Analysis of influencing parameters and basics of determining resistance factors of drilled shafts used in bridge substructures in ho-Chiminh city

On the basis of analysis results of statistical characteristics of resistance bias factor (λR) of the four methods and application of the statistical characteristics of load effect bias factor λD, λL), the other parameters as suggested in Table 3.7, to determine resistance factors of drilled shafts according to 2 methods: first-order reliability method (FORM) and Monte Carlo simulation method (MCS) as outlined in Chapter 2 as follows: - FORM method: Applying formula (2.7), using a spreadsheet on Excel function and using run loop Solver to determine the reliability index (β) corresponds to the values of the assumed resistance factors (ϕ = 0, 4, 0.6, 0.8, 1.05). Next, charting the relationship between β and ϕ; based on this relationship chart to determine the resistance factors corresponding to the target reliability index (βt = 1.64, 2.33, 3.0 and 3.5). Detailed results are presented in Table 4.1; - MCS method: Also apply the formula (2.7), set up the spreadsheets and use the Crystal Ball software (analysis software is integrated in the environment of Excel) to determine the statistical characteristics of state functions f(R,Q) corresponds to the values of assumed resistance factors (ϕ = 0.4, 0.6, 0.8, 1.05), which will determine the reliability index (β) , respectively. Next, charting the relationship between β and ϕ; based on this relationship chart to determine the coefficients of resistance corresponding to the target reliability index (βt = 1.64, 2.33, 3.0 and 3.5). Detailed results are presented in Table 4.1.

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tic load test results due to not try to break the pile. - There is no study regarding the research objectives of this thesis in Vietnam. 5 From the above-mentioned problems, the author proposes the targets, content and research methodology of the thesis as decribed in items 1.6 and 1.7. 1.6. Targets of the topic Quantitative study of factors affecting the estimated resistance results of the four methods compared with actual field resistance of drilled shafts under the ground conditions in the area of HCMC. This means that the author has determined the statistics characteristics of the ratio of the real measured resistance and the expected one (resistance bias factor, λR); To research the basis of determining the resistance factors and to propose the resistance factors for drilled shafts foundations of bridge substructures in HCMC area for the four methods. 1.7. Content and Research Methodology To research the basis of determining the resistance factors for drilled shafts using probability and statistics theory and advanced reliability theory. Specifically, the survey collected from 24 results of static pile load tests in HCM City, the author conducted a study to identify typical statistics of the ratio of the measured and estimated resistances (Resistance bias factor, λR); From that way, the authod determined the resistance factors for the four methods on the basis of reliability analysis. Chapter 2. DETERMINATION OF RESISTANCE FACTORS OF DRILLED SHAFTS BASED ON RELIABILITY THEORY According to AASHTO LRFD, drilled shalfs axial resistance factors according to soil base strength condition are factors determined based on the statistical characteristics of the nominal resistance, mainly calculated from the variability of characteristic parameters of the ground around the pile, the pile size, level of expertise (professional) of human - device participating in the implementation phase of the project and the uncertainty of prediction method for nominal resistance; but also related to the statistical characteristics of load effects through the identification process. 2.1 Method to analyze the statistical characteristics 2.1.1 Determination of minimum size of samples Sample size is estimated by: (2.1) In which: σ and zα/2, zθ: common standard deviation and standard deviation with error probabilities α, θ from the normal distribution; ɛ: allowable error; C: is a constant related to error probability Type I and Type II. 2 /2 2 2 ( ) / z z Cn ( ) (ES) α θ ε σ + = = 6 For example, to determine the sample size for the thesis: With some prediction methods of drilled shafts resistance that accept averaged estimated error of about 50% (=1/FS, FS=2: safety factor) with reliable interval of 0,95 (i.e., α=0,05) and θ = 0,2. Previous studies indicate standard deviations of the resistance bias factor from 0,27 to 0,74. Thus, the effect factor is: ES = 0,5/0,74 = 0,456 and C=7,85. By applying the formula (2.1) to estimate the required sample size for the study: To compare with recommendation of Murad (2013), the number of test piles for the study area at least is ≥ 20 piles. Thus, with 24 results of static axial compressive load tests for drilled shafts in Ho Chi Minh City area can be considered reliable enough for analysis in order to meet the research objectives of the thesis. 2.1.2 Testing method of suitable probability distribution for the random bias factor Through analysis, the Shapiro-Wilk method or the Pearson chi-square (when the sample size is less than 50) is recommended with the following principles: the empirical distribution consists with assumed theoretical distribution (standard or logarithmic, ... ) when the match probability (P) is greater than 0.05. 