giáo trình nền móng của đại học xây dựng bản tiếng anh

NATIONAL UNIVERSITY OF CIVIL ENGINEERING DIVISION OF SOIL MECHANICS AND FOUNDATION ENGINEERING FOUNDATION ENGINEERING (FOR THE ENGLISH COURSE) NGUYEN BAO VIET LE THIET TRUNG HA NOI - 2013 National University of Civil Engineering i CONTENTS CONTENTS .i LIST OF FIGURES iii PREFACE v CHAPTER 1: INTRODUCTION CHAPTER 2: SHALLOW FOUNDATIONS 2.1 Introduction 2.2 Main Components of Shallow Foundations 2.3 Contact Pressure Distribution beneath Base of Footing 2.3.1 Contact Pressure Distribution of Spread Footing 2.3.2 Contact Pressure Distribution of Wall Footing 10 2.3.3 Net Load Applied on Footing Base 10 2.3.4 Vertical Stress Increase 10 2.4 Ultimate Bearing Capacity of Shallow Foundation 12 2.4.1 General .12 2.4.2 Terzaghis Bearing Capacity Theory 13 2.4.3 The General Bearing Capacity Equation 17 2.4.4 General Bearing Capacity Equation in Practice 19 2.4.5 Safety Factor and Allowable Load-Bearing Capacity 20 2.4.6 Bearing Capacity of Layered Soils: Stronger Soil underlain by Weaker Soil .20 2.5 Shallow Foundation Design .21 2.5.1 Introduction 21 2.5.2 Design Procedure for Shallow Foundation 21 2.5.3 Geotechnical Analyses and Design 22 2.5.4 Structural Footing Design 25 CHAPTER 3: SOIL IMPROVEMENT .30 3.1 Sand Replacement 31 3.2 Sand Compaction Piles 32 3.2.1 Characteristics of Sand Compaction Piles 34 3.2.2 Sand Compaction Pile Working Procedure .35 3.2.3 Applied Assumptions in Calculation of Sand Compaction Piles 36 Foundation Engineering CONTENTS National University of Civil Engineering ii 3.2.4 Principle of Sand Compaction Pile Analyses 36 3.2.5 Plan layout and Distance of Sand Compaction Pile 37 3.2.6 Estimation of Improved Soil Properties 41 3.3 Vibroflotation 42 3.4 Blasting 44 3.5 Precompression 44 3.6 Stone Columns 45 3.7 Dynamic Compaction 46 3.8 Jet Grouting 48 3.9 Recommendation of Improvement Methods for Soils 49 CHAPTER 4: 4.1 PILE FOUNDATIONS 50 Definitions and classifications 50 4.1.1 Definitions 50 4.1.2 Classifications of piles .52 4.1.3 Advantages and disadvantages of different pile material 58 4.2 Constitution of a Prefabricated Reinforced Concrete Pile 62 4.3 Bearing Capacity of a Single Pile 66 4.3.1 Definitions 66 4.3.2 Pile axial bearing capacity 66 4.4 Design of Low Pile Cap Foundation 74 4.4.1 Design hypotheses .74 4.4.2 Material selection for pile and pile cap 74 4.4.3 Pile dimension selection and pile load capacity calculation 75 4.4.4 Pile quantity and pile arrangement 75 4.4.5 Verification of load applied to pile 76 4.4.6 Verification of the resistance of bearing stratum .77 4.4.7 Calculation of pile foundation settlement 78 4.4.8 Pile cap height 78 4.4.9 Verification of pile when transportation and positioning 81 4.4.10 Selection of hammer for driven piles 82 REFERENCES 83 Foundation Engineering CONTENTS National University of Civil Engineering iii LIST OF FIGURES Figure 2-1 (a) Strip foundation under a wall (b) Strip foundation under columns (c) Spread foundation (d) Mat foundation (1) Footing (2) Wall (3) Column Figure 2-2 Examples of spread foundations Figure 2-3 Examples of shallow foundations (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform Figure 2-4 Examples of mat foundations (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat Figure 2-5 A typical cross section of spread footing Figure 2-6 Reinforcement of a spread footing Figure 2-7 Behavior of foundations with connecting beams Figure 2-8 Ground beam and footing reinforcements Figure 2-9 Settlement profile and contact pressure in sand: (a) flexible foundation; (b) rigid foundation Figure 2-10: Settlement profile and contact pressure in clay: (a) flexible foundation; (b) rigid foundation Figure 2-11: Linear distribution of contact pressure Figure 2-12 2:1 method of finding stress increase under a foundation 11 Figure 2-13 Nature of bearing capacity failure in soil: (a) general shear failure: (b) local shear failure; (c) punching shear failure 12 Figure 2-14 Bearing capacity failure in soil under a rough rigid continuous (strip) foundation 14 Figure 2-15 Bearing capacity of a strip foundation on layered soil 20 Figure 2-16 Two-way shear calculation 26 Figure 