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Bearing capacity of composite foundation consisting of T-shaped soil-cement column and soft clay
Accepted Manuscript Bearing capacity of composite foundation consisting of T-shaped soil-cement column and soft clay Yaolin Yi, Songyu Liu, Anand J. Puppala PII: DOI: Reference:
S2214-3912(17)30219-2 https://doi.org/10.1016/j.trgeo.2018.04.003 TRGEO 168
To appear in:
Transportation Geotechnics
Received Date: Revised Date: Accepted Date:
8 December 2017 19 March 2018 3 April 2018
Please cite this article as: Y. Yi, S. Liu, A.J. Puppala, Bearing capacity of composite foundation consisting of Tshaped soil-cement column and soft clay, Transportation Geotechnics (2018), doi: https://doi.org/10.1016/j.trgeo. 2018.04.003
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Bearing capacity of composite foundation consisting of T-shaped soil-cement column and soft clay Yaolin Yi1, Songyu Liu2, and Anand J. Puppala3 1
School of Civil and Environmental Engineering, Nanyang Technological University,
Singapore, 639798, Singapore 2
Institute of Geotechnical Engineering, Southeast University, Nanjing, 210096, China
3
Department of Civil Engineering, University of Texas at Arlington, Arlington, TX 76019, USA
ABSTRACT: The T-shaped column is a soil-cement column with two diameters, which is installed by foldable deep mixing blades for soft clay treatment. As a variable-diameter column, its design method is not well established, and this study focuses on the bearing capacity of composite foundation consisting of T-shaped columns and soft clay. A laboratory model test was employed to study the bearing capacity, stress distribution, and failure mode of the composite foundation. Twelve full-scale loading tests were performed in the field to study the geometrical parameters of composite foundation affecting on its bearing capacity. The experimental results indicated that the bearing capacity of composite foundation increased with increasing of the cap length and column, and decreasing of the column spacing. The experimental results also revealed that the column failure might occur at the small-diameter column just below the column cap, which then led to the soil failure nearby. By including this additional failure mode, the design method for conventional column was adapted to estimate the bearing capacity of composite foundation consisting of T-shaped column and soft clay, and the method was validated by the experimental data.
Keywords: Deep mixing; T-shaped column; Composite foundation; Bearing capacity; Estimation.
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Introduction Soil-cement columns installed by deep mixing method are widely used for soft clay treatment in many countries [1, 2, 6, 8, 9, 12, 14, 21, 22, 27]. The estimation of the vertical bearing capacity of composite foundation consisting of columns and soft clay is essential to the design of deep mixing projects [2, 6, 11]. Coastal Development Institute of Technology (CDIT) [6] assumes that all the overburden pressure above the composite foundation concentrates on the columns, which ignores the contribution of the bearing capacity of soft clay, resulting in highly conservative design and increase of cost. In China, the bearing capacity of composite foundation (qsc) is estimated according to Equation 1 [11]. However, the qsc calculated by Equation 1 should not be higher than the bearing capacity of the underlain soil; otherwise, the qsc can be conservatively estimated with Equation 2. qsc as
Qc (1 as )qs Ac
qsc qt
Plf s A
(1)
(2)
where as is area replacement ratio; Ac and Qc (force) are sectional area and ultimate bearing capacity of single column; qs is ultimate bearing capacity of untreated ground, and β is its reduction factor; P and A are perimeter and area of foundation, respectively; l is column length; fs is friction; qt is ultimate bearing capacity of underlain soil.
Equations 1 and 2 are corresponding to different failure modes. Since the unconfined compressive strength of column is limited, typically 200-2000 kPa in clay [3], the column may fail subjected to vertical loading; this has been confirmed by
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previous studies [13, 31]. Assuming that the strength of column is the same along depth, the column failure appears at a very shallow depth, which then induces the soil failure nearby (Fig. 1a), due to that the failure strain of column is much smaller than that of soil [6]. Hence, the qs can be estimated as a composite of those of single column (Qc) and soil (qs), with a reduction factor (β) used for the qs, as shown in Equation 1. Since the failure occurs around column top, the Qc is dominated by the column strength, and Equation 1 can be replaced with Equation 3. When the underlain soil is very weak (Fig. 1b), the failure may occurs in the underlain soil; in this case, the column-treated ground can be considered as a block. For conservative estimation, the failure surface can be simplified as that shown in Fig. 1b, and the qsc can be estimated through Equation 2. The principle of the above-mentioned method (Fig. 1 and Equations 1-2) is similar to that proposed by Bergado et al. [2] for composite foundation consisting of soil-lime columns and soft clay. For practical short-term estimation, the fs (Fig. 1b) can be determined as the undrained shear strength of the soil (Su), and the qt is 6-9Su depending on the foundation shape [2]. However, the existing method is only used for the conventional column with a constant diameter.
qsc as qu (1 as )qs where qu is unconfined compressive strength of column.
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(3)
Fig. 1. Failure modes of composite foundation consisting conventional column and soft clay Liu et al. [16] developed a T-shaped column with two diameters; there is a large-diameter column cap at the shallow depth, and hence the column shape is similar to “T”. Both laboratory and field tests demonstrated that the T-shaped column yielded less total, differential, and post-construction ground settlement under embankment load in comparison with conventional column [16, 29]. As a variable-diameter column, its design method is not well established. For single T-shaped column, Yi et al. [30] found that the failure was at the small-diameter column under the cap. This finding indicates that Equations 2 and 3 may not properly estimate the qsc of composite foundation consisting T-shaped columns and soft clay, as its failure behavior may be different from that shown in Fig. 1. Hence, in this study, a laboratory model test was firstly employed to study the bearing capacity, stress distribution, and failure mode of the composite foundation consisting of T-shaped column and soft clay. Then, twelve full-scale loading tests were
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also performed in a field site to study the geometrical parameters of composite foundation affecting on its bearing capacity. Last, the design method for conventional column was adapted to estimate the bearing capacity of composite foundation consisting of T-shaped column and soft clay, and the data from the laboratory and field loading tests were used to verify its applicability.