2.1.3 Correction method for statistical characteristics of random bias factor For foundation structures, the laws of probability distributions of random bias factor often match or nearly match the normal standard distribution or standard logarithm. Through research, the authod proposes two correction methods of statistical characteristics for logarithmic distribution form according to the the principle (Allen, 2005): Based on the graph of the cumulative probability function to examine the conformity with one of the two cases, 1) consistent with the entire collection data (FTAD method -fit to All data) or 2) only consistent with the area of small values at distribution tail (BFTT-Best method fit to tail) (Figure 2.1) Figure 2.1. Cumulative probability density function of resistance bias factor 1 2 3 2 7,85 17,2 17( ) 0,5 / 0,74 n samples ( ) = = > 7 2.2 Reliability Analysis Method When analyzing the reliability, the incident probability is the condition that the limited state has been reached. The adjustment factors are selected to ensure that incident probability of each limited state is very small and acceptable. The probability density functions of load effects (Q) and resistance (R) with the assumption of two independent normally distributed variables (Figure 2.2). Safety range or the safety factor is the difference between R and Q, the quantitative quantity for the safety is reliability or safety probability, Ps: P( ) P( - 0) ( )sP R Q G R Q β= > = = > = Φ (2.2) Incident probability: Pf is calculated as: ( )P 0 1- 1 ( )f sP G P β= < = = − Φ (2.3) In which: Φ(.): normalized distribution functions; β: index of reliability. Index of reliability is determined based on averaged number and standard deviation as follows: 2 2 -R QG G R Q µ µµ β σ σ σ = = + (2.4) Figure 2.2. Normalized distribution probability density functions Figure 2.3. Normal Logarithm distribution probability density function If R and Q follows the normal logarithm distribution, safety range, G, is determined as follows: (Figure 2.3): G=ln(R)-ln(Q)=ln(R/Q) (2.5) Here, β is determined as the ratio of logarithm averaged number G and logarithm standard deviation, ξG. G Gβ ξ = (2.6) 2.3 Methods to determine pile body resistances The thesis has researched four methods to determine the pile body resistance: Method in accordance with the safety factor of the design philosophy of allowable stress (ASD); first-order secondary moment 8 method (FOSM); First-order reliability method (FOSM); Monte Carlo method (MCS). After analyzing the advantages and disadvantages of these four method, the author proposes to select Monte Carlo analysis method to determine the resistance factorss. Safety range, G, is applied to determine resistance factors as R and Q follow the normal logarithm distribution: ( ) f( , ) ln ( ) D R D L L D D L L Q QR Q G Q Q λ γ γ ϕ λ λ + = = + (2.7) 2.4 Propose a procedure and pattern to determine the resistance factors The procedure and pattern to determine the pile resistance factors comply with the ensurement basis of target reliability as follows: 1. To determine limited state according to soil base strength conditions for drilled shafts (22TCN272-05, AASHTO LRFD), strength state function: g(R,Q)=ϕR – (γDQD+γLQL)= λR(γDk+γL)/ϕ - (λDk+ λL); 2. To select statistical parameters of design load effect (Q) and load factors: the representive is static load bias factor (λD) and live load effect bias factor (λL) complied with the standard AASHTO LRFD. 3. To analyze the statistical characteristics of resistance (R): the representive is resistance bias factor, λR, which is the ratio of measured ultimate resistance (Rtd) and predicted nominal resistance (Rdt): a. To determine the measured ultimate resistance Rtd from results of pile static load tests according to soil base condition, this is the trial load value at a settlement of 5% of pile diameter or merged settlement pile (AASHTO LRFD 2012, TCVN 9393-2012); b. To predict the nominal resistance (Rdt) based on calculation theory; c. To determine the resistance bias factor, λR=Rtd/Rdt; d. To analize, calculate the statistical parameters (μ, σ) and to verify the form of distribution density function (standard, logarithm,..) suitable for λR; 4. To analyze and to determine the resistance factors of drilled shafts (ϕ) on the basis of analyzing reliability follwing Monte Carlo method with the target reliability index satisfied, βt; 5. To recommend to correct the resistance factors for calculation method. The above procedure is shown in Figure 2.4. 9 Figure 2.4. Analysis model to determine pile resistance factors on the basis of ensuring the target reliability index Results obtained in Chapter 2 - Recommend to use relative random resistance bias factor (λR) with a minimum sample size of 20 to analyze statistical characteristics. When choosing a probability distribution function (cumulative), it is needed to consider between 2 cumulative distribution functions which fit to the entire real values (FTAD) and cumulative distribution function calibrated in accordance with the actual value area at the tail of distribution (BFTT). - Recommend to use Monte Carlo method to analysis the reliability as a basis for determining pile resistance factors and to use the first-order reliability method (FORM) for validation. - Propose a procedure and a pattern to determine pile resistance factors as shown in item 2.4. Chapter 3. ANALYZING THE PARAMETERS INFLUENCING TO RESISTANCE FACTORS OF DRILLED SHAFTS USED IN BRIDGE SUBSTRUCTURES IN HO CHI MINH CITY  Define the failure condtion of drilled shafts piles based on soil base (AASHTO LRFD, 5% pile diameter of merged) Determine limit state based on soil base for drilled shafts piles (strength, service states) Strength state function: g(R,Q)=ϕR – (γDQD+γLQL)  Determine statistical characteristics for 2 random variables (R: resistance, Q: load effect): Representive of R is resistance bias factor, λR=Rtd/Rdt Representive of Q is load effect bias factor, (λD, λL)  Determine λR, is the ratio of measure ultimate resistance, Rtd and predicted nominal resistance, Rdt  Apply the statistical characteristics to deadload and live load effect bias factor (λD, λL) according to AASHTO LRFD  Analysis and calculate the statistical characteristics (μ, σ, V) and verify distribution density function (standard, loga…) suitable for λR Determine reliability index, β and incident probability, Pf Select target reliability index βt (refered to AASHTO LRFD: βt=3,0)  Determine resistance factors ϕ based on Monte Carlo (MCS) method or fisrt-order reliability method (FORM)  Compare and evaluate the study results with other literature 11 Propose to correct resistance factors for estimated axial resistance method following soil base strength condition  Evaluate the reliability index 10 The