Structural Design of Field Plate Load Test Equipment to Determine In situ Bearing Capacity and Settlement of Clayey Soil

- The study is to design field-operated plate load test equipment to overcome the problem of predicting bearing capacity and settlement of clayey soil on site using the conventional/traditional methods of short-duration plate load test where a hydraulic jack is used in conducting the test. Ashby's method of material selection was used for the selection of a suitable material for each of the components. The 12 mm thickness was obtained as the minimum safe thickness for the applied load of 500 kg on the lever arm. The I-section frame that support the entire system has sectional modulus of 19.4 cm 3 and 4 mm thickness. The equipment will use a lever arm mechanism to conduct an in-situ test that will take long-duration on clay soil where the dissipation of pore water from the clayey soils takes a longer time to complete as against the current conventional method of plate load test that is in use. The equipment will offer several advantages in terms of cost, reliability, portability, authenticity, and user friendly.


INTRODUCTION
Plate load testing equipment is an in-situ testing equipment used in determination of in-situ soils bearing capacity [1][2][3]. Testing of the mechanical properties of soil at field conditions have proven to be more accurate and reliable due to the preservation of the soil structure as against laboratory test which can be affected by sample disturbance [4,5]. The use of in-situ plate loading tests have been in use over the years to determine the bearing capacity of in-situ soil deposits as well as the settlement of the soils under each of the applied loadings. In almost all the plate loading devices in use over the years, Jack has always been used to apply loading on the device and the deformation recorded for each load application [6]. However, the use of jack for load application cannot give sustained loading for a relatively long period of time thereby making it difficult to allow for pore pressure desipation when the equipment is used on in-situ saturated clay soils [7].
The existing in-situ field plate load tests will give accurate and reliable results for the design of shallow foundations on sandy and silty soils [8,9]. These accuracies cannot be guaranteed on in-situ saturated clay soils due to lack of sufficient time for the pore water to decipate and may give erroneous bearing capacity results [10].
An innovative in-situ field plate loading test device was then conceived with gravity loading which can be applied and sustained for a long period of time to allow for pore water dissipation before the next loading increment [11]. The minimum dimension of plate to be used for in-situ field plate loading device is specified to be 30cm due to pressure bulb that will be generated from the base plate [12]. This minimum size of base plate will affect the magnitude of the weight that will be applied to give substantial applied stress since the weight will be divided by the cross-sectional area of the base plate. Invariably, large applied weight is required which cannot be applied directly without any form of load magnification, hence the introduction of a lever arm. The lever arm was designed and used to magnify the load applied to the device so as to achieve high applied stress [13][14][15][16]. The study by [17] which conducted a plate load test on the field where a load was applied to the plate through a hydraulic jack against a heavy kentledge of sandbags, in 5 equal load increments of 100 kPa is a typical example of field plate load test using hydraulic jack for load application. The settlement of the plate during the test was measured at two manually recording dial gauges placed on the plate at diagonally opposite locations on a field. The pressure recorded by the pressure gauge attached to the hosepipe connecting a manually operated hydraulic jack to control the pressure applied to the plate assembly was observed to drop when allowed for some period of time [15,18]. Assuming a maximum load to be applied to this equipment and all the steel members to be used must be structurally designed to allow it resist loadings without buckling or failure in bending. The aim of this study therefore is to carry out structural design and analysis of all the steel members required to construct this equipment [18]. Figure 1 shows the flow chart used for the structural design of the in-situ plate load test equipment. Design consideration and maximum loading assumptions were made on the chosen concept followed by the material selection, calculations, design analysis and development of the computer aided design (CAD) model as shown in the flow chart.

Material Selections
Ashby's method of material selection was used for the selection of a suitable material for each of the components of the plate load test equipment. The criteria were considered in the following order: material properties, fabricability, availability, and cost of the material. The method uses Young Modulus verse relative cost per volume, strength verse relative cost per volume and Young Modulus verse density, [19]. The focus of the material selection adopted is to make the equipment more cost-effective, meet strength requirements, be light in lightweight and resistant to failure. There are many sources of reliable and consistent data on material properties and other information which includes governmental agencies, trade associations, engineering societies, textbooks, research institutes and material producers [20].