Experimental methods Laboratory model test The set-up of laboratory model test is illustrated in Fig. 2. The diameter (d1) and length (l1) of the column cap were 110 and 100 mm, respectively, and the diameter (d2) and length (l2) of the small-diameter column were 50 and 500 mm, respectively. The column was installed in the centre of the soft clay, which was accommodated in a cylindrical mold (Fig. 2); the mold was made from stainless polyethylene, and it had a height of 1000 mm and inner diameter of 300 mm. A 20-mm-thick stainless acrylic plate was used as the loading plate, and it had a diameter of 160 mm, i.e. the area replacement ratio of the cap (as1) and small-diameter column (as2) were 0.47 and 0.10, respectively. The above-mentioned parameters were selected according to common practical values and a model scale of 1/10. A 20-mm-thick sand mat, constrained by a polyvinyl chloride (PVC) tube with diameter slightly large than that of the loading plate, was placed between the loading plate and ground surface. Two pressure cells were placed on the surface of column and soil, as shown in Fig. 2; the thickness and diameter of the pressure cells were 7 and 17 mm, respectively. Yi et al. [30] reported a procedure to prepare small-scale T-shaped column in laboratory for loading test; the exactly same
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materials and procedure were used in this study, and hence the details were not repeated here. The mini-vane shear test was conducted at the center of the prepared clay, and the Su values were 9, 7, and 11 kPa at the bottom, middle, and top, respectively. The column had an unconfined compressive strength around 500 kPa.
Fig. 2. Set-up of the laboratory model test (not to scale) The loading test on composite foundation was performed as per a slow maintained-load procedure as detailed in Han and Ye [10]. Several load levels, started from zero to failure load, were gradually applied on the loading plate. Each load level should reach the stability criteria before applying of the next higher load level; the criteria was that the rate of plate settlement was less than 0.1 mm per hour. When the cumulative plate settlement reached one tenth (1/10) of its diameter or a load level was applied for 24 hours without satisfying the stability criteria, the composite foundation
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was considered as failed. The load level corresponding to failure was determined as the failure load, and the one before it was the ultimate bearing capacity, qcs, of the composite foundation. For comparison, another loading test was conducted on the soft ground without column. Since the diameter of the mold was only 1.86 times that of the loading plate, it caused boundary effect to the loading tests; however, it would not affect much on the compassion between column-treated and untreated grounds, as well as the failure mode of the composite foundation. Upon completion of loading, the column was extruded for observation of failure; two samples were also cut from the small-diameter column and tested for unconfined compressive strength, which were 467 and 534 kPa, very similar to the results in Yi et al. [30].
Field test The field site was in Suzhou, Jiangsu Province, China. The ground water table was at a depth of 1.0 to 1.5 m. The depth and property of the soil layers, determined according to Comprehensive Institute of Geotechnical Investigation and Surveying (CIGIS) [7], are listed in Table 1. The loading tests were conducted on six composite foundations (C1 to C6 in Table 2) consisting of T-shaped columns and soft clay with varying geometrical parameters. All the columns had a total length (l) of was 16.5 m. Four of the columns (C1, C2, C3, and C4) had the same diameters of column cap (d1=1.0 m) and small-diameter column (d2=0.5 m), but different cap lengths (l1), i.e. 2 m for C1, 3 m for C2 and C3, and 4 m for C4. The column dimensions (d1=1.2 m, d2=0.6 m, and l1=4 m) in C5 and C6 were the same, but their column spacing were different. All the columns
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were arranged in a triangular pattern, and the column spacing was in a range of 2.0-2.6 m as shown in Table 2. Table 1. Depth and property of soil layers in field Undrained Depth of layer Bulk density
Water content
Plastic limit
(%)
(%)
Soil layer
Liquid limit (%) Void ratio bottom (m)
(g/cm3)
shear strength (kPa)
Crust
0.5-1.5
NM
NM
NM
NM
NM
NM
Soft clay
13.8-15.4
1.66-1.79
41.2-59.0
20.9-30.3
43.2-63.1
1.24-1.67
17-39
Silty clay
15.8-16.5
2.05-2.09
21.4-26.0
17.6-26.7
36.0-36.2
0.62-0.70
NM
Stiff clay
NM
NM
NM
NM
NM
NM
NM
Note: NM-not measured.
Table 2. Geometrical parameters and qsc of composite foundations in field Column
Diameter
Length
Diameter of
Total
Column
Diameter
Ultimate
ID
of cap
of cap
small-diameter
length of
spacing
of loading
bearing
d1 (m)
l1 (m)
column
column
S (m)
plate
capacity
d2 (m)
l (m)
(m)
qsc (kPa)
C1
1.0
2.0
0.5
16.5
2.0
2.1
240
C2
1.0
3.0
0.5
16.5
1.8
1.9
300
C3
1.0
3.0
0.5
16.5
2.2
2.3
240
C4
1.0
4.0
0.5
16.5
2.0
2.1
270
C5
1.2
4.0
0.6
16.5
2.4
2.5
265
C6
1.2
4.0
0.6
16.5
2.6
2.7
240
Ordinary Portland cement, with a content of 255 kg/m3, was used for the field column installation. The tap water and cement, with mass ratio of 0.55, were pre-mixed to produce slurry (i.e. wet mixing method) and then injected into the ground with a
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pressure around 300 kPa. A construction machine equipped with foldable mixing blades was used to install the T-shaped column as illustrated in Fig. 3. To better mix the cement slurry with the soil, the outer and inner shafts (Fig. 3) of the mixing blades rotated oppositely, as suggested by Shen et al. [25], Shen et al. [24], Chai et al. [5] and Chai et al. [4]. The machine and construction parameters for the installation of T-shaped column were the same as those in Liu et al. [16]. At 28 days, the unconfined compressive strength of the columns, determined based on cored samples, was in range of 740-1930 kPa, with an average value of 1260 kPa and coefficient of variation of 0.18.