parameters that influence the results of determining of pile resistance factors described in Figure 3.1. Figure 3.1. Parameters influencing to determinging of resistance factors (φ) 3.1 Uncertainty factors and statistical characteristics of load effect In Vietnam, there is no research conditions to determine the rules of distribution of load effects, the author proposes to apply the statistical characteristics and other factors regulated by the AASHTO LRFD design as:γL=1,75, λL=1,15, VL = 0,18; γD = 1,25, λD=1,08, VD = 0,13, QD/QL =3. where: λD and λL are deadload and live load effect bias factor. VD and VL are variation coefficients of dead load and live load; the ratio QD/QL is of dead load and live load. 3.2 Uncertainties affecting to drilled shafts resistance The uncertainties affecting the predicted pile resistance should be analyzed to determine the resistance factors for methods to ensure required reliability and they are divided into four main groups: 1). The diversity, the unusual geological structure; 2). The error of measurement (measuring, surveying, testing of characteristic parameters of the material, structure or soil base); 3). The model error and 4). Quality of project administration and construction experience (According to Phoon and Kulhawy (1999), Paikowsky (2004)). To describe the general characteristics of these uncertainties, relative random resistance bias factor (λR) as outlined in Chapter 2 can be used. 3.3 Analyzing selection of methods to predict drilled shafts resistance On the basis of several popular methods of pile resistance prediction in Vietnam and overseas, the author selected four methods according to soil base condition as mentioned in the research scope. Real geological layer profile Model of (MH) soil base Model MH applied for design CKN Result in (φ) Target reliability index (βt) Abnormal profile + measurement error (khả át ) Error due to MH: MH predict uncertain R Statistical error discrebing factos: MH predicts uncertain Q γ (ϲ, φo, N,…) γ (ϲ, φo, N,…) Su (qu,…) μ ± σ μ ± σ Quality of construction organization, management and operation based on reliability analysis 11 The formula to determine the unit resistance at the pile tip and pile shaft according to the two standards are briefly introduced in Table 3.1 and Table 3.2. 3.4 Selection of method to determine actual measured ultimate resistance of drilled shafts Table 3.1. Summary of formula to determine nominal unit resistance of drilled shafts according to 22TCN 272-05 and AASHTO LRFD 2012 22TCN 272-05 (brief RO88-272) AASHTO LRFD 2012 ( brief OR99-AL12) Unit shaft resistance, qs Unit tip resistance, qp Unit shaft resistance, qs Unit tip resistance, qp 1. Cohesive soil (clay, soil with clay dust content higher 50%) qs= α Su (MPa) Su(MPa) α <0,2 0,55 ...-.. ... 0,8-0,9 0,31 >0,9 - qp=Nc Su ≤4 (MPa), where: 6[1 0,2( / )] 9cN Z D= + ≤ , với Su ≥0,024MPa; 0,67*6[1 0,2( / )] 9cN Z D= + ≤ with Su <0,024MPa qs= α Su (MPa), where: α =0,55, với / 1,5u aS p ≤ 0,55 - 0,1( / -1,5)u aS pα = with 1,5 / 2,5u aS p≤ ≤ qp=Nc Su ≤4 (MPa), where: 6[1 0,2( / )] 9cN Z D= + ≤ với Su ≥0,024MPa; 0,67*6[1 0,2( / )] 9cN Z D= + ≤ with Su <0,024MPa 2. Discrete soil (sandy soil, soil with sand dust content higher 50%) ' 0,19 vs q βσ= ≤ , with 0,25≤β≤1,2 where: 31,5 7,7 10 zβ −= − × qp=0,057N,with N≤75; =4,3pq , with N>75 ' 0,19 vs q βσ= ≤ , with , 25≤β≤1,2 where: 31,5 7,7 10 zβ −= − × , with N60≥15; 360 (1,5 7,7 10 ) 15 N zβ −= − × , with N60 <15 qp=0,057N60, with 0,57N60≤50; 0.8' ' 600,59 *p a v vq N p σ σ =   , with N60 >50 Table 3.2.Summary of formula to determine nominal unit resistance of drilled shafts according to TCXDVN 205-98 and JRA 2002-Part IV Russian method in TCXDVN 205-98 (brief SNIP-205) JRA 2002-Part IV (brief SHBP4-JRA02) Unit shaft resistance, qs Unit tip resistance, qp Unit shaft resistance, qs Unit tip resistance, qp 1. Cohesive soil (clay, soil with clay dust content higher 50%) 2≤ qs ≤100(kPa), Refered to table A.2, with 0,2 ≤ IL≤ 1 and 1m≤ htb ≤35m 250≤qp≤4500 (kPa), table A.7, with, 0 ≤ IL≤ 0,6 and 3m ≤hmc≤40m qs =qu/2 or qs =c or =10N≤150(kPa) qp = 3qu or =60N ≤ 9000(kPa) 2. Discrete soil (sandy soil, gravel, soil with sand dust content higher 50%) 15≤qs≤100(KPa), Refered to table A2, for medium tight sand has grain components: coarse, fine, dust. If tight state used, then qs increased by 30%; and 1m≤htb≤35m qp=0,75.β(γ1'.dp.Ako+ α.γ1.hmc.Bko), with: β; Ako; α; Bko refered to table A.6, with 24o ≤ ϕο≤ 39o, 4 ≤h/d≤25 and 0,8≤d≤4m qs =2N≤200(kPa) Sandy soil, gravel: qp=70N≤3000(kPa), with N≥30; Hard gravel: qp =5000(kPa), with N≥50 12 To ensure the consistency with the design philosophy of drilled shafts in LRFD method, the author proposes to select actual measured resistance value in accordance with the AASHTO LRFD standards as outlined (referred to as AASHTO method) when analyzing to determine resistance factors. In AASHTO LRFD 2007, actual measured pile body resistance is the load at which settlement of pile top equals 5% of pile diameter or pile is merged (Figure 3.2). Figure 3.2. Trial loading and settlement relationship 3.5 Analyzing the statistical characteristics for resistance bias factor of drilled shafts based on soil base strength in Ho Chi Minh City 3.5.1 Survey to collect data base of static axial compressive load tests to serve for current research. The survey collected 24 profiles of static axial compressive load tests for drilled shafts (including geological survey reports, topographical, design dossiers and dossiers of pile construction quality management) which meet the requirements of statistical studies in Figure 3.3, Table 3.3 and Table 3.4 (see details in Appendix 1). Characteristics of this data set is the same method of construction in bentonite mortar (wet technology); geological conditions are similar mixture soil (cohesive and discrete): mud clay, silt, clay, loam, sand, clay sand (mainly forming pile skin resistance ); but different in size (diameter from 1m-2m, length from 25m-85m) and location (Table 3.3). 