NOTE

Interpretation of uplift load tests on belled piers in Gobi gravelZeng-zhen Qian, Xian-long Lu, Xue Han, and Rui-ming Tong

Abstract: Belled piers are widely applied in Gobi gravel to withstand axial tensile loads for transmission towers in NorthwestChina. This study evaluates the pullout performance of belled piers in Gobi gravel. Forty-one full-scale belled piers were installedat seven sites, and pullout load testing was conducted for each foundation. In general, the uplift load – shaft-head displacementcurves of the belled piers in Gobi gravel approximately exhibited an initial linear, a curvilinear transition, and a final linearregion, and their capacities should be interpreted from the load test results. Four representative uplift interpretation criteria(Chin, slope tangent, tangent intersection, and L1–L2) were used to evaluate the capacity of each belled pier. The results wereinterrelated to establish a generalized correlation among these interpreted capacities using a mean normalized uplift load–displacement curve. Based on these analyses, the relative interrelationships of these criteria were established, and the use ofthese methods was suggested.

Key words: belled piers, Gobi gravel, uplift, load tests, capacity, gravelly soils.

Résumé : Les pieux éclatés sont largement utilisés dans les graviers du Gobi, dans le Nord-Ouest de la Chine, afin de supporterles efforts de tension axiale qui s’exercent au niveau des pylônes de transmission. La présente étude évalue la performance al’arrachement de pieux éclatés dans les graviers du Gobi. Quarante-et-un pieux éclatés de taille réelle ont été installés a septemplacements différents et des essais d’arrachement ont été réalisés au niveau de chaque fondation. D’une façon générale, lescourbes représentant le déplacement de la tête de fût en fonction de la charge de soulèvement des pieux éclatés présentaient unepremière section linéaire, suivie d’une section courbe et d’une dernière partie linéaire, les valeurs de la capacité des pieux éclatésdevant être interprétées a partir des résultats des essais réalisés. Quatre critères d’interprétation du soulèvement représentatifs(plateau, tangente de la pente, intersection des tangentes et L1–L2) ont été utilisés pour évaluer la capacité de chaque pieu éclaté.Les résultats ont été reliés les uns aux autres afin d’établir une corrélation généralisée entre ces capacités interprétées d’unecourbe moyenne normalisée représentant le déplacement en fonction de la charge de soulèvement. À partir de ces analyses, lesliens de corrélation relatifs entre ces critères ont été établis et l’utilisation de ces méthodes a été proposée. [Traduit par laRédaction]

Mots-clés : pieux éclatés, graviers de Gobi, soulèvement, essais de charge, capacité, sols graveleux.

IntroductionGobi is a common geological formation in Northwest China,

especially in Xinjiang, Inner Mongolia, and Gansu Province. Inrecent years, the construction of electrical transmission systemsspanning from West to East China has been planned. Thus, theconstruction of foundations in Gobi formation gravel (“Gobigravel”) for transmission towers is unavoidable. Recently, belledpiers have been increasingly used in Gobi gravel to resist axialtensile loads for transmission towers. The shaft of a belled pier iscylindrical, terminating at its base in a circular slab of greaterdiameter than the shaft. The advantage of belled piers is that theycan effectively mobilize the uplift shear resistance of the undis-turbed soil above the enlarged base and thus are superior tostraight-sided shafts. The field test results (Qian et al. 2014a) indi-cate that the uplift load–displacement curves of belled piers inGobi gravel will not provide a well-defined peak or asymptoticvalue of the load; therefore, the capacity needs to be defined by an“interpreted failure load” using appropriate criteria.