Fig. 3. Illustration of installation of T-shaped column in field Twenty-eight days after column installation, the vertical loading test on composite foundation consisting of one column and the corresponding untreated soil was conducted. Two tests were conducted for each type of composite foundation. The section area of the loading plate, circular steel with 30-mm thickness, was the same as that of the one-column influence area, which was determined by the column spacing and arrangement. The diameters of the loading plates are shown in Table 2. The sand mat, with 100 mm thickness, was placed between the column top and steel plate. The loading
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test procedure was the same as that for the laboratory test. Additionally, settlements during the unloading stages were also measured for the field tests.
Results and discussion Laboratory model test The laboratory loading test results, in terms of pressure-settlement curves, are presented in Fig. 4. The settlements of both grounds are negligible under the first applied pressure (21 kPa), since the soft clay was prepared by pre-consolidating with 24-kPa vertical pressure [30]. Thereafter, the untreated ground exhibits nonlinear pressure-settlement curve before failure due to the deformation behavior of the soft clay. On contrary, the pressure-settlement curve of T-shaped column-treated ground is nearly linear before failure. This is because the column was underlain by a thin stiff sand layer, and the settlement behavior of the composite foundation under rigid loading plate is dominated by that of the column, which has a relatively linear stress-strain behavior. The ultimate bearing capacity, qcs, of the untreated ground is determined as 51 kPa, close to the calculated value (56 kPa) according to Skempton [26] using the average Su of the soft clay (9 kPa). This result indicates that the boundary effect is insignificant for the laboratory loading tests. The qcs of the T-shaped column-treated ground is 117 kPa, which is twice that of the untreated ground, i.e. the column considerably increased the bearing capacity of the soft ground.
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Fig. 4. Pressure-settlement curves of laboratory loading tests The measured stresses on the column and soil are presented in Fig. 5. The back-calculated stress on the loading plate, using the measured stresses and areas of the column and soil, was also shown in Fig. 5 along with the applied stress. The back-calculated stress-time curve generally agreed with that of the applied stress, although there was certain dispersion between them. Both the stresses on column and soil increased after applying of each load level (Fig. 5); thereafter, the soil stress decreased with time due to consolidation. The drop of the column stress and increase of the soil stress shortly after the applying of the final load level indicated the failure of the composite foundation. Fig. 5 also shows that the column stress was significantly higher than the soil stress at the same time due to the higher stiffness of the column compared to that of the clay; this contributed to the enhanced bearing capacity of composite foundation. Before applying the final load (i.e. under the load level of ultimate bearing capacity), the soil stress was 26 kPa, indicating the stress reduction factor, β, was 0.5;
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the column stress was 198 kPa, which was also lower than its unconfined compressive strength (~500 kPa), i.e. the column cap did not fail.
Fig.5. Vertical stresses on soil, column, and plate Fig. 6 is the picture of extruded column after loading, showing evident shear failure surfaces at the small-diameter column just under the cap, similar to that observed for loading test only on single column (not composite foundation) [30]. It is noted that the horizontal fracture in the middle of small-diameter column was induced by the excavation. The visual observation indicated that the failure occurred at the small-diameter column just under the cap, which then induced the soil failure nearby. This failure behavior was due to that the cap had a much larger section area (4.8 times) than the small-diameter column. Consequently, the additional stress in the small-diameter column just under the cap was considerably greater than that in the cap, and this stress concentration resulted in shear failure in the small-diameter column. This failure behavior is different from that of composite foundation consisting conventional
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column and soft clay, where the failure firstly occurred around the column top.
Fig. 6. Excavated T-shaped column after loading test Field test As the load plates had varying diameters, the plate settlements were normalized by their diameters, and then plotted against the applied vertical pressures as shown in Fig. 7. The failures of all the loading tests were determined by the settlement criterion (>10% plate diameter). After unloading, the rebound deformation was very limited, confirming the failures were researched for all the tests. It is noted that one more load level was applied after the settlement reached 10% plate diameter for some of the loading tests (e.g. Fig. 7a), because the technicians were not confident at first. For all the tests, the failure load was determined as that reached 10% plate diameter, and the qcs was that prior to the failure load. Different from the laboratory result (Fig. 4), the linear pressure-settlement relationship only observed when the applied pressure was relatively low for the field loading tests (Fig. 7), and then the settlement increased non-linearly with the pressure. This is because the columns in the field were underlain by relatively stiff clay layer, not bedrock, while there was only 50-mm-thick dense sand between the column and rigid mold bottom in laboratory.
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(a)
(b)
Page 14
(c)
(d)
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(e)
(f) Fig. 7. Pressure-settlement/plate diameter curves of loading tests in field: (a) C1, (b) C2, (c) C3, (d) C4, (e) C5, and (f) C6. Fig. 7 also indicates that there is certain dispersion between two loading curves for
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most the composite foundations. This is mainly due to the strength variability of columns induced by the field construction process [15, 18, 19, 23, 28]. Nevertheless, the determined qcs were the same for the same composite foundation. Compared to the qcs in this study, the column heterogeneity affected more on the bearing capacity of single column (Qc) [30]. This is because the bearing capacity of the soil, which had much lower variability that the column, was a major component of the composite foundation. Although the column installation process caused disturbance to the surrounding soil with a limited distance, the soil strength recovered with time [20, 24, 25]. Table 2 lists the qcs of the composite foundations determined from loading tests. The geometry parameters of C1 and C4 composite foundations are the same except for the cap length (l1), which are 2 m for C1 and 4 m for C4; the qcs of C1 and C4 were 240 and 270 kPa, respectively, indicating the qcs increased with l1. The C2 and C3 had the same geometries of the single columns, but the C2 had smaller column spacing, which resulted in a greater qcs (300 kPa) compared to that of the C3 (240 kPa); this was confirmed by comparison of C5 and C6. The C4 and C5 had very similar qcs, although the column spacing of the C4 (2.0 m) was considerable lower than that of the C5 (2.4 m); this indicated that increasing of the column (and/or cap) diameter also increased the bearing capacity of composite foundation. The C1, C3, and C6 yielded the same qcs, due to the multiple effects of column (and/or cap) diameter, spacing, and length on the qcs.