2-17 Wide-beam shear calculation 27 Figure 2-18 Flexure reinforcement calculation 28 Figure 3-1 (a) Completed sand replacement (b) Partial sand replacement 31 Figure 3-2 Sand compaction pile test of Basore and Boitano (1969): (a) Layout of the compaction piles; (b) Standard penetration resistance variation with depth and S 33 Figure 3-3 Sand compaction pile mandrel tip 34 Figure 3-4 Characteristic of sand compaction piles for a spread footing 35 Figure 3-5 Sand compaction pile working procedure 36 Figure 3-6 Principle of sand compaction pile analyses 37 Figure 3-7 Compaction area for (a) strip footing and (b) spread footing 38 Figure 3-8 Plan layout of sand compaction piles (a) equiangular triangle (b) Square 40 Foundation Engineering LIST OF FIGURES National University of Civil Engineering iv Figure 3-9 Vibroflotation unit 42 Figure 3-10 Compaction by the vibroflotation process 43 Figure 3-11 Principles of precompression 44 Figure 3-12 Sand drain 45 Figure 3-13 Prefabricated vertical drain (PVD) 45 Figure 3-14 (a) Stone columns in a triangular pattern; (b) stress concentration due to change in stiffness 46 Figure 3-15 Rig of Dynamic compaction 47 Figure 3-16 Dynamic compaction, working procedure 47 Figure 3-17 Effects of soil Improvement by Dynamic compaction & Vibroflotation 48 Figure 3-18 Jet grouting 49 Figure 3-19 Site improvement methods as a function of soil grain size 49 Figure 4-1: Low pile cap foundation High pile cap foundation 52 Figure 4-2: Steel pile cross section 53 Figure 4-3: End bearing pile 54 Figure 4-4: Friction or Cohesion pile 54 Figure 4-5: under-reamed base enlargement to a bore-and-cast-in-situ pile 55 Figure 4-6: Concrete driven piles system 56 Figure 4-7: Drilling auger types: short section single flight double flight 57 Figure 4-8: Bored pile phasing: Site preparation Positioning Excavation Rebar installation Conrete pouring Pile completion 58 Figure 4-9: Different cross section of piles 63 Figure 4-10: Detailed design of prefabricated reinforced concrete pile 63 Figure 4-11: Cross section of a square pile 64 Figure 4-12: Stirrup bar: separate bar and spriral bar 64 Figure 4-13: Details of pile toe 64 Figure 4-14: Steel grid at pile top Hook rebar 64 Figure 4-15: Steel plate at the pile top 65 Figure 4-16: Details of pile connection 65 Figure 4-17: s c khỏng bờn qci v s c khỏng m i qcn thớ nghi m CPT 68 Figure 4-18 Typical static load test arrangement showing instrumentation 70 Figure 4-19: Two P-S curves types (a, b) and T-S curve (c) 71 Figure 4-20: Piles arrangement in side view 75 Figure 4-21: Piles arrangement in plan view 76 Figure 4-22: Equivalent raft 77 Figure 4-23: damage pile cap by column 79 Figure 4-24: damage of pile cap by pile reaction 80 Figure 4-25: Rebar area calculation schemas 81 Figure 4-26: Pile transportation verification 81 Figure 4-27: Pile positioning verification 82 Foundation Engineering LIST OF FIGURES National University of Civil Engineering v PREFACE Soil mechanics and foundation engineering have developed rapidly during the last fifty years Intensive research and observation in the field and the laboratory have refined and improved the science of foundation design This text book of Foundation Engineering is edited for undergraduate civil engineering students, who have passed the soil mechanics course, which is a prerequisite for the foundation engineering course The text is composed of four chapters with examples and problems, and an answer section for selected problems The chapters are mostly devoted to the geotechnical aspects of foundation design and briefly described as follows Chapter of introduction gives an overview of foundation engineering Chapter presents on the concept of shallow foundation and focus analyses and design of spread footing and wall trip footing on several types of sub-soils The structural design of footing according to the Vietnamese codes also mentioned in detail in this chapter Chapter introduces various types of soil improvement in that sand cushion and sand compaction piles are concentrated in analyses and design also Chapter is dedicated for deep foundation of prefabricated piles The estimation of geotechnical and in structural