Description of the Innovative Plate Load Test Equipment
The plate load test equipment shown in Figure 10 is an innovative field in-situ test equipment that is structurally designed and constructed to determine the bearing capacity and settlement of foundation on in-situ saturated clay soils. The equipment uses a straight lever arm mechanism with a parallel force acting in the same plane Figure 2. The equipment will be loaded incrementally through the load hanger known as effort, P attached to the lever arm and balance load W, at the opposite end to produce an equilibrium of weight on a fulcrum which will then be transmitted to the square base plate of dimension 300mm x 300mm and 25mm thick [20]. It has been specified that the load shall be applied in cumulative equal increments up to 1 kg/cm 2 (100 kPa) or ( 1 5 ⁄ ) of the estimated ultimate bearing capacity. Also, [5] states that the load should be applied in cumulative equal intervals of not more than 1.0 ton/ft 2 (95 kPa) or one-tenth ( 1 10 ⁄ ) of the estimated bearing capacity. However, in this study, the load will be applied at the lever arm through a load hanger in order of 5 kg, 10 kg, 20 kg, 40 kg, 80 kg, 160 kg, and 320 kg as reported by [21] and [5] respectively. This is because the dissipation of pore water pressure from clay soils is gradual and requires slow incremental loadings from smaller to higher loads. Each load placed on the lever arm will be maintained for 24 hours before the next incremental loadings.

Lever Arm Design
A first-class type of lever mechanism ( Figure 2) was used as a lever arm for the plate load test equipment because the fulcrum is located in between the load and the effort. An I-section was used for the lever arm to minimize the twisting along both axes due to the overhand loads. Therefore, the lever arm was designed for strength, rigidity and the dimensions of the lever arm were determined using equations (2)(3)(4)(5).

Figure 2. Lever arm
The fulcrum F, is between the load and effort is termed the first type of lever. In this case, effort arm is greater than the load arm.
where, P = Loads (N), W = balancing load (N), L= distance from P to the fulcrum F (mm), X1 = Distance from Balancing load W to fulcrum (mm).

5,000 N = 795 mm
And therefore, the moment , acted on the lever arm equation (7) is express as; = × (7) = 4,000,000 / According to [22], the sectional modulus of the I-section in Figure 3, was computed using equations (8) and (9). From figure 3, the breath. B and depth, D of the I-section is given by B = 2.5t and D = 6t. Where t, is the thickness. Therefore, sectional modulus, Z, is given by equation (8) as explain by [22] = ( 2 ⁄ ) From the proportion of I-section Figure 3, equation (9) was used to determine sectional modulus, Z The yield stress of mild steel is 220 MPa [22], according to equation (10), bending stress of the lever arm was obtained as; = where, M = moment However, the thickness t, of the lever is calculated from the equation (10) 220 = 4,000,000 12.3 3 where, Thickness t, = Therefore, from [23], the I-section ISMB 125 was chosen. The values of the Lever arm section are shown in Table 2. Therefore, the bending stress, σ, for the lever section was computed from equation (10). According to [22] the allowable bending stress, | | is given by equation (11) 4,000,000 71800 = . Therefore, for a factor of safety 2, the maximum bending stress of 28N/mm 2 is below the permissible value of 110 N/mm 2 the design is safe.