Estimation method The laboratory model test revealed that the failure of the composite foundation might be induced by the shear failure at the small-diameter column just below the cap, which then
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caused soil failure nearby, as shown in Fig. 8. According to this failure behavior, the qcs has three major contributions, including the (1) strength of small-diameter column, (2) bearing capacity of the soil under the cap, and (3) friction surrounding the foundation around cap (Fig. 8). Hence, the qcs can be estimated from Equation 4, which was adapted from Equations 1 and 2. qsc as 2 qu (1 as 2 )qs1
Pl1 f s1 A
(4)
where as2 is area replace ratio of small-diameter column; l1 is cap length; fs1 is average friction around cap; qs1 is ultimate bearing capacity of soil under cap.
Fig. 8. A possible failure mode of composite foundation consisting T-shaped column and soft clay Additionally, if the cap diameter is very small, the T-shaped column will behave similarly to the conventional column; as shown in Fig. 1a, the column failure may appear around the column top, and the qcs can be calculated from Equation 3 using the area replacement ratio of cap (as1). As shown in Fig. 1b, the failure of the composite foundation may occur in the underlain soil if it is too weak; in this case, the qcs is
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calculated using Equation 2. The minimal value calculated from Equations 2, 3, and 4 is the qcs. The experimental data form the laboratory and field tests were used to verify the above-mentioned equations. Since the loading time for laboratory and field tests was relatively short (less than one day for each test), they were generally considered as in undrain condition for soft clay. Assuming undrained condition, the friction (fs) was determined as the average undrained shear strength of soil. Because only the vane shear test was only conducted for the soft clay layer, the fs1 was determined as the average value of soft clay around cap (Su1), and the qs1 was determined from Su1 using the Skempton [26] method. For the field tests, this assumed the crust layer had the same properties as those of soft clay at shallow depth, resulting in a slight underestimation of qsc when using Equations 3 and 4. The fs was determined as the average undrained shear strength (Su) of all the soft clays, and the qt was determined from Su using the Skempton [26] method. This assumed all the soil layers had the same properties as those of the soft clay layer, leading to a significantly underestimation of qsc when using Equation 2. The average measured column strength (qu) was used for calculation. Based on the results obtained from the laboratory test, β was determined as 0.5. It is worth noting that β should not be constant for all the conditions, e.g. it can be affected by the relative stiffness of column and soil, and the β in the laboratory test should not be the same as that in the field tests. Since the β was not measured for the field tests, the value of 0.5 was also used for the calculation of field tests. Table 3 lists all the mechanical parameters of the soil and column used for calculation. Table 3. Mechanical parameters of soil and column used for calculation
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fs1
fs
qs1
qs
qt
qu
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
Laboratory
11
9
76
56
81
500
Field
19
24
140-162
117
216
1260
Test
The qcs calculated from Equations 2, 3, and 4 are listed in Table 4. For each case, the calculated qcs from Equations 4 is considerably lower than from Equations 2 and 3, suggesting the failure mode in Fig. 8 occurs for the T-shaped column-treated ground, consistent with the observation after excavation in the laboratory model test. The calculated qcs from Equations 4 is 0.81-1.03 times of the corresponding measured values. For the field loading tests, all the calculated qcs are smaller than the corresponding measured values except for only one case (C3); the underestimation should be due to the neglecting of the crust layer during calculation. Overall, the comparison indicates that Equation 4 can properly estimate the qcs of T-shaped column-treated ground for preliminary design purpose. Table 4. Calculated and measured qsc Field columns
Lab Method column
C1
C2
C3
C4
C5
C6
Equation 2
216
970
1050
970
803
850
905
Equation 3
251
331
391
331
296
335
286
Equation 4
111
195
261
278
234
252
217
Measurement
117
240
300
270
240
265
240
The qcs calculated from Equation 2 is the maximum calculated values for each of the field composite foundation, which is more than three times of the corresponding measured value, despite that very conservative soil properties have been used for
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calculation. This is not surprising, as the industry practice in China has found that the failure mode in Fig. 1b is unlikely to occur for most of the conventional column-treated grounds, and the qcs is dominated by Equation 3, not Equation 2 [17]. For the laboratory test, the qcs calculated from Equation 2 is slightly smaller than that calculated from Equation 3, due to the very limited column length in the laboratory test. For the field composite foundations, the qcs calculated from Equation 3 is relatively close to that calculated from Equation 4, indicating the failure mode in Fig. 1a is also possible if the cap diameter is small enough. For the six field tests, the calculated values from Equation 3 is 1.2-1.4 times of the corresponding measured values, i.e. it is overestimated the experimental data, although the conservative qs has been used for calculation by neglecting the crust layer.
Conclusions Laboratory and field tests were performed to study the bearing capacity of composite foundation consisting T-shaped column and soft clay under vertical loading. The field tests indicated that the bearing capacity of composite foundation increased with increasing of the cap length and column diameter, as well as decreasing of the column spacing. The laboratory test revealed that the failure of composite foundation might be induced by the shear failure at the small-diameter column just below the cap, which then caused soil failure nearby. By including this additional failure mode, the design method for conventional column was adapted to estimate the bearing capacity of composite foundation consisting of T-shaped column and soft clay, and the method was validated by the experimental data. Nevertheless, further study is still needed to investigate the
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relative stiffness and strength of the column and soil affecting the bearing capacity and failure behavior of composite foundation, which can be conducted through numerical modeling.
Acknowledgments The authors sincerely appreciate the help from Zhu Zhiduo, Xi Peisheng, Li Chen, Zhang Bafa, and Zhu Zhihua for this study.