bearing capacity of piles is mentioned based on both theories and practices Structural pile-cap design is an important content in this chapter After this course, the students can get the basic knowledge in foundation engineering They could calculate and design foundation in some simple cases This is the first step for an engineer in geotechnical and foundation engineering Thanks are due to all members of Geotechnical and Foundation Engineering Division of National University of Civil Engineering for their help and encouragements during the preparation of this text I am also grateful for several helpful suggestions of Prof Vu Cong Ngu and Assoc Prof Pham Quang Hung The Authors Dr Nguyen Bao Viet Dr Le Thiet Trung Foundation Engineering PREFACE National University of Civil Engineering CHAPTER 1: INTRODUCTION All structures resting on the earth must be carried by an interface element called foundation A foundation is the lowest part of a structure that transmits to, and into, the underlying soil or rock all loads of the super-structure and also its self-weight The term super-structure is commonly used to describe the engineered part of the system bringing loads to the foundation, or substructure especially for buildings and bridges However, foundations also may carry only machinery, support industrial equipment (pipes, towers, and tanks) act as sign base, and the like Therefore it is better to describe a foundation as a part of the engineered system that interfaces the load-carrying component to the ground It is evident that a foundation is the most important part of the structures or engineering system The design of foundations of structures such as buildings, bridges, and dams generally requires knowledge of such factors as: (a) The load that will be transmitted by the superstructure to the foundation system, (b) The requirements of the local building code, (c) The behavior and stress-related deformability of soils that will support the foundation system, and (d) The geological conditions of the soil under consideration To a foundation engineer, the last two factors are extremely important because they concern soil mechanics The geotechnical properties of a soil such as its grain-size distribution, plasticity, compressibility, and shear strength can be assessed by proper laboratory testing In addition, recently emphasis has been placed on the in situ determination of strength and deformation properties of soil, because this process avoids disturbing samples during field exploration However, under certain circumstances, not all of the needed parameters can be or are determined, because of economic or other reasons In such cases, the engineer must make certain assumptions regarding the properties of the soil To assess the accuracy of soil parameters whether they were determined in the laboratory and the field or whether they were assumed the engineer must have a good grasp of the basic principles of soil mechanics At the same time, he or she must realize that the natural soil deposits on which foundations are constructed are not homogeneous in most cases Thus, the engineer must have a thorough understanding of the geology of the area that is, the origin and nature of soil stratification and also the groundwater conditions Foundation engineering is a clever combination of soil mechanics, engineering geology, and proper judgment derived from past experience To a certain extent, it may be called an art When determining which foundation is the most economical, the engineer must consider the superstructure load, the subsoil conditions, and the desired tolerable settlement Foundation Engineering INTRODUCTION National University of Civil Engineering In general, foundations of the structures may be divided into two major categories: (1) Shallow foundations (2) Deep foundations Spread footings, wall footings, and mat foundations are all shallow foundations In most shallow foundations, the depth of embedment can be equal to or less than three to four times the width of the foundation Pile and drilled shaft foundations are deep foundations They are used when top layers have poor load-bearing capacity and when the use of