Design for fulcrum
The fulcrum, in Figure 4, is the point at which the lever arm turns relative to the frame of the plate load test equipment. The pin (see Figure 4) at the fulcrum is subjected to a shearing load and therefore, designed using equations (12) and (13). The diameter of a pin was determined from equation (13), and combining equations (12) and (13) yielded equation (14); where, is Load on fulcrum pin where, t=3mm, and L is the length of the pin equation (14).
= 11 / 2 ok A bushing 3 mm thick was inserted in the pinhole. Therefore, the diameter D, of the hole in the fulcrum equation (16). The diameter is taken twice the diameter of the hole L equation (17). Induce bending stress, from equation (18), = 21,875 Also, the sectional modulus Z, of the material is given by equation (9). Therefore, the bending induced , is expressed by equation (10) The induce bending stress | σ |, is within safe limits, yielding stress equation (11) is calculated as; | | = ℎ = 2.725 / 2 is ok.

Design for the pin at fulcrum and loading arm pin
The fulcrum pin connects the lever arm and the load transfer column through a revolute joint. Therefore, the pin is subjected to shearing stress as shown in Figure 5. And the pin load is given by equation (18). While equations (19), (20), and (21) are for the length of the pin, maximum bending moment, and sectional modulus of the materials respectively.
If the pin is going to fail due to the bearing of the pin of the fulcrum, then the pin diameter is determined by equation (19). From equation (13), However, from equation (12), the shear stress on fulcrum pin is determined as Since the end is forked and therefore the thickness of each eye, equation (20), The inner diameter of each eye, D. The maximum bending moment on the fulcrum pin at Y-Y, from equation (21), and the sectional modulus of the fulcrum section is given in equation (22). Bending stress-induced, from equation (9).

DESIGN OF THE FRAME
The frame is an assembly where the lever arm and the load are placed, the frame consists of I-beam and I-section column. The load is transferred to the crossing beam and in turn, transferred to the column as shown in Figure (

Design of crossing beam
The cross beam is used to support the load from the lever arm and transfer it to the column. It is designed using equation (23) and is shown in Figure 6. The proportion of the support beam is taken as t = thickness, h = depth as 5t. The result is shown in Table 3. Moment of inertial I, [24] equation (23). The Sectional Modulus Z, is calculated using equation (24) From [22], the yield stress of mild steel was taken as 220 Mpa. The thickness of the load transfer column was estimated using equation (9) Table 3.

Load transfer column
The load transfer column is a slender column attached to the fulcrum that transfers the dead load to the base of the foundation. The load transfer column is shown in Figure 7. Using Euler's method to design for the cripple load as shown in equations (25), (26), and (27). Shear stress at equation (33) and the results are shown in Table 4. The moment of inertial in the X-axes, Ixx, and the Moment of inertia in the Y-axes, Iyy,, for the transfer column is given below, (3 )  Since the value of ⁄ lies between 3 and 3.5. The I-section is quite satisfactory [22].
However, [23]. The I-section chosen for the column is ISLB 75. As shown in Table 4. Consider the moment of inertia for both axes. The radius of gyration Kxx and Kyy [24] is given in equations (29) The least radius of gyration of the section is considered. However, Kxx is the least radius of gyration hence used in equation (28). The effective length of fixed and pinned end le, equation (31) and slenderness ratio λ, [24] equation (32).
Z= 11.82 cm 3 However, [23]. The I-section chosen for the column is ISLB 75. As shown in Table 5. Consider the moment of inertia for both axes. The radius of gyration Kxx and Kyy from equation (29) and equation (30). The least radius of gyration of the section is considered. However, Kxx is the least radius of gyration hence used in equation ( Hence the column is designed as a long column. However, since the column is fixed, the effective length is le = 2 = 1,500 mm. Shear Stress τ, from equation (33), = = 7 / 2 ≦ 220 N/mm 2 . Hence the design is ok

Design of loading arm
The loading arm is made up of mild steel with a circular cross-section and attached to the lever arm. The area of the loading arm was calculated using equation (34) and diameter d,

Design of loading arm pin
The loading arm pin is calculated using equation (19). Let's consider failure due to the bending of the pin at the loading arm and check for shear stress, from equation (15) = 1 × 1 1 = 26 1 = 1.25 1 = 32.5 = 2 4 × 2 = 4.71 t according to [22] Since the end is forked and therefore the thickness of each eye from equation (20). The inner diameter of each eye, d1, The maximum bending moment at Y-Y, from equation (21), and Sectional modulus from equation (22). The bending stress induced from equation (10