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Engineering 134(6), 845-854. 25. Shen S-L, Miura N, Koga H (2003) Interaction mechanism between deep mixing column and surrounding clay during installation. Canadian Geotechnical Journal 40(2), 293-307. 26. Skempton AW (1951) The bearing capacity of clays. Building Research Congress 1, 180-189. 27. Terashi M (2003). The state of practice in deep mixing methods. Proceedings of the 3rd International Specialty Conference on Grouting and Ground Treatment, ASCE GSP 120, 25-49. 28. Terashi M, Kitazume M (2011) QA/QC for deep-mixed ground: current practice and future research needs. Proceedings of the Institution of Civil Engineers-Ground Improvement 164(3), 161-177. 29. Yi Y, Liu S, Puppala A (2016) Laboratory modelling of T-shaped soil–cement column for soft ground treatment under embankment. Géotechnique 66(1), 85-89. 30. Yi Y, Liu S, Puppala AJ, Xi P (2017) Vertical bearing capacity behaviour of single T-shaped soil–cement column in soft ground: laboratory modelling, field test, and calculation. Acta Geotechnica, 1-12. 31. Yin J, Fang Z (2006) Physical modelling of consolidation behaviour of a composite foundation consisting of a cement-mixed soil column and untreated soft marine clay. Geotechnique 56(1), 63-68.
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S2214-3912(17)30219-2 https://doi.org/10.1016/j.trgeo.2018.04.003 TRGEO 168
To appear in:
Transportation Geotechnics
Received Date: Revised Date: Accepted Date:
8 December 2017 19 March 2018 3 April 2018
Please cite this article as: Y. Yi, S. Liu, A.J. Puppala, Bearing capacity of composite foundation consisting of Tshaped soil-cement column and soft clay, Transportation Geotechnics (2018), doi: https://doi.org/10.1016/j.trgeo. 2018.04.003
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Bearing capacity of composite foundation consisting of T-shaped soil-cement column and soft clay Yaolin Yi1, Songyu Liu2, and Anand J. Puppala3 1
School of Civil and Environmental Engineering, Nanyang Technological University,
Singapore, 639798, Singapore 2
Institute of Geotechnical Engineering, Southeast University, Nanjing, 210096, China
3
Department of Civil Engineering, University of Texas at Arlington, Arlington, TX 76019, USA
ABSTRACT: The T-shaped column is a soil-cement column with two diameters, which is installed by foldable deep mixing blades for soft clay treatment. As a variable-diameter column, its design method is not well established, and this study focuses on the bearing capacity of composite foundation consisting of T-shaped columns and soft clay. A laboratory model test was employed to study the bearing capacity, stress distribution, and failure mode of the composite foundation. Twelve full-scale loading tests were performed in the field to study the geometrical parameters of composite foundation affecting on its bearing capacity. The experimental results indicated that the bearing capacity of composite foundation increased with increasing of the cap length and column, and decreasing of the column spacing. The experimental results also revealed that the column failure might occur at the small-diameter column just below the column cap, which then led to the soil failure nearby. By including this additional failure mode, the design method for conventional column was adapted to estimate the bearing capacity of composite foundation consisting of T-shaped column and soft clay, and the method was validated by the experimental data.
Keywords: Deep mixing; T-shaped column; Composite foundation; Bearing capacity; Estimation.
Page 1
Introduction Soil-cement columns installed by deep mixing method are widely used for soft clay treatment in many countries [1, 2, 6, 8, 9, 12, 14, 21, 22, 27]. The estimation of the vertical bearing capacity of composite foundation consisting of columns and soft clay is essential to the design of deep mixing projects [2, 6, 11]. Coastal Development Institute of Technology (CDIT) [6] assumes that all the overburden pressure above the composite foundation concentrates on the columns, which ignores the contribution of the bearing capacity of soft clay, resulting in highly conservative design and increase of cost. In China, the bearing capacity of composite foundation (qsc) is estimated according to Equation 1 [11]. However, the qsc calculated by Equation 1 should not be higher than the bearing capacity of the underlain soil; otherwise, the qsc can be conservatively estimated with Equation 2. qsc as
Qc (1 as )qs Ac
qsc qt
Plf s A
(1)
(2)
where as is area replacement ratio; Ac and Qc (force) are sectional area and ultimate bearing capacity of single column; qs is ultimate bearing capacity of untreated ground, and β is its reduction factor; P and A are perimeter and area of foundation, respectively; l is column length; fs is friction; qt is ultimate bearing capacity of underlain soil.
Equations 1 and 2 are corresponding to different failure modes. Since the unconfined compressive strength of column is limited, typically 200-2000 kPa in clay [3], the column may fail subjected to vertical loading; this has been confirmed by
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previous studies [13, 31]. Assuming that the strength of column is the same along depth, the column failure appears at a very shallow depth, which then induces the soil failure nearby (Fig. 1a), due to that the failure strain of column is much smaller than that of soil [6]. Hence, the qs can be estimated as a composite of those of single column (Qc) and soil (qs), with a reduction factor (β) used for the qs, as shown in Equation 1. Since the failure occurs around column top, the Qc is dominated by the column strength, and Equation 1 can be replaced with Equation 3. When the underlain soil is very weak (Fig. 1b), the failure may occurs in the underlain soil; in this case, the column-treated ground can be considered as a block. For conservative estimation, the failure surface can be simplified as that shown in Fig. 1b, and the qsc can be estimated through Equation 2. The principle of the above-mentioned method (Fig. 1 and Equations 1-2) is similar to that proposed by Bergado et al. [2] for composite foundation consisting of soil-lime columns and soft clay. For practical short-term estimation, the fs (Fig. 1b) can be determined as the undrained shear strength of the soil (Su), and the qt is 6-9Su depending on the foundation shape [2]. However, the existing method is only used for the conventional column with a constant diameter.
qsc as qu (1 as )qs where qu is unconfined compressive strength of column.
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(3)
Fig. 1. Failure modes of composite foundation consisting conventional column and soft clay Liu et al. [16] developed a T-shaped column with two diameters; there is a large-diameter column cap at the shallow depth, and hence the column shape is similar to “T”. Both laboratory and field tests demonstrated that the T-shaped column yielded less total, differential, and post-construction ground settlement under embankment load in comparison with conventional column [16, 29]. As a variable-diameter column, its design method is not well established. For single T-shaped column, Yi et al. [30] found that the failure was at the small-diameter column under the cap. This finding indicates that Equations 2 and 3 may not properly estimate the qsc of composite foundation consisting T-shaped columns and soft clay, as its failure behavior may be different from that shown in Fig. 1. Hence, in this study, a laboratory model test was firstly employed to study the bearing capacity, stress distribution, and failure mode of the composite foundation consisting of T-shaped column and soft clay. Then, twelve full-scale loading tests were
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also performed in a field site to study the geometrical parameters of composite foundation affecting on its bearing capacity. Last, the design method for conventional column was adapted to estimate the bearing capacity of composite foundation consisting of T-shaped column and soft clay, and the data from the laboratory and field loading tests were used to verify its applicability.
