Adityaraj Rathore

REPORT ON PILE CAPACITY GEOTECHNICAL ENGINEERING DATE 13/4/2020 1|P ag e Table of Contents CHAPTER 1: DEEP FOUNDATION AND PILES FOUNDATIONS ............................. 5 1.1: MATERIAL SELECTION CRITERIA.............................................................................................................. 5 1.2: ACCORDING TO THE DESIGN LOADS ....................................................................................................... 5 1.3: TYPES OF PILES – ACCORDING TO THE FUNCTION OF THE PILES ............................................................... 6 CHAPTER 2: PILE CAPACITY (BEARING CAPACITY) ............................................. 8 2.1: STATIC PILE LOAD METHOD .................................................................................................................... 8 2.2: BEARING CAPACITY OF A SINGLE PILE ..................................................................................................... 8 2.3: PILE CAPACITY IN SAND ........................................................................................................................ 10 2.3.:1 HORIZONTAL SOIL PRESSURE ........................................................................................................ 10 2.3.:2 CRITICAL DEPTH............................................................................................................................ 10 2.4: PILE CAPACITY IN CLAY ......................................................................................................................... 13 CHAPTER 3: LOAD TRANSFER IN PILES ................................................................. 15 3.1: LOAD TRANSFER IN PILES (PURE END BEARING) .................................................................................... 15 3.2: LOAD TRANSFER IN PILES (PURE FRICTION) ........................................................................................... 15 CHAPTER 4: LOAD TEST ON PILES .............. 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BOOKMARK NOT DEFINED. 4.1: WORKING PILES ................................................................................................................................... 16 4.2: TEST PILES............................................................................................................................................ 16 4.3: PROCEDURE (ACCORDING TO THE IS-) PART IV) ..................................................................... 17 4.4: DYNAMIC PILE FORMULA ..................................................................................................................... 17 4.4.:1 ENGINEERING NEWS FORMULA .................................................................................................... 17 4.4.:2 MODIFIED HILEY FORMULA .......................................................................................................... 17 4.4.:3 USEFULLNESS OF DYNAMIC FORMUALE IN PILE CAPACTY .............................................................. 17 CHAPTER 5: PILES IN GROUP .................................................................................... 18 5.1: INTRODUCTION ................................................................................................................................... 18 5.2: EFECIENCY OF A PILE GROUP ................................................................................................................ 18 5.3: PILES IN CLAY ....................................................................................................................................... 19 5.3.:1 PILES IN BLOCK FALIURE (Qg)......................................................................................................... 19 5.3.:2 PILES IN INDIVIDUAL FALIURE ....................................................................................................... 19 5.4: PILE IN SANDS ...................................................................................................................................... 20 5.4.:1 PILE IN BLOCK FALIURE ................................................................................................................. 20 5.4.:2 PILES IN INDIVIDUAL FALIURE ....................................................................................................... 20 CHAPTER 6: APPLICATION OF GROUP PILE.......................................................... 21 6.1: PROBLEM A PILE GROUP CONSISTS OF NINE FRICTION PILES IN CLAY SOILS. THE DIAMETER OF EACH PILE IS 0.4 M AND THE EMBEDDED LENGTH IS 9 M. CENTRE TO CENTRE PILE SPACING IS 1.2 M. SOIL CONDITIONS ARE SHOWN. DETERMINE (I) THE BLOCK CAPACITY OF PILE GROUP USING A FACTOR OF SAFETY OF 3, (II) ALLOWABLE GROUP CAPACITY BASED ON INDIVIDUAL PILE FAILURE (USE A FACTOR OF SAFETY OF 2, ALONG WITH THE CONVERSE-LABARRE EQUATION FOR PILE GROUP EFFICIENCY), AND (III) DESIGN CAPACITY OF THE PILE GROUP (FROM SWAYAM GIVE REFERNCE)......................................................................... 