13 Geological characteristics at the testing place can be considered as the representative for the type of the cohesive and discrete mixture soil in HCM City in particular, the layer profile is formed from river sediments, sea (clay mud, muddy sand, sandy loam, sandy clay and sand). Stratigraphic distribution: the top layer is soft soil (clay mud, sand mud) with up to 35m in thickness, the SPT index (N <5); the beneath layers are clay layer, sandy clay, sand and clay sand at the depth up to 100m, the SPT index (N = 10 to > 50 (Table 3.3, Appendix 2, 4). PT4 TỈNH ĐỒNG NAI Huyện Cần Giờ TỈNH LONG AN TỈNH BÌNH DƯƠNG Huyện Củ Chi PT6 PT1 1 PT22 PT24-PT25 PT10PT26-PT27 PT16-PT18 PT7-PT9 PT3 PT2 PT1 PT5 PT12 PT19-PT21PT23 TP HỒ CHÍ MINH Huyện Cần Giờ 18 19 0 1 2 4 1 5 17 TP.HỒ CHÍ MINH KÝ HIỆU TÊN CỌC CT1 TP1NL CT2 TPRC CT3 TP02LG CT4 TPCY CT5 TPCTL CT6 TPCTN CT7 TPABCL CT8 TPB1CL CT9 TPB3CL CT10 C1SG2 CT11 T96CC CT12 TPB-1MT1 CT13 TPB-2MT1 CT14 TPB-3MT1 CT15 TPB-4MT1 CT16 TPB-5MT1 CT17 TPB-6MT1 CT18 DP55-CO152 CT19 DP143-CO152 CT20 TP1BTT CT21 TP2BTT CT22 PTP1LM CT23 PTP2LM CT24 PTP3LM PT22-PT24 Figure 3.3. 24 locations plan of static axial compressive load tests in Ho Chi Minh city Table 3.3. Characteristics statistics of 24 drilled shafts under static axial compression testing Pile name Location Length/ Diameter, L(m)/D(m) Measured resistance (kN) Geological characteristics Construction method Soil Type of soil material (body/toe) East-West Avenue project – Ho Chi Minh City, District 6, 8, 1 and 2: From CT1-CT9 CT1 Nuoc Len bridge, Km0+800 54,9/1,2 7.554 Cohesive and discrete Clay mud, sandy mud, clay sand, clay/Clay sand wet (Bentonite) CT2 Rach Cay Bridge, KM3+700 59,5/1,2 10.440 Clay mud, clay sand, clay, sandy clay/Fine sand CT3 Lo Gom Bridge, Km4+725 71,8/1,5 14.712 Clay mud, clay sand, sandy clay/Clay sand CT4 Y-Shaped Bridge, Km10+680 25,7/1,0 5.542 Sandy clay, Grevel dust sand/ Clay CT5 Ca Tre Lon Bridge, Km17+017 39,1/1,2 8.041 Clay, clay sand/Dust sand CT6 Ca Tre Nho Bridge, Km17+677 54,4/1,2 11.673 Clay mud, sand clay, clay sand/Gravel clay sand CT7 A&B Bridge, Cat Lai Intersection Over-Passing Bridge, Km21+300 38,1/1,0 5.572 Clay mud, sand clay, clay sand/ Gravel clay sand CT8 67,0/1,0 12.000 Organic clay, clay/clay sand CT9 58,8/1,2 14.760 CT10 Sai Gon 2 Bridge, Q.BT-Q2, 74,0/1,2 40.810 Mud, clay sand, clay, clay sand, sand clay/Sand clay wet CT11 Can Bridge, Km7+958, HCM-LT-DG Express 79,3/2,0 16.346 Cohesive and discrete Organic clay, clay/clay sand wet 14 Pile name Location Length/ Diameter, L(m)/D(m) Measured resistance (kN) Geological characteristics Construction method Soil Type of soil material (body/toe) CT12 Can Bridge, LT: P7-17- _P7-22, Metro No.1, Ben Thanh-Suoi Tien, HCM 40,2/1,0 7.070 Cohesive and discrete Clay mud, clay sand, clay, sand dust /dust sand wet CT13 77,5/1,5 27.727 Clay mud, clay sand, average sand, dust clay /dust sand CT14 75,4/1,2 19.672 Clay mud, average sand, dust clay / average sand CT15 Can Bridge, LT: P13-39 _P13-41, Metro No.1, Ben Thanh-Suoi Tien, HCM 26,7/1,0 6.428 Clay mud, average sand, dust clay / average sand wet CT16 55,4/1,5 27.727 Gravel fine sand, gravel clay, sandy clay/dust sand CT17 46,8/1,2 17.942 Gravel fine sand, gravel clay/average dust sand CT18 Office Building, 152 Đien Bien Phu, BT, HCM 85,0/1,5 22.171 Cohesive and discrete Mud, clay, clay sand/Clay sand wet CT19 83,0/1,0 13.538 CT20 Ben Thanh Tower, 48-50 Le T. Hong Gam, D.1, HCM 76,0/1,2 30.970 Cohesive and discrete Clay mud, sandy clay, clay sand/Clay sand wet CT21 74,0/1,5 30.656 CT22 Lotte Mart Binh Duong, D.Thuan An, Binh Duong (near Sai Gon river) 49,4/1,5 16.554 Cohesive and discrete Organic clay, clay, sand clay, coarse – fine sand/ Coarse-fine sand wet CT23 49,2/1,2 14.041 CT24 50,0/1,0 11.289 Table 3.4. Synthetic table of survey data of experimental results of drilled shafts under static load test in HCMC area and comparision with a number of research works of foreign authors Work of Data Characteristics collected from static loading pile tests Geology/Location n (pile) L(m) D(m) Rtd (kN) Construction method/static loading Present thesis Cohesive and discrete mixture soil/HCM city 24 25-85 1-2 5.542-40.810 wet/static loading Liang (2009) Clay/America 15 4,91-31,32 0,46-0,91 1.373-4.903 Combined (dry, wet, wall tube)/Static loading&Osterberg- Cell Clay/America 18 4,91-30,5 0,36-0,91 113-7.551 Murad (2013) Cohesive and discrete mixture soil / Louisiana& Mississippi(America) 32 10,7-42,1 0,61-1,83 2.108-27.125 Combined (dry, wet, wall tube)/Static loading&Osterberg- Cell Notation: n-number of piles; D-diameter; L-length, Rtd-actual measured resistance Comment: From table 3.3 and 3.4, it can be found that: 24 document sets mentioned above are similar to data from studies of some foreign authors on the general nature of the survey data collected. Thus, the 24 sets of data are sufficiently reliable to carry out a study to identify the resistance factors of foundation piles for bridge substructures in HCMC area. 15 3.5.2 Analysis of data statistic characteristics Statistical analysis data includes: 1. Estimated nominal resistance (Rdti) according to the four methods mentioned above with the geological survey data and the actual size of the pile; 2. Actual measured resistance (Rtdi) which is testing load value corresponding to the settlement by 5% of pile diameter or the load causes the pile merged. The analyzed results were listed in Table 3.5. Use R-software to analyze the statistical characteristics for this resistance bias factor (mean, Rλ , standard deviation, σλR, coefficient of variation, VλR) and appropriate distribution rules. Analytical results are presented in Table 3.5 and Figure 3.4-3.7. The study results summarized for a comparison with some research results abroad are presented in Table 3.6. Table 3.5. Actual measured and predicted nominal resistances, statistical characteristics of resistance bias factor (λR) of drilled shafts according to 4 methods for 24 piles under static load tests Pile name Length/ Diameter, L(m)/D(m) Measured resistance Rtdi(kN) Predicted nominal resistance, Rdt(kN) and resistance bias factor (λRi) based on: RO88-272 OR99-AL12 SNIP-205 SHB4-JRA02 Rdti λRi Rdti λRi Rdti