Bearing Strength of Concrete Pedestals Partially Loaded at Early Ages: An Experimental Work Mitigating Failure Risk

Abstract

In many construction applications, including bridge pedestals, concrete corbels, and concrete anchors, the concrete’s local compressive strength attribute (bearing) is crucial. One of the benefits from concrete’s bearing is its role in mitigation construction failure risk and increase the safety of the buildings. The local compression characteristics of fully hardened concrete were the primary focus of earlier study, with less attention paid to early age concrete (less than 28 days). In order to evaluate the bearing qualities of early age concrete—here defined as the first month—the current experimental program is being carried out. While the bearing plate’s area (Ab), which was placed in the middle of each block’s top surface, differed in dimension (100 × 100 mm, 80 × 80 mm, 60 × 60 mm, and 40 × 40 mm), the concrete pedestals’ size remained constant at 250 × 250 × 200 mm. Tests were conducted on sixteen concrete supports. Four equal groups of samples were created, and each group underwent testing at a different age (T = 3, 7, 15, and 28 days). In each group, unloaded-to-loaded area is varied (A₁/A_b = 6.25, 9.76, 17.36, and 39). The failure, bearing stress–slip curve, ultimate bearing strength and ultimate associated deformation of the tested concrete supports were studied. The results showed that the compressive and tension strengths increased by 178% and 244% when the concrete age reached 28 days compared to 3 days-concrete. As A₁/A_b or/and concrete age increased, the bearing characteristics improved more. The ultimate bearing strength increased by 51%, 56.5%, and 69.5% at $\sqrt{{\displaystyle \frac{A_1}{A_b}}}$ = 6.25 when the samples’ concrete age increased from 3 to 7, 15, and 28 days. The main contribution of this study is a novel formula to forecast the concrete’s bearing strength while accounting for the impact of the concrete’s age and the ratio $\sqrt{{\displaystyle \frac{A_1}{A_b}}}$.

1. Introduction

For steel buildings, concrete foundations must be used as one of the most common construction materials here. The concrete’s hardening time is one of the biggest obstacles in this industry. Engineers frequently have to finish the stages of installing metal columns on concrete foundations in fewer than 28 days. Early concrete behavior research has become crucial, and there are currently few studies in this area. Furthermore, excavation disturbance and redistribution of initial ground tension frequently cause damage or failure to the project’s surrounding rock during underground engineering excavation causing several environmental and safety risks. Support systems are put in place to improve the surrounding rock’s function and make digging and subterranean engineering construction building easier. In engineering practice, concrete support is a frequently used construction technique. However, it usually takes a long time for the mechanical qualities of plain concrete to reach their design levels. This long time is also considered as construction risks and should be considered carefully.

Since Lew and Richard’s seminal study, which painstakingly recorded concrete features at different early stages (one, two, three, five, seven, fourteen, twenty-eight and forty-two days) of concrete development, there has been significant advancement in the investigation of early-age concrete features [1]. Numerous researchers, including Kim et al. [2], Kanstad et al. [3], Roziere et al. [4], and Mamand et al. [5], have also attempted to comprehend the mechanical characteristics of early-age concrete, including its elastic modulus, compression and tension advantages, and strain-stress behavior. These results highlight concrete’s effectiveness during its initial phases of development. Swaddiwudhipong et al. [6] used the simple tension experiment to examine the tensile strain capacity of the concrete with uniaxial tension at an early age in order to ascertain early-age strength. According to the experimental findings, the maximum tensile strain of concrete is a largely unrelated variable.

When a concentrated area of the concrete surface is significantly loaded, the bearing (local compression) strength of the concrete is essential for preserving structural stability at the support increasing the safety and decreasing the possibility of construction failure risks. So, when designing concrete beds, bridge pedestals, concrete corbels, concrete anchors, concrete anchorage, and column–footing connections, bearing strength is essential. Significant concentrated loads were applied to these structural supports, which could compromise the structure’s structural soundness. Massive concentrated loads on the concrete’s surface could cause an unequal distribution of loads, which would cause local collapse before structural breakdown. Additionally, the post-tensioned anchoring zone is one of the applications on the bearing condition in concrete constructions because anchors introduce concentrated prestressed force into the structure. The following criteria must be met in order to ensure safety under the loaded bearing plate: (1) the concrete should have enough ultimate resistance to prevent local failure in the local loading region before the overall structure is damaged; (2) ductile breakdown rather than fracture should be encouraged; and (3) fractures must be monitored to maintain a dependable serviceability stage under small loading level. Therefore, it is important and required to look at the concrete’s bearing capacity. Thus, this is the subject of the current research.