21 6.2: APPLICATION OF BEARING CAPACITY OF PILE IN CLAY ........................................................................... 22 2|P ag e 6.2.:1 PROBLEM : A 400-mm diameter concrete pile is to be driven into a clay soil. Properties of the soil are: Unconfined compressive strength, qu = 120 kilo-Newton/m2, γ = 19.8 kilo-Newton/m3. The pile’s design capacity is 350 kilo-Newton. Determine the pile’s required length if the factor of safety is 2. ........ 22 6.2.:2 PROBLEM 2 A 300-mm diameter and 15 m long pile is driven in a normally consolidated clay deposit of great depth. Estimate the safe load assuming c = 100 kilo-Newton/m2, adhesion factor α = 0.8 and a factor of safety of 2.0. ............................................................................................................................ 23 BIBLIOGRAPHY ...................................................................................................... 24 3|P ag e LIST OF TABLES TABLE 1.1 LOAD CAPACITY OF THE DIFFERENT MATERIAL PILES (IIT KHARAGPUR, 2020) .................................................................................................. 5 TABLE 1.2 LENGH OF THE PILE ACCORDING TO THE MATERIAL TYPE (RAO, N.D.) ............................................................................................................................... 7 TABLE 2.1 VALUES OF K & DELTA (RAO, 2014).......................................................... 11 4|P ag e TABLE OF FIGURES FIGURE 1.2 TENSION OR UPLIFT PILE .......................................................................... 6 FIGURE 1.1 END BEARING,FRICTION,COMPACTION,COMBINED PILES ............. 6 FIGURE 1.3 BATTER PILE ................................................................................................. 6 FIGURE 1.4 ANCHOR PILES .............................................................................................. 6 FIGURE 1.5 SHEET PILE .................................................................................................... 7 FIGURE 1.6 LATERAL PILE .............................................................................................. 7 FIGURE 2.1 COMBINED PILE WITH QULT,QS AND QT ................................................. 8 FIGURE 2.2 BEARING CAPACITY VARIATION ALONG THE DEPTH ..................... 10 FIGURE 2.3 VALUES OF NQ FOR PILE FORMULA (GOPAL RANJAN, 2014) ........... 12 FIGURE 2.4 RELATIVE DENSITY OBTAINED FROM N VALUES (RAO, N.D.) ......... 12 FIGURE 2.6 BEARING CAPACITY FACTOR, NQ FOR DRIVEN PILES (CODES, N.D.) .................................................................................................................................... 12 FIGURE 2.5 ANGLE OF INTERNAL FRICTION (RAO, 2014; ALEKSANDER, 1976). 13 FIGURE 2.7 ADHESION FACTOR FOR PILES DRIVEN IN CLAY (CODUTO, 1994) 13 FIGURE 3.1 LOAD TRANSFER IN COMBINED PILES (NPTEL, IIT KHARAGPUR, 2020) ........................................................................................................................... 15 FIGURE 3.2 LOAD TRANSFER IN PURE BENDING PILE (NPTEL, IIT KHARAGPUR, 2020) ........................................................................................................................... 15 FIGURE 3.3 LOAD TRANSFER IN COMBINED PILES (NPTEL, IIT KHARAGPUR, 2020) ........................................................................................................................... 15 FIGURE 4.1 PLATE LOAD TEST (ANON., N.D.)................................................................ 16 FIGURE 5.1 ARRANGEMENT OF PILES (AEFS, 2019) ................................................. 18 FIGURE 5.2 PILE GROUP WITH DENOTIONS (B, N.D.) ................................................ 19 FIGURE 6.1 PILES ARRANGEMENT OF THE PROLEM 6.1 (NPTEL, IIT KHARAGPUR, 2020) ........................................................................................................................... 21 5|P ag e Chapter 1: DEEP FOUNDATION AND PILES FOUNDATIONS The foundations which are considered for the transfer of loads from the weaker strata of soil to the stronger (rock) strata of the soil are termed as Deep foundations. The piles are the type of deep foundations. Pile foundations Piles are slender like column or long cylinders, made from the materials like concrete, steel, timber etc. which are used to support the structure and transfer the load at the desired depth either by end bearing or skin friction Their diameter is generally less than 750 mm . Pile foundations are more expensive as compared to the shallow foundations. These types of foundations are used when we want the foundation to yield higher bearing capacity and settlement due to some of the situations mentioned below. They are generally used to for the following situations: • High ground-water table • Non-uniform heavy loads from the structure are imposed. • When there is a possibility of scouring. • Possibility of the soil excavation due to the poor soil condition and high depth. • When it is impossible to keep the foundation, trenches dry by pumping or by different measures. The piles can be classified according to material, according to the function, according to the installation etc. Here we are discussing the material selection criteria of the piles. 