λRi Rdti λRi CT1 54,9/1,2 7.554 9.253 0,820 8.836 0,850 7.127 1,060 5.868 1,290 . . . . . . . . . . . CT24 50,0/1,0 11.289 7.806 1,450 7.372 1,530 9.398 1,200 7.615 1,480 Averaged number of bias factor λR, Rλ 1,066 1,153 1,215 1,203 Standard deviation of λR, σλR 0,308 0,351 0,246 0,368 Variation coefficient of λR, VλR 0,289 0,304 0,202 0,306 Most suitable distribution (Standard or logarithm distribution) loga Ps=0,80 loga Ps=0,56 loga Ps=0,99 loga Ps=0,39 (Notation: Ps: Appropriate probability of aussumed distribution (Standard or logarithm) compared to standardization distribution, determined based on Shapiro-Wilk method (appropriate condition: PS≥0,05)) Hình 3.4. Distribution density vs.distribution inspection for resistance bias factor, λR (Rtd/RdtRO88-272), (RO88-272: Resee&O’Neill(1988) method) Stand.Distri.Validation (Shapiro-Wilk): PS= 0.13>0.05 suitable to standard distribution Standard Distri.: Rλ =1,066;σR = 0,308 Standard logarit distribution μlnλ=0,026 σlnλ=0,278 Loga.Distri.Validation (Shapiro-Wilk): Ps= 0.80>0.05 suitable to logarithm distribution 16 Figure 3.5. Distribution density vs.distribution inspection for resistance bias factor, λR (Rtd/RdtOR99-AL12), Figure 3.6. Distribution density vs.distribution inspection for resistaonce bias factor, λR (Rtd/RdtSNIP-205) Figure 3.7. Distribution density vs.distribution inspection for resistance bias factor, λR (Rtd/RdtSHB4-JRA02) Table 3.6. Comparison of analytical results of statistical characteristics in literature Prediction method/Specification Soil Construction method Statistical characteristics of resistance bias factor, λR Note Pile number Rλ σλR VλR Distribution RO88-272: Reese& O’Neill (1988)/ 22TCN272-05 (AASHTO LRFD Cohesive and discrete Wet (Bentonite) 24 1,067 0,302 0,283 loga Results of this thesis 1,029 0,276 0,268 loga* Clay Wet 10 1,290 0,348 0,270 Paikowsky Stand.Distri.Validation (Shapiro-Wilk): Ps=0.18>0.05 suitable to standard distribution Loga.Distri.Validation (Shapiro-Wilk): Ps= 0.56>0.05 suitable to logarithm distribution Stand.Distri. Rλ =1,153 σR=0,351 Stand.loga. Distri. μlnλ=0,099 σlnλ=0,301 — - Expected line of standard distribution o – Actual measured value (Lnλ) — - Expected line of standard distribution o – Actual measured value (Lnλ) Stand.Distri.Validatio n (Shapiro-Wilk): Ps= 0.55>0.05p Loga.Distri.Validatio n (Shapiro-Wilk): Ps= 0.997>0.05 suitable to logarithm distribution Standard distribution Rλ =1,215; σR =0,246 Stand.loga. Distri. μlnλ=0,176 σlnλ=0,198 Stand.Distri.Validation (Shapiro-Wilk): Ps= 0.01<0.05 not suitable Loga.Distri.Validation (Shapiro-Wilk): Ps= 0.39>0.05 suitable to logarithm distribution Standard distribution Rλ =1,203;σR =0,368 Stand.loga. Distri. μlnλ=0,146 σlnλ=0,279 — - Expected line of standard distribution o – Actual measured value (Lnλ) 17 Prediction method/Specification Soil Construction method Statistical characteristics of resistance bias factor, λR Note Pile number Rλ σλR VλR Distribution 1998)/ (Cohesive, discrete soil) and sand Wall tube 21 1,040 0,302 0,290 loga (2004) Combined 44 1,190 0,357 0,300 loga Clay Combined (dry, wet, wall tube) 53 0,90 0,423 0,47 loga Sand 32 1,71 1,026 0,60 loga OR99-AL12: O’Neill& Resee (1999)/ AASHTO LRFD 2012/ (Cohesive, discrete soil) Cohesive and discrete Wet 24 1,155 0,356 0,308 loga Results of this thesis 1,076 0,316 0,294 loga* Cohesive and discrete Combined 34 1,270 0,381 0,300 loga Murad (2013) 1,330 0,52 0,391 loga* Clay Combined 15 1,122 0,302 0,269 loga Liang (2009) 0,902 0,107 0,118 loga* Sand Combined 18 2,262 1,004 0,444 loga 1,482 0,453 0,306 loga* Comment: From Tables 3.5&3.6 and Figures 3.4 to 3.7, it can be seen that: The dispersion of predicted resistance values or resistance bias factor of SNIP-205 method is at least, the 3 remaining methods have more dispersion and nearly equal (Fig. 3.4-3.7); Resistance bias factor (λR) of the four methods as mentioned above follows the standard logarithmic distribution law (Probability testing in accordance with logarithms distribution of Shapiro-Wilk is Ps > 0.05). In which, SNIP-205 method is the most consistent with the logarithmic distribution (because most consistent probability: Ps = 0.997), followed by RO88-272 method (Ps = 0.8) and last is SHB4-JRA02 method (Ps = 0.39) (Table 3.5 and Figures 3.4-3.7); Averaged value ( Rλ ) of resistance bias factor in SNIP-205 method is maximum ( Rλ =1,215), followed by SHB4-JRA02 method ( Rλ =1,203) and minimum value is of RO88-272 method ( Rλ =1,066); Variation coefficient (VλR) of resistance bias factor of SNIP-205 method is the smallest (VλR=0,202 dispersion of at least λRSNIP-205), followed by RO88-272 method (VλR =0,289) and of the method SHB4-JRA02 is maximum (VλR =0,306); The study results of statistical characteristics of resistance bias factor of drilled shafts for the four methods are reliable, quite similar, and consistent with some studies in literature (Table 3.6). 3.6 Determining statistical characteristics of parameters that affect to determination of resistance factors of drilled shafts 18 Through the selection and research outcome as above, the author recommends statistical characteristics of the parameters effecting to the determination of pile resistance under cohesive and discrete mixture soil base condition in Ho Chi Minh City area, as summarized in Table 3.7. Results obtained from Chapter 3 In the framework, the obtained results quantified parameters influencing the resistan factors of drilled shafts through statistical characteristics of relative random resistance bias factor. Based on the result of the analysis, evaluate and quantify statistical characteristics of parameters effecting to the resistance factors of drilled shafts according to soil base strength condition for four above methods (RO88-272, OR99-AL12, snip-205, SHB4-JRA02), the following conclusions can be made: - Statistical characteristics of the resistance bias factor (λR, the ratio of the measured resistance/predicted resistance) have fully reflected all uncertainty properties of parameters affecting to predicted results of pile resistance under soil base condition. With