Numerous interpretation criteria (e.g., van der Veen 1953; Chin1970; DeBeer 1970; Fuller and Hoy 1970; Davisson 1972; O’Rourkeand Kulhawy 1985; Hirany and Kulhawy 1988, 1989, 2002) havebeen recommended for interpreting the capacity from the com-

pression and uplift load test results. As found in practice, differentfailure definitions lead to different recommendations for design.Research on this issue has been conducted (Chen 2004; Chen et al.2008; Chen and Chu 2012) using a broad database of axial upliftload tests on drilled shafts in gravelly and nongravelly soils, whileChen and Fang (2009) and Marcos et al. (2013) focused on compres-sion load test interpretation criteria for drilled and driven piles,respectively. However, belled piers in Gobi gravel and drilled shaftsin gravelly and nongravelly soils differ in the foundation type, theconstruction method, and the soil property, which can affect theirrelative uplift behaviors. Therefore, it is of particular interest toexamine the criteria and the procedures for assessing uplift loadtest results of belled piers in Gobi gravel.

This note attempts to extend the early contributions by intro-ducing the results of 41 full-scale uplift load tests performed onbelled piers at seven sites in Xinjiang and Gansu Province. Thesedata were interpreted using four representative uplift capacityinterpretation criteria (Chin, slope tangent, tangent intersection,and L1–L2) to define various elastic, inelastic, and “failure” statesfor each belled pier. The results were compared statistically andgraphically, and a generalized correlation among these states us-ing a mean normalized uplift load–displacement curve for belledpiers in Gobi gravel was established.

Received 5 March 2014. Accepted 30 October 2014.

Z.-z. Qian. School of Engineering and Technology, China University of Geosciences, No. 29 Xueyuan Road, Haidian District, Beijing 100083, China.X.-l. Lu and R.-m. Tong. China Electric Power Research Institute, No. 15, Xiaoying East Road, Haidian District, Beijing 100192, China.X. Han. College of Architecture and Civil Engineering, Heilongjiang Institute of Science and Technology, Harbin 150027, China.Corresponding author: Zeng-zhen Qian (e-mail: zzqian@cugb.edu.cn).

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Can. Geotech. J. 52: 1–7 (2015) dx.doi.org/10.1139/cgj-2014-0075 Published at www.nrcresearchpress.com/cgj on xx xxx xxxx.

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Test site and soil propertiesIn this study, seven sites were selected for the field tests. Four of

these sites are located in Gaotai County (GTC), Shandan County(SDC), Jinchang City (JCC), and Jiuquan City (JQC) in Gansu Prov-ince, while the rest are located in Yanhu (YH), Ershili Dian (ERD),and the Wild Animal Zoo (WAZ) in the Xinjiang Uygur Autono-mous Region.

Because of the lithology, soil composition, and extremely dryenvironment, the Gobi region is covered primarily by coarse-grained soil. The most significant components of Gobi gravel aresandstone, quartz schist, quartzite, granite, and diorite, associ-ated with small intrusive clayey and sandy soils. The particle-sizedistribution of 68 specimens of Gobi gravel soil was achieved bysieve analysis tests according to ASTM D 422 (ASTM 2007), asshown in Fig. 1. The parameters that typically describe the shapeof the particle-size distribution curve, Cu = 47.0–81.0, Cc = 1.1–2.6,indicate that Gobi gravel can be classified as well-graded gravelwith cobbles (GW), according to the Unified Soil ClassificationSystem (ASTM D 2487 (ASTM 2011)). However, as may be seen fromFig. 1, the cobble-size content of Gobi gravel is about 30%. Accord-ing to the previous studies by Chen (2004) and by Kulhawy andChen (2009), there are some limitations in the Unified Soil Clas-sification System (USCS) procedure when applied to soils withsignificant very coarse fractions. In their studies, the ExpandedBurmister Soil Identification System (EBSIS), based on the sameframework of the Burmister Soil Identification System (BSIS)(Burmister 1958, 1970), is recommended to improve the overallsoil identification, description, and classification, particularly forsoils containing very coarse fraction. The identification with thisexpanded system should be done in two steps. Based on the meangrain-size curve shown by the solid line in Fig. 1, the Gobi gravelsoil contains four main fractions (stone, gravel, sand, and fines),ranging from a maximum size of medium Stone (600–200 mm) toSilt (<0.075 mm). The quantity of the fine-grained fraction (Silt)would be estimated as about 1% (, trace−), while the quantity of thecoarse-grained fraction (>2 mm) would be estimated as 75%–85%(little−,). Examination of the sand fraction would indicate roughlyequal amounts of the medium and fine subgroups, but morecoarse. This information results in the EBSIS step 1 identification:COARSE FRACTION little−, c+ m f Sand, trace− Silt. The EBSIS step 2