1.1: MATERIAL SELECTION CRITERIA • Timber piles • Concrete pile • Cast in place concrete • Steel piles • Steel H section • Composite piles Here is the table indicating type of loads which determine the material of the piles to be used for the project. 1.2: ACCORDING TO THE DESIGN LOADS Table 1.1 LOAD CAPACITY OF THE DIFFERENT MATERIAL PILES (IIT KHARAGPUR, 2020) TYPE OF PILE Wood Composite Cast in place concrete Precast Reinforced Concrete Steel pipe Concrete filled Steel H - Section LOADS IN TONS (1 TON = 8.896 KILO-NEWTON- 6|P ag e Materials used for construction of pile foundations, also depend on the factor of the length. The material of the piles depends upon different length of the piles. The depicting table is shown for that purpose. 1.3: TYPES OF PILES – ACCORDING TO THE FUNCTION OF THE PILES This classification gives us the type of piles according to the function of the piles. There are many piles which can be done under this classification, but we will under look only end bearing piles and friction piles. In almost all the cases (practically mentioning) the combination of the end bearing, and the friction pile are used. • End bearing piles • Friction Piles • Tension or uplift • Compaction • Anchor • Batter • Laterally loaded • Sheet All the piles further used will be driven piles and hence we are further in this article going to look only at the driven piles. Figure 1.1 TENSION OR UPLIFT PILE Figure 1.2 END BEARING,FRICTION,COMPACTION,COMBINED PILES Figure 1.4 BATTER PILE Figure 1.3 ANCHOR PILES 7|P ag e Figure 1.5 SHEET PILES Figure 1.6 LATERAL PILE Table 1.2 LENGH OF THE PILE ACCORDING TO THE MATERIAL TYPE (RAO, n.d.) PILE TYPE Steel H and pipe Steel shell and cast in place Precast concrete AVAILABLE MAXIMUM LENGTH Very long piles: short sections are driven, and additional sections are field welded to obtain a desire length. Typically, between 30-40 meters Solid small cross section up to 60 ft, large diameter cylinder pile can be up to 61 meters long 16-23 meters depending on the equipment Cast in place concrete Under reamed piles Up to 30 meters 8|P ag e Chapter 2: PILE CAPACITY (BEARING CAPACITY) The capacity of the pile to resist the shear failure is termed as bearing capacity of pile. Mathematically, the total allowable load divided by the factor of safety is evaluated as the bearing capacity. Here the two types of piles which are discussed in this section are: End bearing piles & Friction piles. The bearing capacity of a single pile can be determined by some predetermined methods, some of which are mentioned here. The methods consist of Static load method which relates shear strength as determined from the laboratory or in situ sites. Similarly, the other tests. The bearing capacity of the pile foundation are determined by 4 methods, which are • Static load method • Dynamic load method • Correlation with penetration • Load test Firstly, in this bearing capacity of the pile is determined by the static load method. In single pile bearing capacity, we must say that instead of using the above mentioned two piles; the combination of both the piles should be used for the bearing capacity calculation. The Q(total) evaluated from them must be considered final for the bearing capacity. In the group pile, firstly we must define the terms like group efficiency by the Converse-Labarre equation, the different pile spacing for different conditions would be mentioned. Let’s start with the bearing capacity theories of single pile and pile groups 2.1: STATIC PILE LOAD METHOD The bearing capacity of piles is determined in 2 ways: 1. Bearing capacity of a single pile 2. Bearing capacity of piles in group 2.2: BEARING CAPACITY - SINGLE PILE The bearing capacity of the single pile consists of: Figure 2.1 COMBINED PILE WITH Qult,Qs AND Qt • Friction Pile • End Bearing Pile • Both friction and end bearing pile The piles which are used consists of the combination of both the friction and the end bearing piles. So firstly, we will look at the formula of the combined piles. Here as shown in Figure 2.1 COMBINED PILE WITH Qult,Qs AND Qt, Pu, Psu, Psu can be considered as Qult, Qs, Qt. So, from the figure, we can derive that Qult = Qs + Qt Qs=fs As 9|P ag e = skin friction (surface area of pile) Qs is the total load exerted by the surrounding soil on the pile in the opposite direction of the load. (here the load is in the downward direction) It is the frictional force exerted by the soil on the pile fs= f (soil & pile) Qt = ft At = tip resistance (tip area of pile) Qt is the pile capacity exerted by the soil below the tip of the pile. ft = f (soil) Qult = Qs + Qt Qult is the total capacity of the pile towards the loading. The summation of the Qs and Qt is the Qult For the decision of the allowable load to be determined, the ultimate load is not to be considered, for that we have to add a safety factor, to be on the safer