Geotechnical Engineering - Math Problem Example

Running Head: GEOTECHNICAL ENGINEERING Student’s Name: Course Code: Lecture’s Name: Date of presentation: Question 1 a. Methods of Slope Stabilization i) Alteration of soil geometry. b. Enhancement of soil strength.Work out Slice No. W (kN/m) αn Sin αn Cos αn ΔLn(m) Wn Sin αn (kN/m) Wn Cos αn (kN/m) 1 621 65 0.906 0.423 3.1 562.6 262.7 2 765.9 48 0.743 0.669 3.0 569.1 512.4 3 786.6 35 0.574 0.819 3.0 451.5 644.2 4 738.3 24 0.407 0.914 3.0 300.5 674.8 5 641.7 14 0.242 0.970 3.0 155.3 622.4 6 489.9 5 0.087 0.996 3.0 42.6 487.9 7 324.3 5 0.087 0.996 3.0 28.2 323.0 8 131.1 14 0.242 0.970 3.0 31.7 127.2 Σ 24.1 2141.5 3654.6 FS = Σ{ΔLn}{c} + Σ { Wn Cos αn } tan Ø Σ { Wn Sin αn } Fs = 24.1(19) + 3654.6 tan 30 2141.5 Fs = 1.2 Question 2 a. Effective Rankine pressure K0 = 1- sin 30 = 0.5 Effective Rankine pressure at Z = 0 z = 0, σ’v = 0, σ’h = 20kN/m Effective Rankine pressure at Z = 3 m σ'0 = 3(19) = 57 kN/m2 σ'h = K0 σ'0 = 0.5 x 57 = 28.5 kN/m2 Effective Rankine pressure at Z = 6 m σ'0 = 6(21) = 126 kN/m2 σ'h = K0 σ'0 = 0.5 x 126 = 63 kN/m2 b. Active pressure distribution diagram 0 1 3m 28.5kN/m2 2 3 6m 63.5kN/m c. Rankine active force per unit length Lateral force P0 = Area 1 + Area 2 + Area 3 = ½ (3 x 28.5) + 3(63.5 – 28.5) + {½ x3(63.5 – 28.5) = 85.5 + 105 + 52.5 = 243 kN/m Z = Σ moment of pressure diagram about the base P0 = 85.5 (3+3/3) + 105(3/2) + 52.5 (3/3) 243 = 2.27 m Question 3 a) Area of footing, A= 3x3=9m2 The average effective stress at the middle of 216.045KN/m2 For consolidated clays, compression Index, Cc= 0.007(LL-10), Where LL= Liquid Limit, in % Therefore LL=0.007(40-10)=0.21 Cs= 0.3Cu= 0.30.21=0.063 Therefore; =6.2m b) Time for consolidation, , where =0.197, and Drainage distance =11m Therefore, =79.45sec Question 4 a) Types of shallow foundations Spread Footing Foundations This type of foundation is common in residential buildings, and has a wider bottom part than the wall bearing the structural loads. This wider section helps in spreading weight of the building over a wider surface area. This type of foundation is common in many commercial buildings that incorporate basement but are not sufficient for high rise buildings. Mat- Slab Foundations This type of shallow foundation is meant to distribute heavy increased wall and column loads over the entire building floor area. This helps to decrease the contact pressure in comparison with other spread footings. They are constructed at the basement bottom or near the surface and can be several meters thick on high rise buildings. Slab-on-grade Foundation This refers to a practice where a concrete slab meant to the foundation of a building is created from a mould prepared into the ground. Concrete is then poured into the mould, allowing no space between the structure and ground. These types of foundations are applicable best in areas with extensive clay soil cover. b) Footing area= 3mx3m Sand unit weight, =21KN/m3 Angle of Friction, Ø=35˚ Depth of base footing= 1.5m Calculate: Ultimate Allowable Capacity=,  From the Bearing capacity vs. friction angle graph above, for Ø=35˚ the bearing capacities are as follows; =45, =35.4, =50 + (Df) ()+0.5( (Bf )( NY) =3(45) +10.5(1.5)(35.4)+0.5(21)(3)(50) =2267.55KN/m3 Allowable Capacity, =, ==755KN/m3 The allowable column load, Q= (755) B2 =755x (3x3) = 6802.65KN/m3 c) Strip footing width= 2m Depth= 1m Saturated unit weight= 21 KN/m3 Cu=15kN/m =35˚ = Strip Footing, =1.3C Where, =45, =35.4, =50, and C= 15.2kN/m2 Therefore, = (1.3x21x45) +(9.81x2x35.4)+(0.5x9.81x1x50) =2168.30kN/m2 Where FS is factor of safety Therefore, FS===3.6 Question 5 a. Types of piles and their advantages i) Displacement piles: These types of piles can be inspected prior to being driven to the ground, thus the quality is likely to be enhanced. Distortion during piling is low or zero which is the main reason as to why they are cost effective in comparison to other classes of piles. Their adaptability to such forces as compression and lateral makes them a preferred choice. The fact that they can be manufactured from all sorts of materials ranging from timber to steel makes them more advantageous. ii) Bored Piles: They are basically piles that require excavation beforehand. The main advantage of such piles is that the dimensions can easily be varied at the site. Vibrations can be minimized in bored piles as the soil samples picked from the excavations can be tested to check the strength. The working