each method as well as each form of geology, there will be different statistical characteristics; - Results of research on statistical characteristics of the resistance bias factor of drilled shafts under soil base condition initially contribute to the basics of determining the resistance factors for the pile under geological Table 3.7. Summary of proposed statistical characteristics of parameters effecting to pile resistance factors according to soil base strength Name of statistical variable (Resistance bias factor, λ) Statistical characteristics Note Distribution λ ( ln λ ) σλ (σlnλ) Vλ 1. Representive for resistance: Resistance bias factor, (λR:actual measured resistance/predicted resistance) * as a logarithm distribution corrected to be consistent with values at the tail area of the distribution method “Best fit to tail (Allen, 2005)”; Values inside the bracket (.) are averaged ones ( ln λ ) and standard deviation (σlnλ) of logarithm distribution. RO88-272 (Reese&O’Neill (1988)) loga 1,067 (0,026) 0,302 (0,278) 0,283 loga* 1,029 (-0,006) 0,276 (0,263) 0,268 OR99-AL12 (O’Neill&Reese (1999)) loga 1,155 (0,099) 0,356 (0,301) 0,308 loga* 1,076 (0,032) 0,316 (0,288) 0,294 SNIP-205 (TC Nga trong TCXDVN205-98) loga 1,216 (0,176) 0,243 (0,198) 0,200 loga* 1,215 (0,171) 0,270 (0,219) 0,222 SHB4-JRA02 (JRA2002- SHB_Part IV) loga 1,203 (0.146) 0,343 (0279) 0,285 loga* 1,127 (0,089) 0,282 (0,246) 0,250 2. Representive for load effect: bias factor of deadload (λD) and liveload (λL) effects According to 22TCN 272-05 (AASHTO LRFD) Deadload effect, λD loga 1,080 (0,069) 0,140 (0,129) 0,130 Liveload effect, λL loga 1,150 (0,124) 0,210 (0,179) 0,180 Deadload coefficient, γD=1,25; liveload coefficient, γL=1,75; ratio of deadload (D) over liveload (L), D/L=3. 19 conditions with cohesive or discrete soil in HCM City, in which piles are constructed by wet method (bentonite) for four methods as in Table 3.7. Chapter 4. DETERMINATION AND PROPOSAL OF RESISTANCE FACTORS OF DRILLED SHAFTS ACCORDING TO SOIL BASE STRENGTH IN HO CHI MINH CITY 4.1 Selection and proposal of target reliability index for drilled shafts design The selection of the level of reliability or target reliability index relates to the level of reliability that is being used in the design, form of structural damage, the sensitivity of the public and media, owners, lifetime design of the structure and elements of political, economic and social. In Vietnam, there is no conditions for researching the target reliability index, it is recommended to select the index, βt = 3, as directed by the AASHTO LRFD. 4.2 Determination of axial resistance factors of drilled shafts according to soil base strength On the basis of analysis results of statistical characteristics of resistance bias factor (λR) of the four methods and application of the statistical characteristics of load effect bias factor λD, λL), the other parameters as suggested in Table 3.7, to determine resistance factors of drilled shafts according to 2 methods: first-order reliability method (FORM) and Monte Carlo simulation method (MCS) as outlined in Chapter 2 as follows: - FORM method: Applying formula (2.7), using a spreadsheet on Excel function and using run loop Solver to determine the reliability index (β) corresponds to the values of the assumed resistance factors (ϕ = 0, 4, 0.6, 0.8, 1.05). Next, charting the relationship between β and ϕ; based on this relationship chart to determine the resistance factors corresponding to the target reliability index (βt = 1.64, 2.33, 3.0 and 3.5). Detailed results are presented in Table 4.1; - MCS method: Also apply the formula (2.7), set up the spreadsheets and use the Crystal Ball software (analysis software is integrated in the environment of Excel) to determine the statistical characteristics of state functions f(R,Q) corresponds to the values of assumed resistance factors (ϕ = 0.4, 0.6, 0.8, 1.05), which will determine the reliability index (β) , respectively. Next, charting the relationship between β and ϕ; based on this relationship chart to determine the coefficients of resistance corresponding to the target reliability index (βt = 1.64, 2.33, 3.0 and 3.5). Detailed results are presented in Table 4.1. 20 Table 4.2. Comparation of resistance factorss, ϕ, between present study and other literatures in the world Prediction method/specif- ication Soil type- Location Constructio n method/ number of piles λR Factor φ with βt=3 (MCS) Compar- ision Proposi- ng, φ (βt=3) Note λ σλ RO88-272: Reese& O’Neill (1988)/ 22TCN272-05 Cohesive&discrete mixture soil-HCM Wet/24 1,067 0,302 0,54 0,985 0,54 Results of this thesis 1,029a 0,276a 0,55a 1 Clay&sand- America Combined /44 1,190 0,300 0.58 1,055 Paikowsky (2004) Clay -America Combined 0,63 b 1,145 22TCN272-05 Sand-America none - OR99-AL12: O’Neill& Resee (1999)/ AASHTO LRFD 2012/ (Đất dính, rời) Cohesive&discrete mixture soil-HCM Wet/24 1,155 0,356 0,55 1,038 0,53 Results of this thesis 1,076a 0,316a 0,53a 1 Cohesive&discret e mixture soil- America Combined /34 1,270 0,381 0,60 1,132 0,60 Murad (2013) 1,330a 0,52a 0,50a 0,943 Clay -America/15 Combined 1,122 0,302 0,46 0,868 0,45 Liang (2009) 0,902 a 0,107a 0.56a 1,057 Sand-America/18 Combined 2,262 1,004 0,51 0,962 0,50 1,482a 0,453a 0. 