side. So, to decide the allowable load, the Ultimate load carrying capacity has to be divided by the Factor of Safety(FOS) Qallowable= 𝑸𝒖𝒍𝒕 𝑭𝑶𝑺 Qallowable is the allowable bearing capacity, the pile can resist. It is obtained by dividing the Qult by FOS. In the deep foundation, we take the FOS as 1.5 – 2, while in shallow foundation is 2.5 – 3. The total load transmission on the surrounding soil is done by the friction piles or by End bearing piles. This can be expressed as: Qult = Friction + Qtip Qfriction = f Asurface Qtip = q Atip Thus, the above-mentioned formulas are for the combined piles which are the most used in practical purpose. This the Qult in the case of the compression loading, which is undertaken, there is a very rare case on which the tension force Is exerted. In such a case the only change we will observe will be the w weight of the pile added as shown in the Figure 1.1 TENSION OR UPLIFT PILE. In such a case: Qallowable = 𝑸𝒔 𝑭𝑶𝑺 + w, where, w = weight of the pile Qs = Shaft friction Qultimate = ultimate capacity of the pile Qfriction = pile capacity is borne by soil surrounding the pile, by the means of adhesion or friction Qtip = pile capacity furnished by the soil just below the tip of the pile f = unit skin friction or adhesion between the soil and the sides of the pile Asurface = Vertical surface area of the pile (for a circular pile of diameter D and length L, Asurface = π D L) 10 | P a g e Atip = area at the pile’s tip (for a circular pile of diameter D, (A tip = πD2/4) q = ultimate soil bearing capacity of the soil at the pile’s tip (NPTEL, IIT Kharagpur, 2020) In the case of the end bearing pile (only) the Qtip is more dominant, and in the friction pile (only) the Qfriction is more dominant. Now we will see the pile capacity in sand and clay. 2.3: PILE CAPACITY IN SAND Here first, we will note the equation of Qult , which is the total load capacity of the pile. Thus, as per the equation Qult = Qs + Qt Where, Qs = pile capacity furnished by friction & Qt = pile capacity bared by the tip of the pile. So, procedure wise to calculate the total Qult ,we must find the value of Qs which is Qfriction & Qtip So, the Qfriction can be determined as: Qfriction = f Asurface Here the f is obtained by multiplying the coefficient of friction between sand and pile surface (tan 𝜹) and the horizontal soil pressure acting on the pile. This can be mathematically expressed as: f (horizontal pressure) = vertical pressure 2.3.:1 HORIZONTAL SOIL PRESSURE The horizontal soil pressure is considered here as a subsequent topic. The effect of the horizontal pressure on the pile is the function of vertical pressure of the soil near the pile. The vertical pressure of the soil increases, with the increase in the depth. But that also, up to a certain depth. This “certain depth” is termed as “Critical depth”. It is denoted as Dc. below this critical depth the vertical pressure remains constant (more or less). 2.3.:2 CRITICAL DEPTH The critical depth Dc is taken as 10D for loose sandy soil and 20D for dense soil. If it is not mentioned then, accordingly we must assume it based on the application. Effective vertical pressure = σv’ σv ′ = γ Z Depth, z Dc 1 σv ′, max σv ′ = Constant 2 Figure 2.2 BEARING CAPACITY VARIATION ALONG THE DEPTH Now, here as we can say that the pile is divided in two different figures, hence the Q friction calculation must be done by considering two different sections. 11 | P a g e Thus, the integration must be used for the getting the value of f. For the portion 1 as shown in the figure, and as stated earlier, taking the integral from 0 to D c, 𝐷𝑐 f = ∫0 γ z dz k tanδ Similarly, for the portion 2 as shown in the figure 𝐷𝑐 f = ∫0 γ Dc ( L − Dc) k tanδ Thus, the f will be obtained by adding the two portions together, thus adding them we get, 𝐷𝑐 𝐷𝑐 f = [ ∫0 γ z dz k tanδ + ∫0 γ Dc ( L − Dc) k tanδ ] ={ 𝛄𝑫𝟐𝒄 𝟐 + (L – Dc) ( γ Dc) } Thus , the Qfriction = f As As = π D Qfriction =[ 𝛄𝑫𝟐𝒄 𝟐 + (L – Dc)( γ Dc) ] k tan δ (πD) Where, L=length of the pile D= diameter of the pile K = coefficient of active earth pressure tan δ = friction between sand and pile surface The different values of tan δ and k are there for different materials, because all material behaves differently with the sand and hence as a result, the value for different materials are shown below as: (NPTEL, IIT Kharagpur, 2020) Table 2.1 VALUES OF K & DELTA (RAO, 2014) PILE MATERAIL STEEL CONCRETE TIMBER δ 20 .75 ∅ .67 ∅ VALUES OF k LOOSE SAND 0.5 1.0 1.5 DENSE SAND 1.0 2.0 4.0 Now, the calculation of the Qtip , Qtip = q Atip Here, q is the bearing capacity of the pile tip, Atip is the area of the pile at the tip, which is generally circular, so the area can be accumulated as Atip = 𝝅 𝑫𝟐 𝟒 The value of is as governed as in the shallow foundations, here the only change will be the values of the Nq , Nd , N𝛾.Their value are higher than those in shallow foundations, because of the material and the depth of the soil. We had determined the values of q according to the shape factor in shallow foundation. Here the shape of