparison of calculated tensile stresses for wall type 1 and 5: (a) stage 3; (b) stage 5; (c) stage 7 and (d) stage 7 at arch section.

390x575mm (300 x 300 DPI)

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