52a 0,981 Clay -America Combined 0,44c 0,830 AASHTO LRFD 2012 Sand-America Combined 0,54d 1,019 SNIP-205: Tiêu chuẩn Nga Cohesive& discrete-HCM Wet/24 1,216 0,243 0,77 1,055 0,73 Results of this thesis 1,215a 0,270a 0,73a 1 Cohesive& discrete-Russia Combined 0,79 e 1,019 TCXDVN205-98 Table 4.1. Results of determination of resistance factorss (ϕ) for the four resistance prediction method from statistical characteristics Prediction method of drilled shafts resistance Statistical characteristics of resistance bias factor, (λR: ratio of resistances actual measured/predicted), Table 3.7 Method of determinat- ion Resistance factorss (ϕ) corresponding to the target reliability index (βt) Comparison of average error between FORM&MCS Phân phối λ ( lnλ ) σλ (σlnλ) Vλ βt =1,64 2,33 3,0 3,5 RO88-272 (Reese&O’Neill (1988)/ 22TCN272-05) loga 1,067 (0,026) 0,302 (0,278) 0,283 FORM 0,80 0,65 0,53 0,46 1 MCS 0,82 0,66 0,54 0,47 1,023 loga* 1,029 (-0,006) 0,276 (0,263) 0,268 FORM 0,79 0,65 0,54 0,47 1 MCS 0,80 0,66 0,55 0,47 1,019 OR99-AL12 (O’Neill&Reese (1999)/AASHTO LRFD 2012) Loga 1,155 (0,099) 0,356 (0,301) 0,308 FORM 0,83 0,66 0,54 0,46 1 MCS 0,85 0,68 0,55 0,47 1,032 Loga* 1,076 (0,032) 0,316 (0,288) 0,294 FORM 0,79 0,64 0,52 0,45 1 MCS 0,81 0,66 0,53 0,46 1,026 SNIP-205 (Russian method in TCXDVN205- 98) Loga 1,216 (0,176) 0,243 (0,198) 0,200 FORM 1,04 0,89 0,77 0,69 1 MCS 1,05 0,90 0,77 0,69 1,003 Loga* 1,215 (0,171) 0,270 (0,219) 0,222 FORM 1,01 0,85 0,72 0,64 1 MCS 1,02 0,86 0,73 0,65 1,011 SHB4-JRA02 (Japanese Standard JRA2002- SHB_Part IV) Loga 1,203 (0.146) 0,343 (0279) 0,285 FORM 0,90 0,73 0,60 0,51 1 MCS 0,92 0,75 0,61 0,52 1,022 Loga* 1,127 (0,089) 0,282 (0,246) 0,250 FORM 0,89 0,74 0,62 0,54 1 MCS 0,90 0,75 0,63 0,55 1,015 21 Prediction method/specif- ication Soil type- Location Constructio n method/ number of piles λR Factor φ with βt=3 (MCS) Compar- ision Proposi- ng, φ (βt=3) Note λ σλ SHB4-JRA02: Tiêu chuẩn Nhật Cohesive&discrete mixture soil-HCM Wet/24 1,203 0,343 0,61 0,968 0,61 Results of this thesis 1,127a 0,282a 0,63a 1 Cohesive& discrete-Japan Combined 0,34 f 0,540 JRA2002-SHB_Part IV Comments: - Along with the target index reliability (βt), the resistance factors of drilled shafts corresponding to the four methods are proportional to the averaged value of the resistance bias factor, Rλ and inversely proportional to coefficient of variation, VλR; - The analytical results have determined that the resistance factors corresponds to the FORM and MCS methods are nearly equal (difference from 0.3% to 3.2%). Therefore, the thesis using MCS method is reasonable (Table 4.1); - The standardization of results of resistance factorss of the thesis (ϕLA) differs from the results of international studies in foreign countries and the current design standards(ϕNN , ϕTC) about a smaller percentage of less than 14.3% to 44.3%. Specifically as follows (Table 4.2): + For the Resee & O'Neill (1988) method: ϕLA is smaller than ϕTC (= 0.63) equivalently in the standard 22TCN272-05 and ϕNN (= 0.58) of Paikowsky (2004) respectively 14 , 3% and 6.9%. This difference can be explained: Although study results for soil mixture (cohesive and discrete soil type) including clay and sand, but due to different geographical conditions, substrate heterogeneity, measures construction methods and other factors should lead to this error; + For O’Neill&Resee method (1999): ϕLA is smaller than ϕNN (=0,6) of Murad (2013) about 11,7% and greater than ϕTC (=0,48) equivalently in the AASHTO LRFD 2012 about 9,4%. The difference can be explained as above; + Russian method in TCXDVN 205-98: ϕLA is smaller than ϕTC (=0,79) equivalently in the TCXDVN 205-98 about 7,6%; + Japanese method in JRA 2002 JSHB_Part IV: ϕLA is greater than ϕTC (=0,34) equivalently in the JRA 2002 JSHB_Part IV about 44,3%. 4.3 Evaluation and comparison of resistance factors in current applying standards and results of present thesis - Using 24 document sets of drilled shafts with assumed condition of general design parameters: target reliability index, β=3 (incident 22 probability, Pf=0,1%); deadload factor (γD=1,25), liveload factor (γL=1,75); ratio of deadload/liveload (D/L=3); - Predict the design resistance (symboled as RRdti or Rtkdti) based on the four methods (RO88-272, OR99-AL12, SNIP-205 and SHB4-JRA02) orderly with resistance factors obtained from design standards and from present thesis. Results are listed in Table 4.3; - Analyze the statistical characteristics of design resistance bias factor, to be similarly done as the Item 3.5. Analyze the reliability level (using MCS method) to determine the reliability index. Results are presented in Table 4.3; Table 4.3. Predicted design resistances, statistical characteristics of design resistance bias factor of drilled shafts (λtkR) according to the four methods with resistance factors obtained from design standards and from present thesis. Pile name Length/ Diameter, L(m)/D(m) Measured Resistance Rtdi(kN) Predicted design resistance, Rtkdt (kN) and design resistance bias factor (λtkRi) RO88-272 OR99-AL12 SNIP-205 SHB4-JRA02 Rtkdti λtkRi Rtkdti λtkRi Rtkdti λtkRi Rtkdti λtkRi CT1 54,9/1,2 7.554 5.203 (4.997) 1,450 (1,510) 4.745 (4.683) 1,590 (1,610) 5.631 (5.203) 1,340 (1,450) 1.995 (3.579) 3,790 (2,110) . . . . . . . . . . . CT24 50,0/1,0 11.289 4.397 (4.215) 2,570 (2,680) 3.946 (3.907) 2,860 (2,890) 7.428 (6.861) 1,520 (1,650) 2.590 (4.645) 4,360 (2,430) Average number of resistance bias factor, R tk λ 1,850 (1,974) 2,220 (2,177) 1,539 (1,665) 3,780 (1,974) Standard deviation of λtkR, σλR 0,497 (0,570) 0,746 (0,664) 0,312 (0,337) 1,380 (0,605) Variation factor of λtkR, VλR 0,269 (0,289) 0,336 (0,305) 0,203 (0,202) 0,365 (0,306) Most suitable distribution (standard or logarithm) loga Ps=0,87 (0,79) loga Ps=0,75 (0,56) loga Ps=1,0 (0,99) loga Ps=0,19 (0,43) Re-calculation of statistical paprameters according to logarithm distribution Average number based on ln(λtkR), R tk λ 1,853 (1,975) 2,223 (2,180) 1,540 (1,666) 3,774 (1,974) Standard deviation of ln(λtkR), σλR 0,498 (0,559) 0,736 (0,671) 0,308 (0,332) 1,253 (0,565) Variation factor of ln(λtkR), VλR 0,269 (0,283) 0,331 (0,308) 0,200 (0,199) 0,332 (0,286) Reliability analysis Resistance factorss according to specification/ thesis 0,5-0,65 (0,54) 0,4-0,55 (0,53) 0,79 (0,73) 0,34 (0,61) Reliability index, β (based on MCS) 2,954 (3,021) 3,002 (3,126) 2,892 (3,029) 4,548 (3,007) Non-incident probability, Ps(%) ≈99,8 (≈99,9) ≈99,9 (≈99,9) ≈99,8 (≈99,9) 99,9997 (≈99,9) Incident probability Pf (%) ≈0,2 (≈0,1) ≈0,1 (≈0,1) ≈0,2 (≈0,1) 0,0003 (≈0,1) Pf compared with [Pf] 2 (1) 1 (1) 2 (1) 0,003 (1) Results obtained from Chapter 4 - The research results of drilled shafts axial resistance factors based on soil base strength condition (from 0.53 to 0.77) range in the value series of 23 axial resistance factors according to the current design standards (from 0.34 to 0.79) and a few research results abroad (from 0.46 to 0.60); - It can be proposed to select