the pile may be square or may be rectangle, hence the q must be corrected and applied according to the shape factor. q = 𝜸 Df Nq + 0.3 𝜸 𝑫 Nγ for circular piles q = 𝜸 Df Nq + 0.4 𝜸 B Nγ for square piles 12 | P a g e Here D is the diameter of the pile and the B is the width of the pile, Df is the embedded length of the pile Nq and Nγ are the bearing capacity factor. Note – This is a sandy soil, so the cohesion is not considered, hence c=0. The magnitude of the effective vertical pressure of the soil adjacent to the pile is constant below the critical depth. So, for the design criteria we must consider (σv ′)tip Nq, where (σv ′ )tip is the effective vertical pressure adjacent to the pile at the pile tip. In the case of the driven pile the value of the D and B are quite small as a result these terms must be neglected in the equation. So, for the design purpose 𝝅 𝑫𝟐 Q= (σv ′) tip Nq ( 𝟒 ). As we have stated earlier the value of Nq is used here is not as same as that of the shallow foundation, but higher. So, the value of Nq is determined by the means of the graph as stated below. Figure 2.3 VALUES OF Nq FOR PILE FORMULA (GOPAL RANJAN, 2014) Figure 2.4 RELATIVE DENSITY OBTAINED FROM N VALUES (RAO, n.d.) Figure 2.5 BEARING CAPACITY FACTORS, Nq FOR DRIVEN PILES (CODES, n.d.) 13 | P a g e Hence the total capacity that is the Qult can be defined as Qult = [ Nq ( 𝛄𝑫𝟐𝒄 𝝅 𝑫𝟐 𝟒 𝟐 + (L – Dc)( γ Dc) ] k tan δ (πD) + (σv ′) tip ) Here are the overall steps or the procedure for the calculation of the bearing capacity of the piles in sand STEP 1 Write the basic equation of the Qult STEP 2 Determine the Qs STEP 3 Determine the Qt STEP 4 Add it and get the value of Qult Figure 2.6 ANGLE OF INTERNAL FRICTION (RAO, 2014; ALEKSANDER, 1976) 2.4: PILE CAPACITY IN CLAY The bearing capacity of the pile in sand is seen earlier in this article. Now we will look at the pile bearing capacity in the clay. As observed in the sand, there is not such a complication in the calculation of the bearing capacity. Here the soil being a clay soil the f (unit friction) is dependent on the cohesion (c) and adhesion factor (𝜶).Hence it must be written as: f= 𝜶 𝒄 This is the value of f which is known as the unit friction The value of 𝜶 depends on the type of clay, for stiff clays 𝜶 < 1 and for soft clays 𝜶 = 1. c is cohesion. This will determine the type of clay which is either soft or stiff clays. Now we will calculate the Qult bearing capacity of the pile. As per the procedure Qult = Qs + Qtip Qs = f As (Here As =Surface area of the pile) = 𝛼 c As = 𝜋DL 𝛼 c Figure 2.7 ADHESION FACTOR FOR PILES DRIVEN IN CLAY (CODUTO, 1994) Qtip = q Atip q = cNc + 𝜸Df ≅ cNc Only the first term of cNc is used because the term as stated earlier, is in clay. (for ∅ = 0, Nq = 1, N𝛾 = 0 ) 14 | P a g e Nc = 9, here taken generally not given in the numerical, for shallow foundation Nc = 5.1 Hence to reduce the effort by every time applying the same formula, we will take N c=9 every time, hence the formula becomes 𝝅 𝑫𝟐 Qult = (𝝅DL 𝜶 c) + 9c ( 𝟒 ) The above equation gives the bearing capacity of the circular piles in clay. 15 | P a g e Chapter 3: LOAD TRANSFER IN PILES The load transfer mechanism along the depth can be seen deeply and how much role the Qs and Qt plays in a Qult. Thus, the Figure 3.1 LOAD TRANSFER IN COMBINED PILES shows the figure of the load transfer mechanism in the combined piles (end bearing and friction). From the Figure 3.1 LOAD TRANSFER IN COMBINED PILES we can depict that the more displacement is rquired to mobilize the tip resistance. Figure 3.1 LOAD TRANSFER IN COMBINED PILES (NPTEL, IIT Kharagpur, 2020) 3.1: LOAD TRANSFER IN PILES (PURE END BEARING) Similarly, the load transfer graph can be evaluated. The figure explains. The Q (bearing capacity) is constant along the depth, and the skin friction here as seen is totally the y axis, which is the depth of the soil, hence the value is totally dependent on the depth And in the other graph, as the Q (load) increase on the pile, the displacement of the pile also increases and as a result after some amount of displacement the graph remains constant, which means that after some load (which is greater than design load), the pile fails, and the displacement continues. Figure 3.2 LOAD TRANSFER IN PURE BENDING PILE (NPTEL, IIT Kharagpur, 2020) 3.2: LOAD TRANSFER IN PILES (PURE FRICTION) The load transfer mechanism in the pure bending pile is as shown in the Figure 3.3 LOAD TRANSFER IN COMBINED PILES. The graph says as a result, the Q (bearing capacity) does not remain constant along the depth, but it changes along, similarly the skin friction as in the soft clay, it increases from zero to maximum which means it Figure 3.3 LOAD TRANSFER IN COMBINED PILES provides resistance linearly. (NPTEL, IIT Kharagpur, 2020) Here Q(load) on the pile keeps on increasing the tip displacement also increases, but from the graph the value of load it can resist is lower than that of the Pure bending pile depicted from the graph. Thus, the displacement of the pile remains constant after the load, which means that after the pile failure the displacement remains constant. 