To lower the chance of cracking from local compression loading (bearing), early-age concrete’s bearing qualities must be evaluated. Despite the significance of the concrete’s bearing capacity under local loads, there is a dearth of information in the literature. The bearing qualities of early-age concrete—here defined as the first month—cannot be evaluated experimentally. In the current work, a localized compression stress experiment has been created.

Investigations, computer modeling, and mathematical modeling have all been done in relation to concrete’s bearing property. The impacts of a number of variables, such as bearing loading plate rigidity, concrete degree, size impact, dimension ratio (height/width), and local area aspect ratio, on the bearing of concrete were methodically examined by Niyogi [7,8]. He discovered that the most crucial element was the local area aspect ratio, and that as sample dimensions, concrete degree, and height increased, the bearing strength increase factor declined. Breen et al. [9], Haroon et al. [10], and Bonetti [11] have since provided summaries of the failure properties and cracking trends in concrete. The findings demonstrated that the regional area aspect proportion had the greatest influence on the failing properties of concrete specimens under limited area burdens, with a large A1/Ab proportion indicating the wedge breaking failing mechanism. Furthermore, the strut-and-tie theory [9] and the wedge cutting model [12,13] have been put forth to clarify the inner workings of regional collapse, and the associated findings have been mirrored in the requirements for design in a number of nations [14,15]. The localized bearing ability estimation approach taking into account the real stress of high-strength turns in reactive powder concrete [16,17], the consistency of reinforcing restriction effectiveness across the anchorage region [18], and bearing under a combination of local compression and bonding pressure [19] are just a few of the intriguing new attempts on the local compression properties of concrete that have recently been carried out due to the ongoing advancements in material and building science [20,21].

The bearing capacity of steel fiber reinforced recycled aggregate concrete was examined by researchers using different substitutions of recycled concrete aggregate (0, 10, 20, 30, 50, and 100%) [22]. Three 100 × 100 × 100 mm, 150 × 150 × 150 mm, and 250 × 250 × 250 mm concrete blocks have been built. The ratio of loading area to concrete sample was maintained at 2.5 for each of the three block sizes. The results showed that varying the steel fiber ratio significantly improved the bearing strength. Fayed et al. [23] looked into how block size affected the concrete’s final slip, bearing stiffness, and bearing strength. The findings demonstrated that bearing strength and stiffness declined with increasing block size. Yehia et al. [24] conducted an experimental and computational investigation of the impact of the perforations beneath the loaded plate on the bearing capacity of concrete blocks. The hole’s diameter (6, 10, 12, 16, and 18 mm) and depth (20, 40, 60, and 100 mm) were among the variables. Results of tests show that when the hole size to bearing plate area ratio varies between 1.4% and 40%, the ultimate bearing capacity drops by 35%.

The local compression characteristics of fully hardened concrete were the primary focus of earlier study, with less attention paid to early age concrete (less than 28 days). In order to evaluate the bearing qualities of early age concrete—here defined as the first month—the current experimental program is being carried out. In order to comprehend the regional compressive characteristics of early age concrete at 3, 7, 14, and 28 days, a total of 14 specimens were evaluated in this study. When the bearing plate area was changed (A_b= 100 × 100, 80 × 80 mm, 60 × 60 mm, and 40 × 40 mm), the concrete block area-to-bearing plate area ratio (A₁/A_b) or the load concentration ratio was calculated. 6.25, 9.76, 17.36, and 39 were the A₁/A_b values. Since the ratio (A₁/A_b) is the primary factor influencing the bearing strength in the international codes, this study is concentrating on it. Cracking patterns and failure modes were identified. Relationships between bearing stress and deformation were found. The highest levels of bearing toughness, stiffness, and strength were attained. Additionally, the effects of important elements on the concrete’s local bearing capacity were examined, including the concrete’s age, strength, and local area aspect ratio. The main contribution of this study is a novel formula to forecast the concrete’s bearing strength while accounting for the impact of the concrete’s age and the ratio $\sqrt{{\displaystyle \frac{A_1}{A_b}}}$.

