Geotechnical Engineering - Math Problem Example

Student’s Name Instructor’s Name Course Name: Date: 28th November, 2012. Geotechnical Engineering 1.a) there are various method of slope stabilisation used by Geotechnical Engineers among them include ordinary method and Janbu's simplified method. Ordinary method uses slices to produce a safety factor in linear form. In this method, it is assumed that inter-slice forces are negligible since they are parallel to their base. The forces acting on the base in this are calculated by summing up forces that are perpendicular and horizontal. Janbu simplified method is one of the method of slope stabilization which uses correction factor to determine the effect of shear strength. Correction factor is determined by considering the angle of internal friction in a slice, the cohesion in the soil and the shape of the service that fails. The force that is working in the service is determined by adding up all perpendicular forces from the slices. b)- Factor of safety The safety factor against sliding for the trial slip surface using ordinary method of slices. The following formulae will be used; FS= Where cu is shear strength and it is 19.kN/m3, is angle of internal friction of soil which is 30o . l is base length of the slice, u = hw γw cos2 αw where αw = slope of pore water and hw = depth of pore and γw is the unit weight of layer w. ul is to be ignored W= Where is the effective unit weight of the dry soil which is , b is the base of the slide and h is height of the slide which is 3m for all slices except slice 8 which has a base of 3.1m. La=)r2 Where is the internal friction angle of the soil which is 117o. L is base length of the slice Using excel out put the calculation are as follows Soil Properties   Other Data                 c = 19 kPa Radius, R = 9.8 m = 30   Angle, = 117 degrees = 23 (kN/m3) Angle, = 2.04 rads                     γbh       Slice b h bh W (kN) º Wicos  Wisin  1 3.0 1.7 5.10 117.3 14.0 114 28 2 3.0 4.7 14.10 324.3 5.0 323 28 3 3.0 7.1 21.30 489.9 5.0 488 43 4 3.0 9.3 27.90 641.7 14.0 623 155 5 3.0 10.7 32.10 738.3 24.0 674 300 6 3.0 11.4 34.20 786.6 35.0 644 451 7 3.0 11.0 33.00 759.0 48.0 508 564 8 3.1 9.0 27.90 641.7 65.0 271 582 Total= 3645 2152 Ntan 2104.69 kN cR = 380.23 kN             Factor of safety = 1.15             The factor of safety is 1.15. 2. Retaining Wall a. Effective Ranking Pressure To determine ranking active pressure, the following formulas are employed. Where q is the surcharge load and in this case it is 20kN/m and Ka is while is determined using . To begin with, we are given c’ as 0 therefore, the upper layer of sand its coefficient of ranking active pressure is determined as follows, Ka = The lower layer of sand its ranking active pressure coefficient will be determined as follows Ka = Therefore at Z=0, the surcharge will be = 0.333 x 20kN/m = 6.66kN/m2 At a Z=3, the effective ranking active pressure is = 6.66kN/m2 + 0.333 x 3 x19kN/m3 = 25.641kN/m2 At Z=3 but in the lower layer the force will be 3 x 25.641 x 0.333 = 25.615 At Z=6 metres the effective ranking active pressure is = (25.641 x 3 + 3(21kN/m3- 9.81)) x 0.333 =36.79kN/m2 We have assumed the pressure of water to be 9.81kN/m2 B- C. Rankine’s active force per unit length =( ½) H2 K Therefore at Z=0, the Rankine’s active force per unit length will be =( ½) x6.66kN/m2 x 20mx1m =66.66kN/m At a Z=3, Rankine’s active force per unit length is =( ½) x25.641kN/m2 x 19x3m =2,192.31kN/m At Z=3 Rankine’s active force per unit length =( ½) x25.615kN/m2 x 19x3m =2,190.08kN/m At Z=6 metres Rankine’s active force per unit length =( ½) x 36.79kN/m2 x 19x(6mx6m) = 12,582.18kN/m 3. a The consolidation settlement for the soil profile in the diagram with a load of 1800kN which is applied at two metres below the ground by a square footing with a size of 3m by 3m will be determined as follows. Where Sc is the consolidation settlement under the square footing,, e0=1, p’0 is 3 x 19kN/m3 + 10(3 - 2) + Average effective vertical stress before construction which is Average increase in effective vertical stress eo Initial void ratio of the clay layer Initial effective overburden stress, p’ po = (2x19) + 4(1.5x(21-9.81))+3(22-9.81) = 108.14 kN/m Δp= [1800*(3*3)] / [(8+1)*(8+1)] = 200kN/m PAverage = (200+ (2x19) + 4(1.5x(21-9.81))+3(22-9.81) = 200+38+67.14+36.57= 314.71 = 0.02410log3.910 = 0.0142m or 1.427cm b). = 0.0022 days 4. a) Isolated spread footing—this footing is important where the soil is soft like clay soil and requires thick slab which is uniform. Strip footing—is important where a bridge is under construction Strap footing—is constructed to hold a beam since it does not resist any soil reaction b) Pile Foundation Square Footing, Where No is the bearing capacity factor (cohesion), B is the width or diameter of the foundation, D is the effective vertical strength of the soil, Nq is the bearing factor and surcharge friction, is the bearing capacity factor self weight and friction, C is the cohesion strength of the soil. We are given unit weight as 21kN/m3, we have friction as 350, and we have depth base as 1.5m and a square footing of 3 by 3 Where is the ultimate bearing capacity, in this case we will use the formula Where Qu = in this case Nc=45, Nq=35.4, Ny=50 Qu =1.3x0x(45) + 21kN/m3 (1.5m) x 35.4) + 0.4 (21kN/m3 x 3m x 50 = 1115.1 + 1260 =2,375.1kN/m2 Allowable Bearing Capacity It is Qa = Qu Qa = Allowable Column Load (2375.1.1kN/m2+ kN/m2)/9m2 = 351.9kN C. factor of safety Given cu as 15kN/m3 , Nc is 45, is 21kN/m3, is 35.4, is 50, w is 9.81kN/m3 Strip Footing, = 675+396.126+1678.5 = 2749.626 