Experimental methods Laboratory model test The set-up of laboratory model test is illustrated in Fig. 2. The diameter (d1) and length (l1) of the column cap were 110 and 100 mm, respectively, and the diameter (d2) and length (l2) of the small-diameter column were 50 and 500 mm, respectively. The column was installed in the centre of the soft clay, which was accommodated in a cylindrical mold (Fig. 2); the mold was made from stainless polyethylene, and it had a height of 1000 mm and inner diameter of 300 mm. A 20-mm-thick stainless acrylic plate was used as the loading plate, and it had a diameter of 160 mm, i.e. the area replacement ratio of the cap (as1) and small-diameter column (as2) were 0.47 and 0.10, respectively. The above-mentioned parameters were selected according to common practical values and a model scale of 1/10. A 20-mm-thick sand mat, constrained by a polyvinyl chloride (PVC) tube with diameter slightly large than that of the loading plate, was placed between the loading plate and ground surface. Two pressure cells were placed on the surface of column and soil, as shown in Fig. 2; the thickness and diameter of the pressure cells were 7 and 17 mm, respectively. Yi et al. [30] reported a procedure to prepare small-scale T-shaped column in laboratory for loading test; the exactly same
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materials and procedure were used in this study, and hence the details were not repeated here. The mini-vane shear test was conducted at the center of the prepared clay, and the Su values were 9, 7, and 11 kPa at the bottom, middle, and top, respectively. The column had an unconfined compressive strength around 500 kPa.
Fig. 2. Set-up of the laboratory model test (not to scale) The loading test on composite foundation was performed as per a slow maintained-load procedure as detailed in Han and Ye [10]. Several load levels, started from zero to failure load, were gradually applied on the loading plate. Each load level should reach the stability criteria before applying of the next higher load level; the criteria was that the rate of plate settlement was less than 0.1 mm per hour. When the cumulative plate settlement reached one tenth (1/10) of its diameter or a load level was applied for 24 hours without satisfying the stability criteria, the composite foundation
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was considered as failed. The load level corresponding to failure was determined as the failure load, and the one before it was the ultimate bearing capacity, qcs, of the composite foundation. For comparison, another loading test was conducted on the soft ground without column. Since the diameter of the mold was only 1.86 times that of the loading plate, it caused boundary effect to the loading tests; however, it would not affect much on the compassion between column-treated and untreated grounds, as well as the failure mode of the composite foundation. Upon completion of loading, the column was extruded for observation of failure; two samples were also cut from the small-diameter column and tested for unconfined compressive strength, which were 467 and 534 kPa, very similar to the results in Yi et al. [30].
Field test The field site was in Suzhou, Jiangsu Province, China. The ground water table was at a depth of 1.0 to 1.5 m. The depth and property of the soil layers, determined according to Comprehensive Institute of Geotechnical Investigation and Surveying (CIGIS) [7], are listed in Table 1. The loading tests were conducted on six composite foundations (C1 to C6 in Table 2) consisting of T-shaped columns and soft clay with varying geometrical parameters. All the columns had a total length (l) of was 16.5 m. Four of the columns (C1, C2, C3, and C4) had the same diameters of column cap (d1=1.0 m) and small-diameter column (d2=0.5 m), but different cap lengths (l1), i.e. 2 m for C1, 3 m for C2 and C3, and 4 m for C4. The column dimensions (d1=1.2 m, d2=0.6 m, and l1=4 m) in C5 and C6 were the same, but their column spacing were different. All the columns
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were arranged in a triangular pattern, and the column spacing was in a range of 2.0-2.6 m as shown in Table 2. Table 1. Depth and property of soil layers in field Undrained Depth of layer Bulk density
Water content
Plastic limit
(%)
(%)
Soil layer
Liquid limit (%) Void ratio bottom (m)
(g/cm3)
shear strength (kPa)
Crust
0.5-1.5
NM
NM
NM
NM
NM
NM
Soft clay
13.8-15.4
1.66-1.79
41.2-59.0
20.9-30.3
43.2-63.1
1.24-1.67
17-39
Silty clay
15.8-16.5
2.05-2.09
21.4-26.0
17.6-26.7
36.0-36.2
0.62-0.70
NM
Stiff clay
NM
NM
NM
NM
NM
NM
NM
Note: NM-not measured.
Table 2. Geometrical parameters and qsc of composite foundations in field Column
Diameter
Length
Diameter of
Total
Column
Diameter
Ultimate
ID
of cap
of cap
small-diameter
length of
spacing
of loading
bearing
d1 (m)
l1 (m)
column
column
S (m)
plate
capacity
d2 (m)
l (m)
(m)
qsc (kPa)
C1
1.0
2.0
0.5
16.5
2.0
2.1
240
C2
1.0
3.0
0.5
16.5
1.8
1.9
300
C3
1.0
3.0
0.5
16.5
2.2
2.3
240
C4
1.0
4.0
0.5
16.5
2.0
2.1
270
C5
1.2
4.0
0.6
16.5
2.4
2.5
265
C6
1.2
4.0
0.6
16.5
2.6
2.7
240
Ordinary Portland cement, with a content of 255 kg/m3, was used for the field column installation. The tap water and cement, with mass ratio of 0.55, were pre-mixed to produce slurry (i.e. wet mixing method) and then injected into the ground with a
Page 8
pressure around 300 kPa. A construction machine equipped with foldable mixing blades was used to install the T-shaped column as illustrated in Fig. 3. To better mix the cement slurry with the soil, the outer and inner shafts (Fig. 3) of the mixing blades rotated oppositely, as suggested by Shen et al. [25], Shen et al. [24], Chai et al. [5] and Chai et al. [4]. The machine and construction parameters for the installation of T-shaped column were the same as those in Liu et al. [16]. At 28 days, the unconfined compressive strength of the columns, determined based on cored samples, was in range of 740-1930 kPa, with an average value of 1260 kPa and coefficient of variation of 0.18.