processing then would occur. The stone fraction would be esti-mated as 25%–35% (some−), examination of the stone fractionwould indicate there is more fine than medium, and examinationof the gravel fraction would indicate equal amounts of mediumand fine, but more coarse. The resulting step 2 identification isgiven by: CF = m f+ STONE, some−, c+ m f− Gravel (Qian et al.2014b).

In addition, Gobi gravel contains some soluble salts. Laboratorytests were performed to obtain the chemical composition of Gobigravel, and the maximum soluble concentrations of CL−, SO4

2−,and K+ + Na+ salts are 1337.9, 1210.6, and 1253.3 mg/kg, respec-tively. The precipitation of these dissolved salts may have resulted

Fig. 1. Particle-size distribution and soil identification for Gobi gravel. Med., medium.

Table 1. Some properties of Gobi gravel.

Parameter Value

Moisture content, w (%) 0.6–5.2Void ratio, e 0.23–0.25Specific gravity,Gs 2.74–2.76Unit weight, � (kN/m3) 17.2–22.4Maximum dry unit weight, �dmax (kN/m3) 20.8–22.6Minimum dry unit weight, �dmin (kN/m3) 16.2–19.2Coefficient of permeability, k (m/s) 1.3×10−3– 4.4×10−3

Fig. 2. General form and geometrical symbols of belled pier.

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in salt cementation of the particulate soil matrix in Gobi gravel.Therefore, under a very dry environment, Gobi gravel has a highuplift capacity and low compressibility. However, under a satu-rated environment, the salt cementation strength between grainsreduces, the structure is damaged, and the grain movement leadsto a high potential for collapse (Rollins et al. 1994; Nie et al. 2012).The special characteristic of salt cementation of Gobi gravelmakes it different from other soil–rock mixtures (S–RM) (Xu et al.2011), and tower locations must be carefully selected to keep wateraway from the foundations because belling should not be at-tempted below the water table due to the potential instability ofsaturated Gobi gravel. Therefore, proper drainage should be pro-vided for belled pier foundations to be installed in Gob gravel. Thefield tests of belled piers in Gobi gravel were all carried out in anatural arid environment, and additional considerations for col-lapse behavior were not included in the tests and the subsequentdata analysis. It should be noted that these test results are sitespecific and not applicable to other soil conditions.

According to the in situ direct shear tests, the typical ranges ofthe mean and variability coefficient of the internal friction angleof Gobi gravel are 40.6°–43.6° and 0.01–0.26, respectively. The

Table 2. Basic information and analysis results for uplift tests.

Foundation geometry Interpreted capacity, T (kN), and corresponding displacement, s (mm)

Belled piernumber D (m) B (m) b (m) � (°) TL1 sL1 TSTU sSTU TTIU sTIU TL2 sL2 TCHIN sCHIN