16 | P a g e Chapter 4: PILES LOAD TEST The pile load tests are the direct method to determine the design load on piles. It is the most reliable method and is the cast in situ method. This pile load test while using on the cohesive soil should be used very cautiously because of the disturbance of the soil and as a result, the development of pore pressure and inadequate time allowed for consolidation settlement. There are three types of tests, vertical load test, lateral load test and tension test. There are basically two types of tests which are carried out, initial test and the routine test. Initial test is to be carried out on the test piles and as a result to get the working load for the settlement adopted by the pile, and how much is the load that can be applied. Routine test is performed on the working piles for the assessment of the displacement of Figure 4.1 PLATE LOAD TEST (Anon., n.d.) working piles corresponding to the working load. 4.1: WORKING PILES These piles are either driven or cast in situ along with the other piles to carry load from superstructure. The load to be applied on the piles should be one half times the safe load. The allowable settlement should be 12 mm of single piles or 40 mm of group piles, whichever comes earlier. 4.2: TEST PILES This pile is used only for testing and is not used toc carry the load of the superstructure. The minimum test load on the piles should not be less than the twice of the safe load or the load at which the total settlement attains a value of 10% of diameter of piles in single pile and 40 mm in group pile. There are many advantages of the test piles like if the pile capacity is different or settlement is excessive from that desired, the pile length diameter and the details of installation can be adjusted before the installation of other piles. Precautions to be taken before the testing or the results can be misleading: 1. Time should be provided between the installation and the time of test loading i.e. 3 to 4 days. This is the time normally required for the respective soils to regain the strength lost during the driving of the piles. 2. In the concrete piles a minimum time is also required to develop the material strength. 3. The specific location for the installation and testing of the pile must be representative of the overall site if the test results are to be representative of the rest of the piles. It is common practice that engineers must execute while testing conditions of the site. 4. The pile characteristics, such as length, diameter, installation method, must be like those of the piles to be installed. 17 | P a g e 4.3: PROCEDURE (ACCORDING TO THE IS-) PART IV) 4.4: (CODES, 1979)DYNAMIC PILE FORMULA The dynamic pile formula is useful in estimating the pile capacity. These methods emphasize on estimating the capacity of the pile by the means of elastic or dynamic loading. The hammers blows are required for providing the dynamic loads to the pile. Some of the formula for the engineering news are required for the same which are mentioned below as: 4.4.:1 ENGINEERING NEWS FORMULA The dynamic resistance of the soil, Qu is assumed to be ultimate pile load capacity, thus the equation goes as: Qa = 𝑾𝑯 𝑭(𝑺+𝑪) W= weight of the hammer falling through the height H S = real set per blow C= empirical factor F= Factor of safety For single hammer the formula goes as Qa = 𝑾𝑯 𝟔(𝑺+𝟐.𝟓) 𝑾𝑯 For single acting steam hammers goes as Qa = 𝟔(𝑺+ .𝟐𝟓) Because of the advantage that the pile capacity can be determined while driving the pile in the soil it is widely used worldwide and as a result it is worked along and used along with the load test. 4.4.:2 MODIFIED HILEY FORMULA The modified Higley formula is the further extension of the Engineering news formula & as a result the prominent use of the formula is done because it also indicates the losses that occur in the hammer dropping which gives more accurate result. R= 𝑾𝒉𝛈 𝑪 𝑺+(𝟐 ) Where C can be split into C1, C2 and C3 C1 = 1.77 (R/A) C2 = .657 (R/A) C3 = 3.55 (R/A) 4.4.:3 USEFULLNESS OF DYNAMIC FORMUALE IN PILE CAPACTY This formula is eminent because there is no relation between the static pile load capacity & dynamic pile load capacity. These formulas assume of the two free elastic bodies and the pile is not an elastic body. This formula can be used in a pile which is present in free draining materials like coarse sand, graves and pebbles. But for the piles whose pile caps are above the ground then in such a case, this formula cannot be adopted and hence the static pile load formula can be thought of and uploaded. 