shallow foundations will cause considerable structural damage or instability The separation is not strict but in the point of view of a foundation engineer, in analysis and design of a shallow foundation, vertical friction between the foundation and soils is neglected Foundation Engineering INTRODUCTION National University of Civil Engineering CHAPTER 2: SHALLOW FOUNDATIONS 2.1 Introduction Shallow foundations, often called footings, are usually embedded about a meter or so into soil One common type is the spread footing which consists of strips or pads of structural materials which transfer the loads from walls and columns to the soil or bedrock Another common type of shallow foundation is the slab-on-grade foundation where the weight of the building is transferred to the soil through a concrete slab placed at the surface Slab-on-grade foundations can be reinforced mat slabs, which range from 25 cm to several meters thick, depending on the size of the building Concrete is almost universally used for footings because of its durability in a potential hostile environment and for economy Figure 2-1 shows some shallow foundations including strip footings (a) and (b); spread footing (c); and mat foundation (d) Furthermore, in Figure 2-2 there are several common types of spread footing consist of constant footing (a); stepped footing (b); and sloped footing (c) Figure 2-1 (a) Strip foundation under a wall (b) Strip foundation under columns (c) Spread foundation (d) Mat foundation (1) Footing (2) Wall (3) Column Figure 2-2 Examples of spread foundations Various types of shallow foundation which could be used in practice such as combined or connected footings and mat foundations are illustrated in Figure 2-3 and Figure 2-4 Foundation Engineering SHALLOW FOUNDATIONS National University of Civil Engineering Figure 2-3 Examples of shallow foundations (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform Figure 2-4 Examples of mat foundations (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat Foundation Engineering SHALLOW FOUNDATIONS National University of Civil Engineering 70 At the maximum applied load, maintain the load for a minimum of one hour and until the settlement (measured at the lowest point of the pile at which measurements are made) over a one-hour period is not greater than 0.254 mm (0.01 inch) Remove 25 percent of the load every 15 minutes until zero load is reached Longer time increments may be used, but each shall be the same Measure rebound at zero load for a minimum of one hour After 200 percent of the load has been applied and removed, and the test has shown that the pile has additional capacity, i.e., it has not reached ultimate capacity, continue testing as follows Reload the test pile to the 200 percent design load level in increments of 50 percent of the allowable design load, allowing 20 minutes between increments Then increase the load in increments of 10 percent until either the pile or the frame reach their allowable structural capacity, or the pile can no longer support the added load If failure at maximum load does not occur, hold load for one hour At maximum achieved load, remove the load in four equal decrements, allowing 15 minutes between decrements Figure 4-18 Typical static load test arrangement showing instrumentation Test result From the acquisition, the load settlement (P-S) curve can be plotted The capacity of the single test pile can be defined by different criteria In case that the P-S curve show a big evolution (Figure 19.a), where we can find a limit of load Over this limit, the settlement S increases immediately and quickly This limit is corresponding to the inflexion point of the curve The value P of this point is considered as ultimate load capacity of the test pile Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 71 In case without inflexion point remarkable on the P-S curve, (Figure 19.b), the ultimate load capacity Pgh shall be defined in correspondence with the settlement value limit Sgh which: Sgh = 10%D where D pile diameter or Sgh = 2Smax, where Smax settlement measured at P = 0,9 allowable design load Ptk, or Sgh = 2,5%D for bored piles (TCXD 269-2002), or Sgh = .