GTC1 1.72 1.01 0.80 10.0 237 0.54 437 4.78 443 5.99 450 7.29 490 >32.7GTC2 2.65 1.64 1.20 20.0 854 1.85 1247 6.39 1288 8.03 1326 10.10 1526 >39.8GTC3 3.64 2.29 1.60 30.0 1516 1.64 2568 6.87 2788 10.19 2875 12.10 3436 >38.4GTC4 3.73 1.41 1.20 10.0 754 0.99 1989 6.19 2235 11.65 2349 14.80 2725 >37.6GTC5 5.29 2.04 1.60 20.0 2097 0.87 3965 5.85 5378 17.64 6251 29.80 6856 >42.5GTC6 3.93 1.49 0.80 30.0 1088 2.76 1630 7.96 2021 17.37 2203 24.10 2626 >44.4GTC7 6.54 1.81 1.60 10.0 2362 0.95 5038 5.63 6233 10.64 7428 19.75 8962 >32.1GTC8 4.53 1.24 0.80 20.0 1081 1.03 2382 6.07 3425 19.07 3667 25.40 4141 >48.1GTC9 6.82 1.89 1.20 30.0 2306 0.75 4798 5.59 5850 11.24 7286 22.06 8794 >32.5SDC1 1.72 1.01 0.80 10.0 154 1.71 294 7.08 346 12.81 361 14.70 424 >39.3SDC2 2.65 1.64 1.20 20.0 406 0.89 946 5.28 1043 11.37 1097 17.30 1247 >46.5SDC3 3.64 2.29 1.60 30.0 2848 1.34 3508 5.75 3591 7.67 3659 11.00 4092 >39.7SDC4 3.73 1.41 1.20 10.0 1547 4.63 2129 10.05 2255 14.18 2349 17.70 3250 >42.8SDC5 3.93 1.49 0.80 30.0 1415 4.23 2407 11.45 2678 16.21 2768 19.30 3518 >50.8SDC6 4.53 1.24 0.80 20.0 2135 7.68 2838 13.80 3264 19.91 3395 22.42 4939 >45.1JCC1 1.72 1.01 0.80 10.0 327 2.41 524 7.86 555 10.30 576 12.40 735 >34.5JCC2 2.65 1.64 1.20 20.0 1088 3.17 1633 8.64 1650 8.75 1668 11.00 2000 >41.9JCC3 3.64 2.29 1.60 30.0 2844 2.61 4074 7.34 4471 11.19 4524 12.60 5214 >49.5JCC4 3.73 1.41 1.20 10.0 2306 4.73 3120 10.19 3104 9.61 3246 14.80 4292 >30.2JCC5 5.29 2.04 1.60 20.0 2750 1.30 5105 6.29 7937 18.87 8273 22.56 10400 >36.6JCC6 3.93 1.49 0.80 30.0 2325 3.38 2986 8.05 3136 10.79 3211 13.10 4219 >38.7JCC7 6.54 1.81 1.60 10.0 3144 2.31 6692 8.56 8278 17.47 8150 20.17 9480 >37.5JCC8 4.53 1.24 0.80 20.0 2330 2.66 3400 7.39 3930 15.88 4260 24.13 4840 >38.6JQC1 2.05 1.20 0.80 33.7 529 1.25 608 5.16 599 2.28 604 3.90 694 >35.3JQC2 2.60 1.23 0.84 33.0 513 2.28 1163 8.71 1132 7.43 1155 8.50 1830 >16.4JQC3 3.55 1.20 0.80 33.7 658 1.04 1961 6.85 1931 5.23 1955 5.70 2501 >12.4JQC4 3.20 1.40 1.05 30.3 1072 1.39 1823 6.26 1830 6.57 1900 7.79 2153 >20.1JQC5 4.75 1.60 1.05 42.5 3182 6.10 4555 12.43 4378 10.38 4522 11.50 5750 >19.9JQC6 4.08 1.80 1.25 42.5 1778 1.90 3315 7.23 3278 5.24 3288 5.70 3874 >29.5JQC7 4.80 1.85 1.30 42.5 1855 1.40 4410 7.21 4234 6.48 4592 8.50 6397 >22.1YH1 2.54 1.56 1.00 25.0 227 1.60 629 6.40 670 7.82 724 8.90 885 >37.1YH2 4.96 1.36 0.80 25.0 765 0.60 1097 5.03 1706 8.46 2129 10.30 2502 >36.8ERD1 1.88 1.12 0.80 15.0 476 0.90 728 5.80 754 7.72 761 13.80 833 >36.2ERD2 2.54 1.56 1.00 25.0 342 0.70 780 5.30 869 14.72 904 17.60 1037 >44.2ERD3 3.51 2.21 1.20 40.0 928 2.40 2187 6.95 2377 13.23 2637 19.50 3295 >36.6ERD4 3.50 1.32 1.00 15.0 894 1.00 1390 5.09 1848 17.81 1895 30.50 2025 >57.6ERD5 4.60 1.76 1.20 25.0 1756 1.20 2550 6.04 3038 23.71 3300 37.40 4103 >56.9ERD6 4.72 1.81 0.80 40.0 1365 1.10 2188 6.55 3050 18.27 3355 22.30 3714 >41.2ERD7 5.53 1.52 1.20 15.0 2163 1.00 3990 6.48 5922 8.68 6561 12.40 7179 >25.4ERD8 4.96 1.36 0.80 25.0 1424 1.70 2897 6.03 4058 25.80 4228 52.20 4779 >86.8WAZ1 4.70 1.80 1.20 25.0 826 0.60 1657 4.93 1798 7.58 2017 11.70 2509 >31.8