2. Experimental Work

2.1. Materials

2.1.1. Concrete

The same concrete mix was used to cast sixteen concrete pedestals. According to

Table 1. Elements of the concrete (kg/m³).

Basalt Dolomite	Cement	Sand	Water
1280	300	650	150

, the concrete mixture was made up of Portland cement, water, graded crushed basalt dolomite up to 15 mm in size as a coarse aggregate, and sand as a fine aggregate. The ratio of cement to water was 0.5. The grading of fine aggregate was ranging from 0.075 mm to 2.36 mm. Ordinary Portland cement in grade 42.5 was utilized. The CEM I-42.5N cement type has an average compressive strength of 42.5 Mpa after 28 days. This cement has a specific gravity of 3.14 and a specific surface area of 3055 cm²/gm. The cement’s initial and ultimate set times are 60 min and 6 h, respectively, and the cement paste’s consistency is 24%. The concrete mix’s compressive capacity was fixed at 30 Mpa. To determine the concrete mix’s compressive strengths at 3, 7, 15, and 28 days, 150 mm cubes were cast. At the same intervals, the cylinders (150 × 300 mm) were also cast to determine their tensile splitting values.

2.1.2. Bearing Plate

A metal thick plate was used over the surface of the concrete specimens to represent local loading. Normal mild steel (NMS) was the type of steel plate used in this study. The mechanical characteristics of the employed steel materials were assessed by tension testing. The elasticity modulus of NMS is 202 Gpa, and its yield and final resistances are 255 and 355 Mpa, correspondingly.

2.2. Pedestal Sample’s Specification

The local compressive strength of the concrete supports at various ages under 28 days is the main subject of this work. The bearing plate’s (A_b) area and the concrete’s age are the factors. Every concrete block was 250 × 250 mm in cross-section and 200 mm in height. Additionally, every sample used the identical concrete mix. The block’s (A₁) top surface measured 250 × 250 mm. A steel bearing plate was positioned in the center of each block’s top surface to provide bearing stress to that area. The bearing plate’s area (A_b = b × b) measured 100 × 100 mm, 80 × 80 mm, 60 × 60 mm, and 40 × 40 mm. Figure 1 and

Table 2. Sample details.

Studied Parameter	Group	Specimen	Concrete Age (Day)	Pedestal Area A1 (mm)	Plate Area Ab = b × b (mm)	$\frac{{\mathit{A}}_1}{{\mathit{A}}_{\mathit{b}}}$	$\sqrt{\frac{{\mathit{A}}_1}{{\mathit{A}}_{\mathit{b}}}}$	Concrete Cover c (mm)	c/b
Bearing concentration level (A1/Ab) at age = 3 day	G3	3d4p	3	250 × 250	40 × 40	39.06	6.25	105	2.63
		3d6p	3	250 × 250	60 × 60	17.36	4.17	95	1.58
		3d8p	3	250 × 250	80 × 80	9.77	3.13	85	1.06
		3d10p	3	250 × 250	100 × 100	6.25	2.50	75	0.75
Bearing concentration level (A1/Ab) at age = 7 day	G7	7d4p	7	250 × 250	40 × 40	39.06	6.25	105	2.63
		7d6p	7	250 × 250	60 × 60	17.36	4.17	95	1.58
		7d8p	7	250 × 250	80 × 80	9.77	3.13	85	1.06
		7d10p	7	250 × 250	100 × 100	6.25	2.50	75	0.75
Bearing concentration level (A1/Ab) at age = 15 day	G15	15d4p	15	250 × 250	40 × 40	39.06	6.25	105	2.63
		15d6p	15	250 × 250	60 × 60	17.36	4.17	95	1.58
		15d8p	15	250 × 250	80 × 80	9.77	3.13	85	1.06
		15d10p	15	250 × 250	100 × 100	6.25	2.50	75	0.75
Bearing concentration level (A1/Ab) at age = 28 day	G28	28d4p	28	250 × 250	40 × 40	39.06	6.25	105	2.63
		28d6p	28	250 × 250	60 × 60	17.36	4.17	95	1.58
		28d8p	28	250 × 250	80 × 80	9.77	3.13	85	1.06
		28d10p	28	250 × 250	100 × 100	6.25	2.50	75	0.75