[S], where [S] allowable settlement for buildings, - coefficient, normally = 0,2 Figure 4-19: Two P-S curves types (a, b) and T-S curve (c) f Dynamic approach method Most frequently used method of estimating the load capacity of driven piles is to use a driving formula or dynamic formula All such formulae relate ultimate load capacity to pile set (the vertical movement per blow of the driving hammer) and assume that the driving resistance is equal to the load capacity to the pile under static loading they are based on an idealized representation of the action of the hammer on the pile in the last stage of its embedment Usually, pile-driving formulae are used either to establish a safe working load or to determine the driving requirements for a required working load The working load is usually determined by applying a suitable safety factor to the ultimate load calculated by the formula However, the use of dynamic formula is highly criticized in some pile-design literatures Dynamic methods not take into account the physical characteristics of the soil This can lead to dangerous missinterpretation of the results of dynamic formula calculation since they represent conditions at the time of driving They not take in to account the soil conditions which affect the long- term carrying capacity, reconsolidation, and negative skin friction and group effects Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 72 Experimental procedure: After driving pile to some depth (design depth in general), if we apply one drop of a normalized hammer on the pile top, the pile will move down a distance e This e value is defined as the rebound of pile The rebound of pile can be measured after each hammer drop, or can be calculated as average value after a series of hammer drop: e s n s pile movement after n drops n Hammer drop quantity For drop hammer or single action steam, n = 10 For Diesel hammer or double acting steam, n is the hammer drop quantity during minute testing The dynamic formula to determine the pile load capacity is base on the following principle: with same hammer, same drop free height, the pile corresponding to bigger rebound has smaller load capacity Following are some dynamic formulae to calculate the pile load capacity: Where, - Formula of Gexevanov Q k2q n.F n.F n.F Q.H Pgh Qq e Where, - Pgh Ultimate value of pile load capacity e Test pile rebound Q Hammer weight q Weight of pile + cap piece + pile cushion + driver pile (if any), H Drop free height k Collision coefficient, when collision between steel/ iron and wood, k = 0,45 and k2 = 0,2, n Coefficient depending to the pile material and pile driving conditions In case of prefabricated concrete pile and driven method, n = 15 daN/cm2 Formula of TCVN Following TCXD 205-1998, the formula to determine the ultimate pile load capacity is as below: Pgh n.F 4.Q.H Q k q e.n.F Q q This formula is only used when the pile rebound e 2mm In case that measured e < 2mm, it is necessary to use heavier hammer to create bigger rebound e > 2mm Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering - 73 Netherlands formula Pdyn Q.H K1 e.(Q q) Where: K1 safety factor, in general K1 = - Formula of Crandall Pdyn Where Q.H e K2 e .(Q q) e1 pile elastic rebound K2 safety factor, in general K2 = Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 74 4.4 Design of Low Pile Cap Foundation 4.4.1 Design hypotheses The design, calculation of low pile cap foundation is based on following hypotheses: For the low pile cap foundation, all lateral load being equilibrant with soil lateral stress applied to pile cap The pile receive only longitudinal load from pile cap Therefore, the pile cap base level h should be: h 0,7.hmin Q0 hmin tan 45 o '.b , angle of internal friction and volume weight of the soil above the pile cap base level Q0 Total lateral force B pile cap base width, in perpendicular with the lateral force Q0 Each pile of the foundation behaves as a single pile, and without pile group effect The applied load is fully transferred to the piles but not to the soil at pile cap bottom and between piles When verifying the resistance of bearing stratum and calculating pile foundation