Load = (allowable bearing capacity+ ultimate bearing capacity)/Ab Allowable bearing capacity = qu 600kN/m = (+ 2749.626)/2m 2mx 600kN/m = (+ 2749.626)x2m 300kN/m2 + 2749.626= ( Factor safety = 1.109 5. a) There are a number of piles which are used during the foundation; among them are steel piles, concrete piles, timber piles and compost piles. Their advantages are as follows: Steel Piles—steel piles can be either pipe or rolled steel H section piles. These piles are easy to use and they require less energy for installation. The other advantage is that they can penetrate hard strata. They can also carry high loads without been stretched. Concrete Piles—these piles are made of concrete and they are cheap as compared to steel piles and they can resist corrosion. They can bear hard driving force. Timber Piles—timber piles are cheap and easy to use. They can break easily and have difficulty in achieving desired results. b) Factors Considered In choosing the type of pile to use, a number of factors which include Building load to be used. The cost to be incurred. Government policy/environmental control like restrictions to noise and height. The type of ground. Installation method. Rock levels Location and the type of structure. The period that the building is expected to withstand. c) Qs = Ascu Where As is the base area and is 0.25m by 0.25m = 0.0625m2 cu is 35.Kn/m2 and is 0.8 Qs = 0.0625m2 x 35 x 0.8= 1.75kN Qs = 0.0625m2 x 60 x 0.8= 3kN Qu= 3kN+ 1.75kN = 4.75kN 6. Insitu Tests a) The Purpose of Carrying Site Investigation Works is to understand the conditions of the ground which will be used for the intended project. The other purpose for site investigation is to find a suitable location which will be used in construction of the intended facility. b) Two Insitu tests that can be used in site investigation works include standard penetration test and cone penetration test. Standard penetration test This test is used to test the ground which will provide a site for construction of the infrastructure intended. The method tests a ground which is in a borehole which is reached by use of split spoon. Equipment—the equipments that will be required will include;- -Spoon sampler -Hammers -30 in drop -Standard penetration number -18 in penetration Procedures—first, one drives in 18 inch where pros are counted at every 6inches. In driving the hammer Factors affecting results—the results that will be obtained will be affected by; -Using a sample that has been obtained beyond the casing -Using boreholes that are not properly cleaned if they were open when sampling begun -When the team fails to use proper hydrostatic equipment when drilling the borehole. -Attitude of the team will also affect the results. -The method used in drilling will also affect the result such as cased and mud stabilized holes. -The hammer drop systems are anvil size will play an important role in the result that will be obtained. Advantages and disadvantages—Standard penetration test has many advantages which includes the use of parts which have few movements and there is no electrical part that is required. A sample of the site will have to be used. Like any other test, it has its disadvantages such as it requires a lot of time to use it. It can also be poor when it comes to clay soils since it measure using index properties. Cone penetration test—this method aims at testing soil for the purpose of Equipment—a truck is required and should be amounted with CPT ligs, mini cone system, portable CPT system, ramset limited access system, ultraviolet screening tool, membrane interface prop Procedures—the cone will be connected to the loads which are connected to the truck that is carrying the equipment, then the loads are used to penetrate the ground. Pushing the cone to the ground requires a thrust mechanism; however there is a pre-drilling by punching a hole using steel which has a diameter greater than that of a cone Factors affecting results There are a number of factors that affect the result obtained by this method. One of the most important factors is the type of equipment that is used. If proper equipments are not employed, the result will be wrong; the other factor is the friction angle. Drilling should be vertical any angle which is not perpendicular may produce wrong results. Shallow foundation will also affect the result that will be obtained from the exercise. Advantages and disadvantages—Cone penetration test has many advantages which includes its cheaper and fast. It is also continuous and gives type II correlations. This test has disadvantages which include lack of classification due to lack of sample. It cannot be used in areas where there are gravels. c) SPT Number N(60)=NmCnCeCbCrCsCaCBFCc N(60)=STP number adjusted to 60% Nm- measured blow count in the field Cn - overburden correction factor Ce - energy correction factor; Cb- borehole diameter correction factor; Cr- rod length correction factor; Cs- sampling method (liner) correction factor Ca- anvil correction CBF – blow count frequency correction factor; Cc – hammer cushion correction factor Details SPT test results SPT Number SPT Details (seating and test) 75mm 75mm 75mm 75mm 75mm 75mm Firm Greyish brown sandy SILT 13 2 3 3 2 2 1 Works Cited Coduto, Donald, Man-chu Ronald Yeung and William Kitch. Geotechnical Engineering: Principles & Practices. Boston: Prentice Hall, 2010. Print Lommler, John. Geotechnical Problem Solving. NEW York: John Wiley & Sons, 2012. Print. Mamlouk, Michael & John Zanielwski. Materials for Civil and Construction Engineers. New York: Prentice Hall, 2010. Print Read More