18 | P a g e Chapter 5: PILES IN GROUP 5.1: INTRODUCTION The arrangement of the piles in a uniform way forming a rectangle, square shaped with uniform spacing and same length of the piles can be termed as piles in group arrangement. The study of this topic includes many reasons and topics • There is not an individual pile on field, but many instead. • To know the behaviour of all piles in the group when arranged such. • The failure of piles can be expressed and understood for the loading patterns. • In general, the bearing capacity of the pile group is lesser than that of the sum of capacity of individual pile. • The settlement of a pile group is larger than that of individual pile for similar level of loading. • Much more occurrence the than a single pile. • Single pile lacks the overall stability against overturning, a deficiency that is easily overcome by a pile cluster. The different arrangement piles can be taken as Figure 5.1 ARRANGEMENT OF PILES (AEFS, 2019) shown in the figures as shown below. They show how the arrangement is done. So further in this section we will go through the different topics like the group efficiency, arrangement of piles in group as per the requirements. The efficiency of the pile group is less than that of single pile. The piles in a group interact with each other and as a result the interaction of the piles creates the working mechanism and hence as a result, the failure of the pile is determined from it. The interaction of the pile depends on some factors like soil, head fixity condition and the configuration. The load is transferred to the piles by the means of a slab or beam which is termed as pile cap. The pile cap is applied on the piles so that the load which is present on the pile cap can easily and uniformly transfer the load to the piles below it. (NPTEL, IIT Kharagpur, 2020)Now we will take a note on the efficiency of the pile group, the total bearing capacity individually by the single pile and bearing capacity the pile group as a “block”. We will also look at the η as the efficiency. 5.2: EFECIENCY OF A PILE GROUP η= 𝑸𝒈 𝒏𝑸𝒊 where, η = pile group efficiency Here Qg is the gross capacity of the piles & Qi is the individual capacity of the pile and n is the number of the piles in the group. The efficiency of the group is totally different for different kind of piles like, for 19 | P a g e End bearing piles, η = 1 can be assumed Friction pile driven in cohesionless soil , η = 1 may also be assumed Pile group composed of friction pile driven in cohesive soil, η <1 may be assumed There are many methods and formulas to get the value of efficiency, the one I am mentioning here is the Converse-Labarre equation: ηg = 1 - 𝜽 (𝒏−𝟏)𝒎+(𝒎−𝟏)𝒏 𝟗𝟎𝒎𝒏 where, 𝑑 𝜃 = tan−1 𝑠 , degree n= number of piles m= number of rows of piles d = diameter of the pile s = spacing of the piles (IIT KHARAGPUR, 2020), centre to centre For friction piles driven in cohesive soil, Coyle and Suleiman suggested that pile-group efficiency may be assumed vary linearly from a value of 0.7 at a pile spacing of three times the diameter to a value of 1.0 at a pile spacing of eight times the pile diameter. (IIT KHARAGPUR, 2020) The ultimate load capacity is determined as the whatever value of Qug or Qu comes smaller will be adopted for design. 5.3: PILES IN CLAY 5.3.:1 PILES IN BLOCK FALIURE (Qg) The piles in the group are termed as block only in a condition where the pile spacing is less than three times the pile diameter (s ≤ 𝟑𝒅) in clay, group capacity may e considered as a block capacity, and total capacity can be considered by taking it as a pier. (NPTEL, IIT Kharagpur, 2020) (In the figure 5.2 W=Bg, L=Bg) For the pile group considering it as a block, the formula for the pile capacities are as under: Qg = 2D (W+ L) f +1.3 c Nc WL Where, D = depth of pile group W = width L = Length of pile block Figure 5.2 PILE GROUP WITH DENOTIONS (B, n.d.) F = unit adhesion between cohesive soil and pile surface c = cohesion/undrained shear strength pf the soil Nc is the bearing capacity factor (generally taken as 9) 5.3.:2 PILES IN INDIVIDUAL FALIURE The piles in the group can undergo also individual failure if the pile group does not follow the above-mentioned condition ( s ≤ 3𝑑). Then the equation of the driven pile in clay is used as mentioned above which is: 𝝅 𝑫𝟐 Qult = (𝝅DL 𝜶 c) + 9c ( 𝟒 ) 20 | P a g e After performing this application of formula in the above equation, we can get Qult. Then this value of bearing capacity is multiplied by the number of piles and then the value is multiplied by efficiency η and the value obtained is taken as Qg. The value obtained from both is considered and then the value is divided by the FOS. The FOS is here taken between 2.5-3. Whichever yields the smaller value is taken as the Qg and taken as the design load. 5.4: PILE IN SANDS 5.4.:1 PILE IN BLOCK FALIURE The block failure is same as that of the piles group in clay along with the condition. The value of η in here is taken as unity (1).Since there is no compaction of the soil near the pile, so it can never be more than unity. 