settlement, we consider the group of pile cap + piles + soils between piles as an equivalent raft The calculation of equivalent raft has the same procedure as footing foundation (shallow foundation) Pile cap is considered absolutely rigid The piles are restrained connected to the pile cap Where 4.4.2 Material selection for pile and pile cap a Concrete Based on the working conditions of piles, the minimum grade for concrete can be selected as following: Pile to be driven in normal condition: grade 250 Pile to be driven until a very small rebound value: grade 400 b Rebar See paragraph IV.2 Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 75 4.4.3 Pile dimension selection and pile load capacity calculation See paragraph IV.3: [P] = { Pvl, Ptk, PSPT, PCPT } 4.4.4 Pile quantity and pile arrangement Pile quantity: Pile quantity shall be calculated based on the applied load and load capacity of single pile, as below formula: n N tt P Where, Ntt Ultimate value of total vertical load [P] Pile load capacity - Empirical coefficient, taken into account of the load eccentricity varies from 1,2 o Pile spacing and arrangement: In certain types of soil, especially in sensitive clays, the capacity of individual piles within a closely spaced group may be lower than for equivalent isolated pile However, because of its insignificant effect, this may be ignored in design Instead the main worry has been that the block capacity of the group may be less than the sum of the individual piles capacities As a thumb rule, if spacing is more than - pile diameters, then block failure is most unlikely Normally, the spacing = 3d ữ 6d Large concentration of piles under the centre of the pile cap should be avoided This could lead to load concentration resulting in local settlement and failure in the pile cap Varying length of piles in the same pile group may have similar effect The distance from external pile border to pile cap border: = max {(d/10+5cm), 10cm} The arrangement of piles can be by following types: Figure 4-20: Piles arrangement in side view Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 76 Figure 4-21: Piles arrangement in plan view 4.4.5 Verification of load applied to pile In case of centric load applied to the foundation, if the piles quantity was calculated by aforesaid formula, it is not necessary to verify the load applied to each pile In case of non-central load applied to the foundation, we need to verify the load applied to pile when utilization of the building (after construction) The verification conditions include: Pmin + qc > Pmax + qc [P] Where Pmin, Pmax : minimum and maximum load applied to single pile qc pile weight Admissible value of load applied to pile i, coordinates (xi, yi) with origin O (0,0) at pile cap centre, can be determined as below: Pi Where, N n tc tc M y xi x i tc M x yi y i Ntc total admissible vertical load, including applied load, pile cap weight and made soil layer weight Gs, which could be calculated as: G = F.hm with = T/m3 Mxtc Admissible value of moment around axe x Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 77 Mytc Admissible value of moment around axe y Ultimate value of pile reaction, excluded the pile cap weight and made soil layer weight: tt tt M y xi M x tt yi N0 P0i 2 n xi yi yi i My xi x Mx y 4.4.6 Verification of the resistance of bearing stratum N tb/4 cọc chống Nq- Nq- Lớp yếu mỏng ( bỏ qua ) tb/4 Nq- Bq- x Lq- Móng quy - ớc Bq- x Lq- Nq- hc/3 o Nq- 30 Móng quy - ớc H = hm N hc N đất yếu bề dày lớn > 2Lc/3 hmđ Đá (đất) cứng N H = hm N Các lớp đất không yếu hmđ When verifying the resistance of bearing stratum, we consider the group of pile cap + piles + soils between piles as an equivalent raft Different principles to establish the equivalent raft are shown in following schemas: Móng quy - ớc Nq- = N + n gc + Khối l- ợng đất phạm vi H - hmđ Figure 4-22: Equivalent raft Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 78 Conditions for verification of resistance of bearing stratum: p qu N tc N1 N Qc R Fqu p qu max p qu M tc 1,2 R W Where, Ntc, Mtc Admissible load applied to pile cap N1 Weight of pile cap and made soil layer N2 Weight of soil block from pile