Fig. 3. Illustration of installation of T-shaped column in field Twenty-eight days after column installation, the vertical loading test on composite foundation consisting of one column and the corresponding untreated soil was conducted. Two tests were conducted for each type of composite foundation. The section area of the loading plate, circular steel with 30-mm thickness, was the same as that of the one-column influence area, which was determined by the column spacing and arrangement. The diameters of the loading plates are shown in Table 2. The sand mat, with 100 mm thickness, was placed between the column top and steel plate. The loading
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test procedure was the same as that for the laboratory test. Additionally, settlements during the unloading stages were also measured for the field tests.
Results and discussion Laboratory model test The laboratory loading test results, in terms of pressure-settlement curves, are presented in Fig. 4. The settlements of both grounds are negligible under the first applied pressure (21 kPa), since the soft clay was prepared by pre-consolidating with 24-kPa vertical pressure [30]. Thereafter, the untreated ground exhibits nonlinear pressure-settlement curve before failure due to the deformation behavior of the soft clay. On contrary, the pressure-settlement curve of T-shaped column-treated ground is nearly linear before failure. This is because the column was underlain by a thin stiff sand layer, and the settlement behavior of the composite foundation under rigid loading plate is dominated by that of the column, which has a relatively linear stress-strain behavior. The ultimate bearing capacity, qcs, of the untreated ground is determined as 51 kPa, close to the calculated value (56 kPa) according to Skempton [26] using the average Su of the soft clay (9 kPa). This result indicates that the boundary effect is insignificant for the laboratory loading tests. The qcs of the T-shaped column-treated ground is 117 kPa, which is twice that of the untreated ground, i.e. the column considerably increased the bearing capacity of the soft ground.
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Fig. 4. Pressure-settlement curves of laboratory loading tests The measured stresses on the column and soil are presented in Fig. 5. The back-calculated stress on the loading plate, using the measured stresses and areas of the column and soil, was also shown in Fig. 5 along with the applied stress. The back-calculated stress-time curve generally agreed with that of the applied stress, although there was certain dispersion between them. Both the stresses on column and soil increased after applying of each load level (Fig. 5); thereafter, the soil stress decreased with time due to consolidation. The drop of the column stress and increase of the soil stress shortly after the applying of the final load level indicated the failure of the composite foundation. Fig. 5 also shows that the column stress was significantly higher than the soil stress at the same time due to the higher stiffness of the column compared to that of the clay; this contributed to the enhanced bearing capacity of composite foundation. Before applying the final load (i.e. under the load level of ultimate bearing capacity), the soil stress was 26 kPa, indicating the stress reduction factor, β, was 0.5;
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the column stress was 198 kPa, which was also lower than its unconfined compressive strength (~500 kPa), i.e. the column cap did not fail.
Fig.5. Vertical stresses on soil, column, and plate Fig. 6 is the picture of extruded column after loading, showing evident shear failure surfaces at the small-diameter column just under the cap, similar to that observed for loading test only on single column (not composite foundation) [30]. It is noted that the horizontal fracture in the middle of small-diameter column was induced by the excavation. The visual observation indicated that the failure occurred at the small-diameter column just under the cap, which then induced the soil failure nearby. This failure behavior was due to that the cap had a much larger section area (4.8 times) than the small-diameter column. Consequently, the additional stress in the small-diameter column just under the cap was considerably greater than that in the cap, and this stress concentration resulted in shear failure in the small-diameter column. This failure behavior is different from that of composite foundation consisting conventional
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column and soft clay, where the failure firstly occurred around the column top.
Fig. 6. Excavated T-shaped column after loading test Field test As the load plates had varying diameters, the plate settlements were normalized by their diameters, and then plotted against the applied vertical pressures as shown in Fig. 7. The failures of all the loading tests were determined by the settlement criterion (>10% plate diameter). After unloading, the rebound deformation was very limited, confirming the failures were researched for all the tests. It is noted that one more load level was applied after the settlement reached 10% plate diameter for some of the loading tests (e.g. Fig. 7a), because the technicians were not confident at first. For all the tests, the failure load was determined as that reached 10% plate diameter, and the qcs was that prior to the failure load. Different from the laboratory result (Fig. 4), the linear pressure-settlement relationship only observed when the applied pressure was relatively low for the field loading tests (Fig. 7), and then the settlement increased non-linearly with the pressure. This is because the columns in the field were underlain by relatively stiff clay layer, not bedrock, while there was only 50-mm-thick dense sand between the column and rigid mold bottom in laboratory.
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(a)
(b)
Page 14
(c)
(d)
Page 15
(e)
(f) Fig. 7. Pressure-settlement/plate diameter curves of loading tests in field: (a) C1, (b) C2, (c) C3, (d) C4, (e) C5, and (f) C6. Fig. 7 also indicates that there is certain dispersion between two loading curves for
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most the composite foundations. This is mainly due to the strength variability of columns induced by the field construction process [15, 18, 19, 23, 28]. Nevertheless, the determined qcs were the same for the same composite foundation. Compared to the qcs in this study, the column heterogeneity affected more on the bearing capacity of single column (Qc) [30]. This is because the bearing capacity of the soil, which had much lower variability that the column, was a major component of the composite foundation. Although the column installation process caused disturbance to the surrounding soil with a limited distance, the soil strength recovered with time [20, 24, 25]. Table 2 lists the qcs of the composite foundations determined from loading tests. The geometry parameters of C1 and C4 composite foundations are the same except for the cap length (l1), which are 2 m for C1 and 4 m for C4; the qcs of C1 and C4 were 240 and 270 kPa, respectively, indicating the qcs increased with l1. The C2 and C3 had the same geometries of the single columns, but the C2 had smaller column spacing, which resulted in a greater qcs (300 kPa) compared to that of the C3 (240 kPa); this was confirmed by comparison of C5 and C6. The C4 and C5 had very similar qcs, although the column spacing of the C4 (2.0 m) was considerable lower than that of the C5 (2.4 m); this indicated that increasing of the column (and/or cap) diameter also increased the bearing capacity of composite foundation. The C1, C3, and C6 yielded the same qcs, due to the multiple effects of column (and/or cap) diameter, spacing, and length on the qcs.