Concrete Piles—these piles are made of concrete and they are cheap as compared to steel piles and they can resist corrosion. They can bear hard driving force. Timber Piles—timber piles are cheap and easy to use. They can break easily and have difficulty in achieving desired results. b) Factors Considered In choosing the type of pile to use, a number of factors which include Building load to be used. The cost to be incurred. Government policy/environmental control like restrictions to noise and height.

The type of ground. Installation method. Rock levels Location and the type of structure. The period that the building is expected to withstand. c) Qs = Ascu Where As is the base area and is 0.25m by 0.25m = 0.0625m2 cu is 35.Kn/m2 and is 0.8 Qs = 0.0625m2 x 35 x 0.8= 1.75kN Qs = 0.0625m2 x 60 x 0.8= 3kN Qu= 3kN+ 1.75kN = 4.75kN 6. Insitu Tests a) The Purpose of Carrying Site Investigation Works is to understand the conditions of the ground which will be used for the intended project. The other purpose for site investigation is to find a suitable location which will be used in construction of the intended facility. b) Two Insitu tests that can be used in site investigation works include standard penetration test and cone penetration test.

Standard penetration test This test is used to test the ground which will provide a site for construction of the infrastructure intended. The method tests a ground which is in a borehole which is reached by use of split spoon. Equipment—the equipments that will be required will include;- -Spoon sampler -Hammers -30 in drop -Standard penetration number -18 in penetration Procedures—first, one drives in 18 inch where pros are counted at every 6inches. In driving the hammer Factors affecting results—the results that will be obtained will be affected by; -Using a sample that has been obtained beyond the casing -Using boreholes that are not properly cleaned if they were open when sampling begun -When the team fails to use proper hydrostatic equipment when drilling the borehole.

-Attitude of the team will also affect the results. -The method used in drilling will also affect the result such as cased and mud stabilized holes. -The hammer drop systems are anvil size will play an important role in the result that will be obtained. Advantages and disadvantages—Standard penetration test has many advantages which includes the use of parts which have few movements and there is no electrical part that is required. A sample of the site will have to be used. Like any other test, it has its disadvantages such as it requires a lot of time to use it.

It can also be poor when it comes to clay soils since it measure using index properties. Cone penetration test—this method aims at testing soil for the purpose of Equipment—a truck is required and should be amounted with CPT ligs, mini cone system, portable CPT system, ramset limited access system, ultraviolet screening tool, membrane interface prop Procedures—the cone will be connected to the loads which are connected to the truck that is carrying the equipment, then the loads are used to penetrate the ground.

Pushing the cone to the ground requires a thrust mechanism; however there is a pre-drilling by punching a hole using steel which has a diameter greater than that of a cone Factors affecting results There are a number of factors that affect the result obtained by this method. One of the most important factors is the type of equipment that is used. If proper equipments are not employed, the result will be wrong; the other factor is the friction angle. Drilling should be vertical any angle which is not perpendicular may produce wrong results.

Shallow foundation will also affect the result that will be obtained from the exercise. Advantages and disadvantages—Cone penetration test has many advantages which includes its cheaper and fast. It is also continuous and gives type II correlations. This test has disadvantages which include lack of classification due to lack of sample.

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