Note: The symbol (>) expresses that the displacements are greater than the measurement data.

Fig. 3. Belled pier foundation excavation with steel-reinforced cageprior to concrete placement.

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corresponding ranges for cohesive strength and variability coeffi-cient are 10.5–23.0 kPa and 0.12–0.33, respectively. Some otherfield and laboratory tests were also conducted to determine theindex properties for Gobi gravel, as summarized in Table 1.

Foundation installationAt the seven experimental sites described previously, 41 belled

piers were constructed and tested under arid environment.Figure 2 shows the general form and the geometric symbols of a

Fig. 4. Measured uplift load – pier-head displacement curves in field tests: (a) GTC; (b) SDC; (c) JCC; (d) JQC; (e) ERD; (f) YH and WAZ.

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belled pier foundation, where D is the depth from the groundsurface to the bottom of the foundation slab; b is the shaft diam-eter; B is the bell diameter; t is the bedding cushion thickness,which is equal to 0.20 m for all of the belled piers; and � is theangle that the pyramidal or conical surface makes against thevertical. Table 2 presents the dimensions of belled piers in tests.As shown in Table 2, the magnitude of angle � for each belled pieris less than 45°, so that the unreinforced concrete bell would havesufficient stiffness to withstand the shear stresses developed dueto the uplift forces.

Manually excavating the hole to the required diameter anddepth with a pickaxe is a common construction method for towerfoundations in China. The installation of each belled pier consistsof manually excavating the hole to the required dimensions andcasting the reinforced concrete foundation. The construction ofan enlarged circular base should be done in two steps. The firststep was to excavate the shaft to the required depth and diameter,while the second step was conducted to enlarge the circular baseto the required dimension. All the dimensional values in Table 2are the means of the measured data, and all foundation shafts hadtruly vertical faces.

A steel-reinforced cage was prefabricated and lowered into thedesigned position in the foundation pit after completing the ex-cavation. Sulfate-resistant concrete with a 28 day compressivestrength of 25 MPa was poured using the free-fall method. Theconstruction of concrete quality was guaranteed by vibrating dur-ing concrete pouring. Figure 3 shows a belled pier foundation pitwith reinforcement prior to concrete placement. All the belledpiers were allowed to cure for 28 days before performing the upliftload tests.

Loading procedure and test methodAll the tests were conducted with static monotonic loading

without cycling. The same loading, reaction, instrumentation,and data acquisition systems were used for all the tests. The ten-sile load was axially applied through a system comprising a hy-draulic jack, a reaction beam, a loading platform, and a calibratedload cell, which were designed according to the criteria recom-mended in ASTM D3689/D3689M-07(2013)e1 (ASTM 2013). Theslowly maintained load method was adopted in all the tests. Thepullout test was continued to the point of predicted failure, andthen the test was halted. Therefore, there was no drop in upliftresistance after the peak was reached in the load–displacementcurve.