heights are flexible thus they are applicable in a wide range of structures. iii) Micro Piles: The micro piles do not have any vibrations and depending on the type, they are flexible with any type of inclination. They can be extended through sleeve connections to meet the applications that they are meant for. With the application of post grouting, their load bearing capacity can be considerately increased. b. Factors considered when choosing pile types i) The geotechnical and structural coordination of a structure. ii) The function of the structure. iii) The soil structure of a project location. iv) The factor of safety to be achieved. v) Construction and future servicing considerations. vi) Nature of load to be encountered by the pile. c. Workout Wh = 35kN/M2 WP = 60kN/M2 Concrete pile dimensions = 0.25x0.25=0.625m2 The adhesive factor,  FS (skin friction) =2 FS (end bearing) =3 =+ But =9 =9x35x0.625 = 196.875KN = x0.625x0.8 =30KN Therefore =30+ 196.875 = 226.875KN The allowable load on a pile= = = 45.375KN Question 6 a. Purposes for site investigations: i) To establish site suitability. ii) To determine the construction design parameters to be employed. b. Insitu tests i) Penetration Testing The penetration test aims at testing the vulnerability of a soil through underwater vibratory techniques and matching the soil parameters. The penetration test is further subdivided into standard penetration test, cone penetration test and probing all working under the same principle. The main equipment used in this exercise is the penetrometer or penetration hammer which works by being pushed into the soil through hydraulic means. The automatic trip hammer used in the penetration test is digitally controlled and the accuracy obtained from this equipment can give a deviation of up to 2.8%. The hand controlled trip hammer requires the operator to hoist the weight making it an inconsistent means of carrying out the test. On the other hand the slip rope hammers which are widely used in the world require the operator to lift weight attached on a rope via a rig cathead over a constant height in order to give consistent results. The procedure involves drilling a test hole which is then rid of all the disturbed materials. The split rod is then driven to the undisturbed soil giving the exercise a zero level for commencement. Once the drive weight is assembled, the operator releases it from a constant height while observing the reductions in height. These values are used to find out the penetration resistance value “N” which is also known as the N-value. The penetration test is mostly used in profiling, measuring of the static pore pressure through use of piezocone method, soil type identification and checking of the consolidation characteristics of soil. In as much as this is a preferred method in insitu investigations, the results obtained are erratic due factors such as inability by operators to maintain constant hydrostatic head, inadequate cleaning before driving the split rod and improper seating of the sampler spoon. ii) Strength and Compressibility Testing Strength and compressibility parameters are important in determining soil types present in a given site. Among the tests in use include the pressuremeter test, vane test, plate loading test, and the Marchetti dilatometer method. The vane test applies a four bladed vane that is pushed to the ground and rotated at a given torsional force which is then translated to shear resistance. The pressuremeter method applied in both soil and rocks has led to development of dilatometers for application in sites of greater hardness. The pressuremeter is meant to obtain the stiffness or strength of a ground by either radial pressure or resulting deformation. The plate loading tests are carried out in instances whereby the required parameters are the compressibility and the bearing capacity of a soil. In this method, a plate is bedded to the soil and given a constant load and tallied against the increments until shear failure and bearing pressures are achieved. The Marchetti dilatometer test applies the use of a special diaphragm mounted blade that is given a constant expansion while checking the penetration resistance. The main factors affecting the strength and compressibility test is the type of soil, soil disturbance during the experiment, soil failure around the instrument and the strength anitropy of the soil in question. SPT number Standard Penetration Resistance, N30= 3+2+2+1=8 Read More