show configuration of the concrete pedestal samples while Figure 2 shows casting process of all samples. When the bearing plate area was changed (A_b= 100 × 100, 80 × 80 mm, 60 × 60 mm, and 40 × 40 mm), the block area-to-bearing plate area ratio (A₁/A_b) or the load concentration ratio was calculated. 6.25, 9.76, 17.36, and 39 were the A₁/A_b values. Since the ratio (A₁/A_b) is the primary factor influencing the bearing strength in the international codes, this study is concentrating on it. This item was approximated in Table 2 for all samples since the square root of A₁/A_b was included to the bearing formula in nearly all codes. As shown in Figure 1, concrete cover thickness around the bearing plate © was estimated for all samples and listed in Table 2. The c value was 105 mm, 95 mm, 85 mm and 75 mm while concrete cover-to-bearing plate size ratio (c/b) was 2.63, 1.58, 1.06 and 0.75. The sample name denotes the age of the concrete and the area of the bearing plate (for example, sample 7d10p was tested at 7 days under 10 cm plate).

In this study, concrete age was measured at 3, 7, 15, and 28 days to assess its strength development. These time periods align with common testing practices, such as those outlined in the ACI code [15], and are approximately multiples of seven. They correspond to 0.5, 1, 2, and 4 weeks, with 28 days being the standard benchmark for concrete strength, though strength can continue increasing significantly over time. Testing at seven days is useful, as concrete typically reaches about half of its 28-day strength by then, providing early insight into its performance. This allows decision-makers to detect potential issues early rather than delaying corrective actions. The 14-day test, positioned between the 7- and 28-day marks, offers additional assurance for construction managers that the concrete is progressing as expected.

2.3. Test Setup and Measurements

A bearing concrete pedestal testing apparatus is shown in Figure 3. The bearing plate at the top of the concrete sample was subjected to compression pressure using a compression test equipment (NL SCIENTIFIC, Selangor, Malaysia). This apparatus measured the applied stress, and a displacement gauge recorded the bearing plate’s corresponding slip. Slippage beneath the bearing plate (S) was recorded in relation to the applied load (P). Additionally, during testing, cracks were noticed and noted.

3. Test Results and Analysis

3.1. Compression and Tension Tests

The primary metric that has traditionally been employed to describe concrete features for use in design is strength at compression. This is mostly because testing this attribute is simple. Consequently, a lot of research has been done on this metric. Three standard cubes (150 mm side) were prepared and used for the compression testing at 3, 7, 15, and 28 days, according to ECP 203-2018 [25], in order to ascertain the concrete’s compression properties at various ages.

Table 3. Results of the tested cubes.

Sample ID	Compressive Strength fc (MPa)	Increase in the fc (%)	Tensile Strength fct (MPa)	Increase in the fct (%)
3d	11.2	0.00	0.84	0.00
7d	18.5	65.18	1.63	94.05
15d	23.6	110.71	2.11	151.19
28d	31.2	178.57	2.89	244.05

showed the average compression property (f_c) for each level. At 3, 7, 15, and 28 days, the concrete’s f_c was 11.2, 18.5, 23.6, and 31.2 MPa, respectively. As the amount of time following the casting increased, it was observed that the f_c significantly improved. When the concrete age grew to 7, 15, and 28 days, respectively, the f_c rose by 65, 110, and 178% in comparison to 3 days-concrete. Additionally, to ascertain the tension (f_ct) property of the concrete at various ages, splitting tension tests were performed on three standard cylinders (150 mm in diameter and 300 mm in height) at 3, 7, 15, and 28 days. Table 3 showed the average tension property (f_ct) for each stage. At 3, 7, 15, and 28 days, the concrete’s f_ct was 0.84, 1.63, 2.11, and 2.89 MPa, respectively. As the amount of time after the casting increased, it was observed that the f_ct clearly improved. When the concrete age grew to 7, 15, and 28 days, respectively, the f_ct rose by 94, 151, and 244% in comparison to 3 days-concrete.