Interpretation of load test resultsThe experimental results of all the tests are reported as uplift

load against the pier-head vertical displacement in Fig. 4. As maybe seen from Fig. 4, the uplift load–displacement responses al-most follow the same pattern, which are similar to those of drilledshafts under axial uplift loading in gravelly and nongravelly soilsreported by Chen (2004), Chen et al. (2008), and Chen and Chu(2012). These uplift load–displacement curves can generally besimplified into three distinct sectors: initial linear, curve tran-sition, and final linear, as illustrated in Fig. 5. Beyond the end ofthe transition region, a small increase in load produces a signifi-cant increase in displacement. In general, the load–displacementcurves obtained from the uplift loads test did not provide a well-defined peak or asymptotic value of the load; therefore, estimat-ing the uplift failure load needed to be interpreted as done in theprevious studies (Chen 2004; Chen et al. 2008; Chen and Fang2009; Chen and Chu 2012; Marcos et al. 2013). The four interpre-tation criteria shown in Table 3 were used to evaluate the upliftinterpreted failure load or capacity, T, from the load – pier-headdisplacement curve of each belled pier. These four different crite-ria were selected because they represent a distribution of inter-preted results from the lower, middle, and higher bounds as

found in practice (Chen 2004; Chen et al. 2008; Chen and Fang2009; Chen and Chu 2012; Marcos et al. 2013). The interpretedcapacities TL1, TSTU, TTIU, TL2, and TCHIN, as well as the correspond-ing displacements sL1, sSTU, sTIU, sL2, and sCHIN for all the tests areshown in Table 2.

Comparison of different interpretation methodsThe statistics for the interpreted capacities and the correspond-

ing displacements are summarized in Table 4, which includes themaximum, minimum, mean, standard deviation (SD), and coeffi-cient of variation (COV) of the interpreted results. All of the inter-preted capacities were normalized by the failure threshold, TL2, ofthe L1–L2 method. The L1–L2 method could interpret all the loadtest cases, and TL2 is generally defined as the interpreted failureload because, beyond TL2, a small increase in load gives a signifi-cant increase in displacement. Therefore, it was adopted as a basefor comparing the interpretation criteria. Results are compared inthe following text to evaluate the interrelationships and charac-teristics of the methods. Also, note that TL1 was included for ref-erence only. It is not an interpreted failure load or capacity, butthe elastic limit.

The results in Table 4 show that mean interpreted load ratios ofTSTU/TL2, TTIU/TL2, and TCHIN/TL2 range from 0.84 to 1.21, with a COVbetween 0.17 and 0.22. The mean ratio of TL1/TL2 is equal to 0.49,and a COV of 0.35 is obtained. The mean uplift displacementsshown in Table 4 follow the same order trend as the capacities.The mean displacements at the interpreted failure load rangefrom 7.11 mm at TSTU to 16.75 mm at TL2 to >38.16 mm for TCHIN.However, the mean sL1 is 2.01 mm, which implies that the initiallinear region occurs within a very small displacement. The COVvalues for these displacement data are high, with a range of0.33–0.79.

For more direct comparison of the uplift interpretation criteria,the mean normalized load–displacement curve of Gobi gravel foraxial uplift loading is presented in Fig. 6. The corresponding meanratio of each interpretation method to TL2 is plotted against themean displacement. For easy observation, TL1, TSTU, TTIU, TL2, andTCHIN are also marked in Fig. 6.

According to comparisons of load test results in Table 4 andFig. 6, the “slope tangent” method gives the lowest values, whilethe “Chin” method yields the highest values and always lies aboveTL2. The “slope tangent” and “tangent intersection” methods yieldratio values less than 1.0, and are therefore located in the nonlin-ear transition between L1 and L2. Both the “L1–L2” and “tangent

Fig. 5. Sectors of uplift load – pier-head displacement curve anddefinitions of representative interpretation criteria for belled piersin Gobi gravel.

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intersection” methods result in interpreted failure loads that aresignificantly smaller than TCHIN. Therefore, defining the failure loadas TCHIN results in values that are too large, likely because TCHIN isbased on a mathematical model that corresponds to the asymp-tote of the load–displacement curve.

L1 and L2 are convenient reference points within the curve be-cause these points encompass the significant regions of the curve.However, it should be noted that the measured load–displacementcurve would not always possess a final linear region in practice.Nevertheless, these points would be useful to demonstrate thegeneral relationships among the criteria and provide capacity ap-proximations (Marcos et al. 2013). Using L1 as a reference, thecapacity for uplift loading can be approximated as TSTU = 1.82TL1,TTIU = 2.09TL1, TL2 = 2.23TL1, and TCHIN = 2.69TL1. These ratios can beused with caution to interrelate the methods where needed due tolimited load–displacement data.