toe to pile cap base Qc Weight of piles R Admissible strength of the bearing stratum (below the equivalent raft) 4.4.7 Calculation of pile foundation settlement Pile foundation settlement is the settlement of the bearing stratum The calculation done with equivalent raft is the same as shallow foundation 4.4.8 Pile cap height The pile cap height is designed to avoid punching phenomena: - Punching by the column - Punching by the piles a Punching by the column When punching phenomenon by the column, the pile cap is destructed by tensile principal stress on the inclined planes (punching prism) which liaise the column section border to piles row border The working of pile cap in this case is verified without stirrup bars The condition of verification is following: P (bc c1 ) (a c c2 )h0 Rk Where, P Total reaction of all piles positioned between punching prism border and pile cap border ac and bc Length and width of the column section h0 Pile cap working height Rk Concrete tensile strength c1 and c2 Distance between column border and punching prism border and Coefficients which are calculated by following formula: h i 1,5 ci Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 79 N0 h0 c1 c2 Figure 4-23: damage pile cap by column Also, we can only verify the high-risk side of the punching prism, correspondingly to the most important pile reaction The verification consists of following conditions: In case that b > bc + 2h0 : P kRk(bc + h0) h0 In case that b bc + 2h0 : b b P kRk( c ) h0 Where, P - Total reaction of all piles positioned between high-risk side and pile cap border Rk Concrete tensile strength c Width of the high-risk side k = coefficient, k = f ( c/h0 k 1.0 0.75 0.9 0.79 c ) see below table; h0 0.8 0.84 0.7 0.90 0.6 0.97 0.5 1.05 0.4 1.14 0.3 1.25 0.2 1.38 b Punching by the piles When verification with this schema, the verification condition is: Pct .Rk.h0 b Where, - coefficient, determined by following formula: h = 0,7 C If C/h0 0,2 then we use C/h0 = 0,2 ; If C/h0 > then we use C/h0 = for calculation Pct Total reaction of all piles positioned outside of the damage section Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 80 Figure 4-24: damage of pile cap by pile reaction c Calculation of rebar For the calculation of pile cap rebar, we consider the pile cap as a beam restraint at the column border The maximal flexural moments are therefore at the restraint sections I I and II II, for the calculation of longitudinal rebar and transversal rebar respectively Flexural moment at restraint sections: MI-I = (P2 + P4).r1 MII-II = (P1 + P3).r2 Requested area of reinforcement: l,b a F M lng,b 0,9R a h Reinforcement ratio: = Fa / Fb, where Fb concrete area Adequate reinforcement ratio = 0,15% - 0,4% for pile cap The rebar spacing is in general 100 200m Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 81 Figure 4-25: Rebar area calculation schemas 4.4.9 Verification of pile when transportation and positioning Pile transportation During the transportation from pile store location to construction site, the pile is working as a simple beam with two supports (at hooks position) The load applied to the beam is only pile proper weight In order to optimize the working of pile, the positions of the hook are selected to ensure that maximal positive flexural moment is equal to maximal negative value Therefore, the distance from hook position to pile top/ toe is: a = 0,207.l Flexural moment: M = 0,043.q.l2 Where l Length of pile portion q Load uniformly distributed, due to pile proper weight The overload factor n = 1,5 Figure 4-26: Pile transportation verification Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 82 Pile positioning When the pile portion length is 8m, a 3rd hook shall be used for the positioning when pile installation With same principal of optimization, the distance b from this hook to pile top is: b = 0,294.l and M = 0,086.q.l2 Figure 4-27: Pile positioning verification The maximal flexural moment will be used for verification of longitudinal rebar in the pile 4.4.10 Selection of hammer for driven piles The selection of hammer is very important to ensure the driving process but not to destruct the