Due to the difference in concrete resistance (f_c or f_ct) between previous studies, it is preferable to present the results of the f_c or f_ct in a form suitable for comparison with previous studies. Therefore, the concrete resistance at any time (f_c)_t or (f_ct)_t in days was divided by the concrete resistance at 28 days (f_c)₂₈ or (f_ct)₂₈, then the relationship between normalized concrete resistance and the time was drawn in Figure 4. An almost identical similarity was revealed between the evolution of the behavior of concrete in compression and tension over time. It turns out that normalized concrete resistance is directly proportional to time. It is clear that growth is rapid in the first 3 days, and then this growth gradually decreases. The reason for the growth of concrete strength is the continuation of hydration reactions over time. Most of the compounds responsible for strength are produced in the first days after casting. Over time, the concrete gains strength, but slowly.

The compressive response of early strength saltwater and sea sand engineered cementitious composites (ESSECC) was investigated by Wang et al. [26]. With a compressive strength of more than 29.2 MPa in 2 h and more than 54.7 MPa at 28 days, a unique high early strength ECC was created using seawater and sea sand. The findings demonstrated the ductility of ESSECC specimens under uniaxial compression. High compressive strength may be attained with ESSECC early on. At two hours, three days, and seven days, the average compressive strengths were 58.0%, 81.6%, and 86.7% of the 28-day strength, correspondingly.

3.2. Bearing Tests

3.2.1. Collapses of the Concrete Pedestals

At beginning of the loading, the concrete did not crack. With increase of the loading, the cracks appeared at the concrete sample sides at 85–90% of the maximum load. Once the loads that are put on the surfaces of concrete components are greater than the concrete’s capacity, the components will break. Localized harm, particularly near the contact area’s outer border, is a kind of failure mechanism that has been seen during experiments. This finding has been shown to be similar to earlier research [27,28,29,30], where the opposite of pyramid collapse was seen at the contact area’s outside border, as depicted in Figure 5. Throughout the tests, other fail patterns such as splitting wedges, fragile breakage, and breaking crack were noted. It must be mentioned that once loaded areas of 80 mm × 80 mm and 100 mm × 100 mm were utilized, no upside-down pyramid pattern formed. The cracking images indicate that a vertical crack develops within the concrete sample as the applied load progressively rises. The samples then exhibit an opposite pyramid structure when the stress exceeds their limitation amount. The collapsed shapes indicate a conical wedge blasted out from under the steel bearing plate. It turns out that tiny plate areas like 40 mm and 60 mm have larger drops beneath the regional load on the concrete face. In small plate areas, concrete cracks abruptly and rapidly. There was no discernible variation in the amount of collapse caused by the age of the concrete at different plate sizes.

The likelihood of this type of collapse is influenced by the concrete’s compressive strength and the bearing load area. Higher compressive strength reduces the risk of collapse, while a larger bearing area slows and minimizes failure. To prevent such failures in design, a safety factor must be incorporated. This ensures that the design load remains below the concrete’s maximum bearing capacity, preventing it from reaching critical failure limits.

3.2.2. Bearing Stress Versus the Loaded Plate Slip

According to the outcomes of the concrete pedestal samples’ experimental assessments, the link between displacement and bearing stress is given. Figure 6 and Figure 7 show the bearing stress against deformation graph for various plate sizes and concrete ages. The findings demonstrated the nonlinearity of the bearing stress–plate slip correlations. At initial load, the plate slip increased somewhat while the bearing stress increased at a reasonably high pace. Following that, when the loading rose, the plate slips obviously increased while the bearing stress grew at a very sluggish rate. The concrete sample’s loss capacity abruptly decreased after the curve peaked, causing the curve to abruptly decline. It was discovered that a 40 mm plate area resulted in a very steep drop following the curve’s crest, indicating abrupt bombardment collapse—something structural designers do not want. On the contrary, samples with relatively large areas, such as 80 mm, showed a gradual decline after the peak of the curve, which indicates the elongation and slow collapse preferred by the codes. Additionally, a 40 mm plate area resulted in a small slippage about 2.5 mm while the samples with relatively large areas, such as 80 mm, showed a large slippage of the bearing plate (higher than 3.2 mm). Figure 6 shows effect of local area aspect ratio (A₁/A_b) on bearing stress–slip curves at different ages.