It should be noted that the results shown in this manuscript aregeneral behaviors applicable for the belled piers installed in Gobigravel only, and any extrapolation of these results to other differ-ent soil foundations is not recommended.

ConclusionsAxial uplift load tests were conducted on 41 full-scale belled

piers in seven Gobi gravel sites. Four representative interpretationcriteria (Chin, slope tangent, tangent intersection, and L1–L2) wereused to define various elastic, inelastic, and “failure” states for eachbelled pier. The results were compared statistically and graphically,and a generalized correlation among these states was establishedfor belled piers in Gobi gravel using a mean uplift load–displacementcurve. From these analyses, the following conclusions can be drawn:

1. The uplift load–displacement curves of belled piers in Gobigravel can be simplified into three sectors: initial linear, non-linear transition, and final linear region, and the bearingcapacity could be interpreted by the representative upliftinterpretation criteria as done in other studies. Of the fourcriteria examined, the “slope tangent” method gives the lower

bound, while the “Chin” method represents the upper bound,almost by definition, and is always above the measured data.

2. According to the L1–L2 method, L1 is a consistent definition forthe elastic limit, while L2 could be a useful definition for theinterpreted failure load for belled piers in Gobi gravel. Upliftcapacity approximation using L1 for belled piers in Gobi gravelgives TSTU = 1.82TL1, TTIU = 2.09TL1, TL2 = 2.23TL1, and TCHIN =2.69TL1. Using L2, the uplift capacity could be approximated asTL1 = 0.49TL2, TSTU = 0.84TL2, TTIU = 0.94TL2, and TCHIN = 1.21TL2.These ratios can be used to interrelate the methods whereneeded due to limited load–displacement data.

Table 3. Definitions of representative uplift interpretation criteria for belled piers in Gobi gravel.

Method Category Definition of interpreted capacity, T

Chin (1970) Mathematicalmodeling

TCHIN is equal to the inverse slope, 1/m, of the line,s/T = ms + c, where T is the uplift load; s is thetotal displacement; and m and c are the slopeand intercept of the line, respectively.

Slope tangent (O’Rourkeand Kulhawy 1985)

Graphicalconstruction

TSTU occurs at a displacement equal to the initialslope of the load–displacement curve plus0.15 in. (3.8 mm).

Tangent intersection(Housel 1966; Tomlinson1977)

Graphicalconstruction

TTIU is determined as the intersection of two linesdrawn as tangents to the initial linear and finallinear portions of the load–displacement curveand projected to the load–displacement curve.

L1–L2 (Hirany and Kulhawy1988, 1989, 2002)

Graphicalconstruction

TL1 and TL2 correspond to elastic limit and failurethreshold loads, respectively, as shown in Fig. 5.

Table 4. Summary of statistics for interpreted loads and displacements.

Ratios among interpretedloads, T/TL2

Displacement at interpretedcriteria (mm)

Statistics TL1/TL2 TSTU/TL2 TTIU/TL2 TCHIN/TL2 sL1 sSTU sTIU sL2 sCHIN

Maximum 0.87 1.01 1.02 1.58 7.68 13.80 25.80 52.20 >86.80Minimum 0.29 0.52 0.80 1.07 0.54 4.78 2.28 3.90 >12.36Mean 0.49 0.84 0.94 1.21 2.01 7.11 12.05 16.75 >38.16SD 0.17 0.19 0.16 0.22 1.59 2.32 5.68 9.70 >13.84COV 0.35 0.22 0.17 0.18 0.79 0.33 0.47 0.58 >0.36

Fig. 6. Mean normalized uplift load–displacement curve for belledpiers in Gobi gravel.

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AcknowledgementsThe authors wish to thank the National Natural Science Foun-

dation of China (No. 51208480) for support of this project. Theauthors also appreciate the reviewers’ excellent comments, whichhave improved the quality of this note.

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