RESULTS AND DISCUSSIONS
The conventional methods of conducting plate load tests presented in figure 9 use a hydraulic jack to apply pressure to the soil except figure 9f which uses laboratory-based plate load tests. The reaction plate load test uses a truss to serve as canter load is placed above the pit and hydraulic jack is placed at the bottom of the pit and pressure is applied to the truss through the hydraulic jack figure 9a. A gravity plate load test uses sand bag arrange in a platform to provide for canter weight while a hydraulic jack is placed at the bottom of the pit and pressure is applied through the hydraulic jack figure 9b. A truckload is equally used to conduct a plate load test on a pit with a hydraulic jack placed at a pit and pressure applied through the hydraulic jack which will cause deformation or settlement of the soil figure 9c. [25] uses 1.3 tons of reaction beam with 200kN tons hydraulic jack in conducting plate load test on the field figure 9d. Also, [26] conducted plate load tests on the field with the plate load test equipment they developed using an automatic hydraulic jack (see Figure 9e). while laboratory plate load test was conducted using a lever arm in place of a hydraulic jack but the sampling of undisturbed samples for the test was his major challenge (see Figure 9f). The hydraulic jack used for the test described in figure 9 does not sustain the applied pressure for so long [27]. The drop-in pressure from the hydraulic jack will affect the result obtained from the conventional plate load test which will lead to either under design or overdesign of the intended structure.

Sectional modulus of the mechanism
The need for the design of equipment that will not use the hydraulic jack on site on a low permeable clay soil was conceived. The equipment will be very easy to handle and will not require many manpower to operate. Unlike the conventional plate load test equipment in figure 9, this test can be conducted on a developed area where it cannot be accessed by other methods of plate load test equipment The components of the machine were designed for strength and rigidity. The strength of mild steel used in construction of machine parts that will perform the desired function within the allowable working stress [22]. For each of the components, the minimum fail-safe dimension was determined using strength conditions. Sectional modulus is a direct measure of the strength of a beam or column. For the lever arm, a load of 500 kg was applied and a 12 mm thickness was computed as the minimum stress thickness a similar trend was observed [31]. However, sectional modulus was calculated for beams, transfer column and anchor leg for the entire frame as 19.4 cm 3 . The sectional modulus was used in selecting the thickness of web and flanges as 4 mm and 5 mm respectively [23]. The complete Cad model of the field plate load test equipment designed is presented in figure 10. Figure 10. CAD model of field plate load test device

Shear stress of the components
Shear stress is the strength of component against the type of yield when the component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. Shear strength of a components is important for designing the dimensions to be used for the construction of machine components or parts. The minimum thickness of lever arm of 12 mm will induce a maximum bending stress of 56 N/mm 2 , while crossing beams, transfer column and anchor legs will induce a maximum bending stress of 7N/mm 2 which is less than the bending stress of 220 N/mm 2 [22]. Hence the design is safe to carry the load of 500 kg [32]. The fulcrum pin diameter was designed to be 27 mm with a maximum induced shear stress of 4N/mm 2 . Based on the detailed design analysis, the body of the machine could be produced from a C-section having a minimum thickness of 5 mm if the maximum load will not exceed 500 Kg [23].

CONCLUSION
The plate load test equipment described in this paper was designed to standard. All the steel component members were design, analyzed and observed to resist maximum loading during testing without deformation or failure of any of the steel members. The analysis was used for the final development of the plate load test equipment as an alternative to the existing plate load test equipment that uses a hydraulic jack which has been in use for measuring the in-situ bearing capacity and settlement of soil deposits. In conclusion, the equipment is portable when compare with the existing one and will have high advantage when used on saturated clay deposits as it will allow for maximum deformation after dissipation of pore water pressure for each load application before increment of next loading.