resistance factors, ϕ, by the principle of the minimum value in the values calculated by the Monte Carlo method (MCS) with statistical characteristics of resistance bias factor corrected or non-corrected based on the method Best fit to tail-Allen (2005). Specifically, the general resistance factors corresponding target index reliability, βt=3 or Ps=99,9% are proposed as follows: + Resee&O’Neill (1988) method, 22TCN272-05: ϕ =0,54; + O’Neill&Resee (1999) method, AASHTO LRFD 2012: ϕ =0,53; + Russian method in TCXDVN 205-98: ϕ =0,73; + Japanese method in JRA 2002 JSHB_Part IV: ϕ =0,61. GENERAL CONCLUSION With the aim of studying the influencing parameters and determination of the resistance factors of drilled shafts of bridge substructures based on soil base strength condition in Ho Chi Minh City area, the thesis has conducted a survey, research on the drilled shafts in projects located in the area, assess the current state of technology and the quality as well as the contents of design calculations, clarify exists in assessing pile resistance. By applying the methods of statistical probability theory and reliability theory in the field of foundation, the thesis proposed a model for determining resistance factors of drilled shafts based on the statistical characteristics of main influencing parameters. Based on the analysis of 24 samples of representive drilled shafts under static compressive load tests in the area, the thesis initially determines the resistance factors corresponding to other resistance prediction methods according to soil base condition at the area of Ho Chi Minh City. From the results of the study, some general conclusions are raised as follows : 1. Findings of the thesis - Propose a model to determine resistance of drilled shafts of bridge substructures based on statistical characteristics of the ratio (bias factor, λ) of measured value and predicted value of drilled shafts axial resistance with the application of probability statistics theory and reliability theory; - Analyze and quantify the parameters that influence drilled shafts for bridge substructures in cohesive and discrete mixture soil base, constructed 24 by wet method (bentonite) in the Ho Chi Minh City area, through determining the statistical characteristics of the resistance bias factor (λR) for four methods: + Resee&O’Neill (1988) method, 22TCN272-05: Complies with logarithm distribution, averaged value, Rλ =1,067; standard deviation, σλR = 0,302 and variation coefficient, VλR =0,283; + O’Neill&Resee (1999) method, AASHTO LRFD 2012: Logarithm distribution, Rλ =1,155; σλR = 0,356 and VλR =0,308; + Russian method in TCXDVN 205-98: logarithm distribution, Rλ =1,215; σλR = 0,270 and VλR =0,222; + Japanese method JRA 2002 JSHB_Part IV: logarithm distribution, Rλ =1,203; σλR= 0,343 and VλR =0,285. - Propose general resistance factors (ϕ) of drilled shafts according to soil base strength with cohesive and discrete mixture soil base, constructed by wet method (bentonite) in the Ho Chi Minh City area for the following four methods: + Resee&O’Neill (1988) method, 22TCN272-05: ϕ =0,54; + O’Neill&Resee (1999) method, AASHTO LRFD 2012: ϕ =0,53; + Russian method in TCXDVN 205-98: ϕ =0,73; + Japanese method, JRA 2002 JSHB_Part IV: ϕ =0,61. 2. Recommendations - It is able to use the model to determine resistance factors of drilled shafts based on statistical characteristics of the ratio (bias factor, λ) of actual measured value and predicted value to apply for other areas and different geological conditions in Vietnam. - The method of probability statistics analysis and reliability analysis Monte Carlo give the bias factor (λ) so as to determine resistance factors that can be applied for future studies. 3. Orientation of future studies - Conduct additional studies that identify statistical characteristics of resistance bias factor of drilled shafts, especially experimental results of loading test can separatively give tip resistance and shaft resistance such as Osterberg box loading method or normally static loading in which longitudinal strain gauges are attached, ... in regions with different geological characteristics to have a basis for correction of resistance factors for bridge-roadway design standards of Vietnam; - To study the statistical characteristics of loads, firstly highway liveloads to serve for design load grade to correct load factors based on reliability analysis which is suitable with Vietnam condition./. 25 PUBLICATIONS 1. Phuong, Ngo-Chau (2006), "Some issues related to the calculation of pile bearing capacity under current standards and some other standards", Transportation Science Megazine (15), p. 75-84, University of Transport and Communications. 2. Phuong, Ngo-Chau (2012), Analysis and evaluation of predicted pile body resistance of drilled shafts used for bridge substructures in soft soil bases according to design standards 272-05 and AASHTO LRFD Bridge 22TCN 2007, the head of the university-graded research project, University of Transport and Communications, Hanoi. 3. Ngo Chau Phuong, Tran Duc Nhiem (2012), “Some Problems of Estimating the Drilled Shaft Axial Resistance in 22TCN 272-05 And AASHTO LRFD 2007 Specifications”, The International Conference on Green Technology and Sustainable Development, Vol. 1, tr.99- 104, Tp.HCM. 4. Phuong, Ngo-Chau, Nhiem, Duc-Tran, Long, Nguyen-Ngoc (2013), “Some reliable parameters of drilled shafts of bridge substructures obtained from pile body bearing capacity in Ho Chi Minh city according to present specifications,”, Technology Science Conference 13th - Construction technology for sustainable development, Division of Construction technology- Ho Chi Minh Poly-technique University, Construction Publisher, pages 383-393 5. Phuong, Ngo-Chau, Nhiem, Duc-Tran, Long, Nguyen-Ngoc (2013), “A contribution in determining of capacity coefficients of drilled shafts body in bridge substructures for soft soil conditions at different locations in Vietnam”, Vietnam Bridge and Road Magazine (10/2013), p. 34-42, Vietnam Bridge and Road Association, Hanoi.

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