5.4.:2 PILES IN INDIVIDUAL FALIURE The piles in the group can undergo also individual failure if the pile group does not follow the above-mentioned condition ( s ≥ 3𝑑). Then the equation of the driven pile in sand is used as mentioned above which is: 𝝅 𝑫𝟐 Qult = (𝝅DL 𝜶 c) + 9c ( 𝟒 ) Thus, after applying this formula we can multiply the value of Qult by the group of piles which is the number of piles and then the efficiency of the piles. Thus, the procedure remains same for both of driven piles in sand and clay. Thus, the pile group in clays can be written totally as : Qdeg group = min[η∑𝒏𝒊=𝟏 𝑸𝒂𝒊 𝒐𝒓 𝑸𝒃𝒍𝒐𝒄𝒌] 21 | P a g e Chapter 6: APPLICATION OF GROUP PILE 6.1: PROBLEM A pile group consists of nine friction piles in clay soils. The diameter of each pile is 0.4 m and the embedded length is 9 m. Centre to centre pile spacing is 1.2 m. Soil conditions are shown. Determine (I) the block capacity of pile group using a factor of safety of 3, (ii) allowable group capacity based on individual pile failure (use a factor of safety of 2, along with the Converse-Labarre equation for pile group efficiency), and (iii) design capacity of the pile group (IIT KHARAGPUR, 2020) SOLUTION qu = 100 kilo-Newton/m2, 𝛾 = 18.0 𝑘𝑁/𝑚3, 9 piles, L=9meter & s=1.2 Figure 6.1 PILES ARRANGEMENT OF THE PROLEM 6.1 (NPTEL, IIT Kharagpur, 2020) The arrangement of the piles is the same as shown in the figure and can easily be calculated, the step for the for the following is : Firstly, we will calculate the block capacity of the piles 7 then the pile capacity individually, after that the bearing capacity whichever will yield smaller is termed as the final bearing or safe bearing capacity can be adopted. Here data given is. c = (qu/2)=(100/2)= 50kilo-Newton/m2 W=L= (1.2+1.2) = 2.4 f = (𝛼 𝑐) =(.8 x 50) = 40 Nc = 9 (to be adopted) (i) BLOCK CAPAITY The formula for the block capacity is the same as that mentioned in the article of group of piles, block failure. Qg = 2D (W + L) f +1.3 c Nc WL = ((𝛼 𝑐) x (2 x (2.4+2.4) x .4)) + (1.3 x 50 x 9 x 2.4 x 2.4) = ((40) x (3.84)) + (3369.6) = 7659 Qall(g) = (7659/3) = 2553 kilo-Newton (ii) INDIVIDUAL PILE FALIURE Now the calculation of the pile capacity for the individual pile failure is as seen as below & as a result the formula of the individual pile be: 22 | P a g e 𝜋 𝐷2 Qult = (𝜋DL 𝛼 c) + 9c ( 4 ) 3.14 𝑥 .16 = (3.14 x 9 x 2.4 x 50 x 0.4) + (9 x 50 x ( 4 ) =622 kilo-Newton Qall = (622/2) = 311 kilo-Newton Now to calculate the Qg of all the piles, it can be calculated by multiplying : η x Qall x n So, we must calculate here the value of η by Converse-Labarre and hence, the value is 𝑑 Where 𝜽 = tan−1 𝑠 N = number of piles = 3 M=3 D = 0.4 S = 1.2 η = ηg = 1 - 𝜃 (𝑛−1)𝑚+(𝑚−1)𝑛 90𝑚𝑛 6+6 =-∗9)) 12 = 1 - ) = 1 - .27 = 73% efficiency Thus, evaluating it further, we can get values of Qg, hence the values of the individual piles in group is Qg = .73 x 311 x 9 = 2043.27 kilo-Newton Here as we observed that the value of Qg for individual failure is 2050 and the value of Qg Is obtained as 2553 kilo-Newton. Thus, the value of Qg for the individual failure is adopted because it is a lower value amongst both. So, the value of Qg is 2050 kilo-Newton. 6.2: APPLICATION OF BEARING CAPACITY OF PILE IN CLAY 6.2.:1 PROBLEM : A 400-mm dia concrete pile is driven in clay soil. Properties of the soil are: Unconfined compressive strength, qu = 120 kilo-Newton/m2, γ = 19.8 kilo-Newton/m3. the design capacity of pile is 350 kilo-Newton. Determine the pile’s required length if the factor of safety is 2. (IIT KHARAGPUR, 2020) SOLUTION Data given: D = 0.4 m Qu = 120 kilo-Newton/m2 c = (120/2) = 60 kilo-Newton/m2 γ = 19.8 kilo-Newton/m3 FOS = 2 23 | P a g e Qall = 350 kilo-Newton Now here we are right there to find the value of the L of the pile that Is the length of the pile. The value of the Qult = Qall x 2 = 350 x 2 = 700 kilo-Newton Thus, now the value of the L can be found out from the above data, Here we know that the bearing capacity of the pile in clay is calculated by : 𝝅 𝑫𝟐 Qult = (𝝅DL 𝜶 c) + 9c ( 𝟒 ) Therefore, applying it, we get 700 = (3.14 x .4 x L x 1 x 60) + (9 x 60 x (3.14 𝑥 .16) 4 ) 700 – 67.824 = 75.36L L = 8.38 m Thus, the length of the pile is to eb adopted as 8.38m 6.2.:2 PROBLEM 2 A 300-mm diameter and 15 m long pile driven in a normally consolidated clay deposit. Estimate the safe load assuming c = 100 kilo-Newton/m2, adhesion factor α = 0.8 and a factor of safety of 2.0. (IIT KHARAGPUR, 2020) SOLUTION DATA GIVEN D= 0.3 m L = 15 m α = 0.8 FOS = 2.0 c = 100 kilo-Newton/m2 Now the previously mentioned formula of the pile capacity in clay is : 𝝅 𝑫𝟐 Qult = (𝝅DL 𝜶 c) + 9c ( 𝟒 ) Thus, applying the formula Qult = (3.14 x .3 x 15 x .8 x 100) + (9 x100 x( 3.14 𝑥 .9 4 ) Qult = (1130.4) + (6358.5) Qult = 7488.9 kilo-Newton Thus, the total ultimate bearing capacity is 7500 kilo-Newton. Now we will have to calculate the Qallowable for the pile. Qallowable = Qult/2 = (7500/2) = 3750 kilo-Newton Hence the total allowable load is equal to 3750 kilo-Newton. REFERENCES Bibliography AEFS, 2019. AEFS FOUNDATION CIVIL ENGINEER. [Online] Available at: https://www.facebook.com/afesfoundation/posts/- ALEKSANDER, 1976. ULTIMATE LOADS AND SETTLEMENTS OF DEEPFOUNDATIONS IN SAND. Anon., n.d. GCP LAB MANUAL, s.l.: s.n. BEREZANTSEV, n.d. s.l.:s.n. B, T., n.d. Pile Group: Efficiency and Settlement | Pile Foundations | Soil Engineering. p. 2. CODES, I. S., 1979. 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