Group G3 included four samples having three-day age while group G7 composed of samples having seven-day age. Group G15 included four samples having fifteen-day age while group G28 composed of samples having twenty-eight-day age. All four groups showed same trend of the bearing stress–slip curves at different ages. The curve of the sample with a small plate, such as 40 mm, showed the highest load capacity values and the least deformations. In other words, as A₁/A_b increased, the sample resisted higher bearing stresses. At the same level of the deformation (horizontal axis), the bearing stress of the samples subjected to small plate area was higher than that of the samples subjected to big plate area. This noticeable improvement in bearing capacity occurred because the thickness of the concrete surrounding the loaded plate was greater in the samples tested under the small plate. On the contrary, this distance was small in samples with a large plate. The thickness of the concrete surrounding the loaded plate causes enclosure of the loaded concrete portion directly below the plate, which increases the concrete’s resistance and delays collapse.

Bearing resistance is directly influenced by the concrete’s compressive strength—an increase in compressive strength enhances bearing strength. Therefore, a thorough understanding of compressive strength behavior is crucial, as previously discussed [31].

Figure 7 shows effect of concrete age on the bearing stress–slip curves at different A₁/A_b. All four groups showed same trend of the bearing stress–slip curves at different A₁/A_b. The curve of the sample having high age, such as 28 d, showed the highest load capacity values and the least deformations. In other words, as concrete age increased, the sample resisted higher bearing stresses due to the completion of the hardening process. At the same level of the deformation (horizontal axis), the bearing stress of the samples having high age was higher than that of the samples having little age. This improvement in bearing capacity occurred because Hardening reaches advanced levels.

3.2.3. Bearing Strength

Effect of Local Area Aspect Ratio (A₁/A_b)

Figure 8 shows values of ultimate bearing strength (f_bu) of all samples. Group G₃ composed of four concrete blocks (3d10p, 3d8p, 3d6p and 3d4p). All these samples had age equal three days after casting. Sample 3d10p was loaded by steel plate 100 mm at its top while samples 3d8p, 3d6p and 3d4p were tested under steel plates 80, 60 and 40 mm, respectively. It is clear that the smaller the area of the loading plate, the greater the bearing resistance (f_bu) significantly. The f_bu of the samples 3d10p, 3d8p, 3d6p and 3d4p was 28.1, 39, 65 and 99.23 MPa, respectively. In most codes, an equation is presented to calculate bearing resistance (f_bu) based on the square root of the A₁/A_b. So, the relationship between the f_bu and square root A₁/A_b was drawn in Figure 9 for G3-samples. Square root A₁/A_b was 2.5, 3.13, 4.17 and 6.25 for samples 3d10p, 3d8p, 3d6p and 3d4p, respectively. It is clear that as the square root A₁/A_b increased, the f_bu noticeably improved. As listed in

Table 4. Effect of key variables on the ultimate bearing strength at different ages of concrete.

Group	Specimen	Concrete Age (Day)	$\sqrt{\frac{{\mathit{A}}_1}{{\mathit{A}}_{\mathit{b}}}}$	c/b	fbu (Mpa)	Gain in fbu (%)
G3	3d10p	3	2.5	0.75	28.1	0.00
	3d8p	3	3.13	1.06	39	38.79
	3d6p	3	4.17	1.58	65.05	131.49
	3d4p	3	6.25	2.63	99.23	253.13
G7	7d10p	7	2.5	0.75	31.2	0.00
	7d8p	7	3.13	1.06	43.3	38.78
	7d6p	7	4.17	1.58	69	121.15
	7d4p	7	6.25	2.63	150	380.77
G15	15d10p	15	2.5	0.75	34.1	0.00
	15d8p	15	3.13	1.06	51.2	50.15
	15d6p	15	4.17	1.58	85.2	149.85
	15d4p	15	6.25	2.63	155.3	355.43
G28	28d10p	28	2.5	0.75	44.2	0.00
	28d8p	28	3.13	1.06	60	35.75
	28d6p	28	4.17	1.58	94.2	113.12
	28d4p	28	6.25	2.63	168.2	280.54

, the fbu of the samples 3d8p, 3d6p and 3d4p was 38.79, 131.5, and 253.13%, respectively, higher than that of sample 3d10p having 100 mm-bearing plates. In other words, when the $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ increased from 2.5 to 3.13, 4.17, and 6.25, the fbu increased by 38.79, 131.5, and 253.13%, respectively. This finding confirms the commonly accepted theory that raising the percentage of unloaded to loaded area (A₁/A_b) can raise the f_bu. The concrete sample with a greater contact area received the weight that was implied on the concrete sample via a bearing plate. This suggests that before the concrete sample achieves its maximum value, the rise in the vicinity correlates with quality as a function of its ability to carry loads [30].