Estimation method The laboratory model test revealed that the failure of the composite foundation might be induced by the shear failure at the small-diameter column just below the cap, which then
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caused soil failure nearby, as shown in Fig. 8. According to this failure behavior, the qcs has three major contributions, including the (1) strength of small-diameter column, (2) bearing capacity of the soil under the cap, and (3) friction surrounding the foundation around cap (Fig. 8). Hence, the qcs can be estimated from Equation 4, which was adapted from Equations 1 and 2. qsc as 2 qu (1 as 2 )qs1
Pl1 f s1 A
(4)
where as2 is area replace ratio of small-diameter column; l1 is cap length; fs1 is average friction around cap; qs1 is ultimate bearing capacity of soil under cap.
Fig. 8. A possible failure mode of composite foundation consisting T-shaped column and soft clay Additionally, if the cap diameter is very small, the T-shaped column will behave similarly to the conventional column; as shown in Fig. 1a, the column failure may appear around the column top, and the qcs can be calculated from Equation 3 using the area replacement ratio of cap (as1). As shown in Fig. 1b, the failure of the composite foundation may occur in the underlain soil if it is too weak; in this case, the qcs is
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calculated using Equation 2. The minimal value calculated from Equations 2, 3, and 4 is the qcs. The experimental data form the laboratory and field tests were used to verify the above-mentioned equations. Since the loading time for laboratory and field tests was relatively short (less than one day for each test), they were generally considered as in undrain condition for soft clay. Assuming undrained condition, the friction (fs) was determined as the average undrained shear strength of soil. Because only the vane shear test was only conducted for the soft clay layer, the fs1 was determined as the average value of soft clay around cap (Su1), and the qs1 was determined from Su1 using the Skempton [26] method. For the field tests, this assumed the crust layer had the same properties as those of soft clay at shallow depth, resulting in a slight underestimation of qsc when using Equations 3 and 4. The fs was determined as the average undrained shear strength (Su) of all the soft clays, and the qt was determined from Su using the Skempton [26] method. This assumed all the soil layers had the same properties as those of the soft clay layer, leading to a significantly underestimation of qsc when using Equation 2. The average measured column strength (qu) was used for calculation. Based on the results obtained from the laboratory test, β was determined as 0.5. It is worth noting that β should not be constant for all the conditions, e.g. it can be affected by the relative stiffness of column and soil, and the β in the laboratory test should not be the same as that in the field tests. Since the β was not measured for the field tests, the value of 0.5 was also used for the calculation of field tests. Table 3 lists all the mechanical parameters of the soil and column used for calculation. Table 3. Mechanical parameters of soil and column used for calculation
Page 19
fs1
fs
qs1
qs
qt
qu
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
Laboratory
11
9
76
56
81
500
Field
19
24
140-162
117
216
1260
Test
The qcs calculated from Equations 2, 3, and 4 are listed in Table 4. For each case, the calculated qcs from Equations 4 is considerably lower than from Equations 2 and 3, suggesting the failure mode in Fig. 8 occurs for the T-shaped column-treated ground, consistent with the observation after excavation in the laboratory model test. The calculated qcs from Equations 4 is 0.81-1.03 times of the corresponding measured values. For the field loading tests, all the calculated qcs are smaller than the corresponding measured values except for only one case (C3); the underestimation should be due to the neglecting of the crust layer during calculation. Overall, the comparison indicates that Equation 4 can properly estimate the qcs of T-shaped column-treated ground for preliminary design purpose. Table 4. Calculated and measured qsc Field columns
Lab Method column
C1
C2
C3
C4
C5
C6
Equation 2
216
970
1050
970
803
850
905
Equation 3
251
331
391
331
296
335
286
Equation 4
111
195
261
278
234
252
217
Measurement
117
240
300
270
240
265
240
The qcs calculated from Equation 2 is the maximum calculated values for each of the field composite foundation, which is more than three times of the corresponding measured value, despite that very conservative soil properties have been used for
Page 20
calculation. This is not surprising, as the industry practice in China has found that the failure mode in Fig. 1b is unlikely to occur for most of the conventional column-treated grounds, and the qcs is dominated by Equation 3, not Equation 2 [17]. For the laboratory test, the qcs calculated from Equation 2 is slightly smaller than that calculated from Equation 3, due to the very limited column length in the laboratory test. For the field composite foundations, the qcs calculated from Equation 3 is relatively close to that calculated from Equation 4, indicating the failure mode in Fig. 1a is also possible if the cap diameter is small enough. For the six field tests, the calculated values from Equation 3 is 1.2-1.4 times of the corresponding measured values, i.e. it is overestimated the experimental data, although the conservative qs has been used for calculation by neglecting the crust layer.
Conclusions Laboratory and field tests were performed to study the bearing capacity of composite foundation consisting T-shaped column and soft clay under vertical loading. The field tests indicated that the bearing capacity of composite foundation increased with increasing of the cap length and column diameter, as well as decreasing of the column spacing. The laboratory test revealed that the failure of composite foundation might be induced by the shear failure at the small-diameter column just below the cap, which then caused soil failure nearby. By including this additional failure mode, the design method for conventional column was adapted to estimate the bearing capacity of composite foundation consisting of T-shaped column and soft clay, and the method was validated by the experimental data. Nevertheless, further study is still needed to investigate the
Page 21
relative stiffness and strength of the column and soil affecting the bearing capacity and failure behavior of composite foundation, which can be conducted through numerical modeling.
Acknowledgments The authors sincerely appreciate the help from Zhu Zhiduo, Xi Peisheng, Li Chen, Zhang Bafa, and Zhu Zhihua for this study.
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