pile head In case of a light hammer, we need a drop free height higher, drop quantity more numerous, which can destruct the pile head concrete In case of a heavy hammer, it is complicate for displacement and the construction cost is higher The selection of hammer based on the energy capacity: E 25.ptt Where : E Hammer energy capacity [N.m] ptt ultimate pile load capacity [kN] Empirical formula for hammer selection: K Where, K Q q Qq E Hammer adequacy coefficient For double acting steam or diesel hammer: K Simple acting steam: K3 Drop hammer: K2 Hammer weight Weight of pile + cap piece + pile cushion + driver pile (if any), Foundation Engineering PILE FOUNDATIONS National University of Civil Engineering 83 REFERENCES Reference Books Pham Quang Hung & Phan Huy Dong Soil Mechanics, Lecture notes for civil engineering course in English, 2012 V Cụng Ng , Tớnh toỏn v Thi t k Múng nụng; Nh xu t b n Khoa h c v K thu t, 1982; Phan H ng Quõn, N n v Múng, Nh xu t b n Giỏo d c, 2006; Ngụ Th Phong v nnk, K t c u Bờ tụng C t thộp, Ph n K t c u Nh c a, Nh xu t b n Khoa h c v K thu t, 2006; Braja M Das, Principle of Geotechnical Enginering, 7th edition, Cengage Learning, 2010; Braja M Das, Principle of Foundation Engineering, SI, 7th edition, Cengage Learning, 2011; Joseph E Bowles, Foundation Analysis and Design, 5th edition, The McGraw-Hill, 2001; Robert W Day, Foundation engineering handbook: Design and Construction with the 2006 International Building Code, The McGraw-Hill, 2006; Reference Articles Aboshi, H., Ichimoto, E., and Harada, K (1979) The Compozera Method to Improve Characteristics of Soft Clay by Inclusion of Large Diameter Sand Column, Proceedings, International Conference on Soil Reinforcement, Reinforced Earth and Other Techniques,Vol 1, Paris, pp 211216 10 Bachus, R C., and Barksdale, R D (1989) Design Methodology for Foundations on Stone Columns, Proceedings, Foundation Engineering: Current Principles and Practices American Society of Civil Engineers, Vol 1, pp 244257 11 Basore, C E., and Boitano, J D (1969) Sand Densification by Piles and Vibroflotation, Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol 95, No SM6, pp 13031323 12 Burke, G K (2004) Jet Grouting Systems: Advantages and Disadvantages, Proceedings, GeoSupport 2004: Drilled Shafts, Micropiling, Deep Mixing, Remedial Methods, and Special Foundation Systems, American Society of Civil Engineers, pp 875886 13 Hughes, J M O., and Withers, N J (1974) Reinforcing of Soft Cohesive Soil with Stone Columns, Ground Engineering, Vol 7, pp 4249 14 Hughes, J M O., Withers, N J., and Greenwood, D A (1975) A Field Trial of Reinforcing Effects of Stone Columns in Soil, Geotechnique, Vol 25, No 1, pp 3134 Foundation Engineering REFERENCES National University of Civil Engineering 84 15 Ichimoto, A (1981) Construction and Design of Sand Compaction Piles, Soil Improvement, General Civil Engineering Laboratory (in Japanese), Vol pp 3745 16 Leonards, G A., Cutter, W A., and Holtz, R D (1980) Dynamic Compaction of GranularSoils, Journal of Geotechnical Engineering Division, ASCE, Vol 96, No GT1, pp 73110 17 Mitchell, J K (1970) In-Place Treatment of Foundation Soils, Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol 96, No SM1, pp 73110 18 Mitchell, J K., and Huber, T R (1985) Performance of a Stone Column Foundation, Journal of Geotechnical Engineering, American Society of Civil Engineers, Vol 111, No GT2, pp 205223 19 Ohta, S., and Shibazaki, M (1982) A Unique Underpinning of Soil Specification Utilizing Super-High Pressure Liquid Jet, Proceedings, Conference on Grouting in Geotechnical Engineering, New Orleans, Louisiana 20 Murayama, S (1962) An Analysis of Vibro-Compozer Method on Cohesive Soils, Construction in Mechanization (in Japanese), No 150, pp 1015 21 Welsh, J P., and Burke, G K (1991) Jet GroutingUses for Soil Improvement, Proceedings, Geotechnical Engineering Congress, American Society of Civil Engineers, Vol 1, pp 334345 22 Welsh, J P., Rubright, R M., and Coomber, D B (1986) Jet Grouting for support of Structures,presented at the Spring Convention of the American Society of Civil Engineers, Seattle, Washington Foundation Engineering REFERENCES