It is possible to explain the improvements in the bearing resistance (f_bu) due to the smaller bearing plate area if we calculate the thickness of the concrete around the bearing plate. As the plate area decreases, the thickness of the concrete around it increases. As listed in Table 4, the concrete cover-to-bearing plate area ratio (c/b) was 0.75, 1.06, 1.58 and 2.63 in the samples 3d10p, 3d8p, 3d6p and 3d4p, respectively. In this study, we can call this ratio the confinement factor. The greater the confinement factor, the larger the concrete surrounding the local load area will be, which leads to an improvement in the concrete’s resistance and delayed collapse. The splitting that occurs in the concrete surrounding the load plate is delayed the greater this factor is. When the c/b increased from 0.75 to 1.06, 1.58 and 2.63 in the samples 3d8p, 3d6p and 3d4p, respectively, the f_bu increased by 38.79, 131.5, and 253.13%, respectively.

Four concrete blocks (7d10p, 7d8p, 7d6p, and 7d4p) make up group G7. Seven days following casting, all of these samples were the same age. While samples 7d8p, 7d6p, and 7d4p were tested beneath steel plates 80, 60, and 40 mm, respectively, sample 7d10p was mounted onto a steel plate 100 mm at the top. It is evident that the f_bu increases noticeably with decreasing loading plate area. Samples 7d10p, 7d8p, 7d6p, and 7d4p have respective f_bu values of 31.2, 43.3, 69, and 150 MPa. The $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ was 2.5, 3.13, 4.17 and 6.25 for samples 7d10p, 7d8p, 7d6p and 7d4p, respectively. It is evident that the f_bu significantly improved as the square root A₁/A_b raised. Table 4 shows that samples 7d8p, 7d6p, and 7d4p had f_bu values of 38, 121.15, and 380.77 percent, respectively, higher than sample 7d10p with a 100 mm-bearing plate. In other words, when the $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ increased from 2.5 to 3.13, 4.17, and 6.25, the f_bu increased by 38, 121.15, and 380.77%, respectively.

The confinement factor (c/b) for samples 7d10p, 7d8p, 7d6p, and 7d4p was 0.75, 1.06, 1.58, and 2.63, respectively, as indicated in Table 4. The f_bu rose by 38, 121.15, and 380.77 percent when the c/b in samples 7d8p, 7d6p, and 7d4p increased from 0.75 to 1.06, 1.58, and 2.63, respectively.

Group G15 consists of four concrete blocks: 15d10p, 15d8p, 15d6p, and 15d4p. These samples were at the same age fifteen days after casting. It is clear that when the loading plate area decreases, the f_bu rises considerably. The f_bu values of samples 15d10p, 15d8p, 15d6p, and 15d4p are 34.1, 51.2, 85, and 155 MPa, respectively. As the square root A1/Ab increased, it is clear that the f_bu greatly improved. In comparison to sample 15d10p with a 100 mm-bearing plate, samples 15d8p, 15d6p, and 15d4p had f_bu values of 50, 149.15, and 355.77 percent, respectively, as shown in Table 4. In other words, the f_bu increased by 50, 149.15, and 355.77 percent, respectively, when the $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ climbed from 2.5 to 3.13, 4.17, and 6.25. Table 4 shows that samples 15d10p, 15d8p, 15d6p, and 15d4p had confinement factors (c/b) of 0.75, 1.06, 1.58, and 2.63, respectively. When the c/b in samples 15d8p, 15d6p, and 15d4p went from 0.75 to 1.06, 1.58, and 2.63 percent, respectively, the f_bu increased by 50, 149.15, and 355.77 percent.

The four concrete blocks that make up group G28 are 30d10p, 30d8p, 30d6p, and 30d4p. Twenty-eight days after casting, these samples were the same age. It is evident that the f_bu increases significantly as the loading plate area shrinks. Samples 30d10p, 30d8p, 30d6p, and 30d4p have respective f_bu values of 44.2, 60, 94, and 168 MPa. It is evident that the f_bu significantly improved as the square root A1/Ab rose. As seen in Table 4, samples 30d8p, 30d6p, and 30d4p had f_bu values of 35.75, 113, and 280.54 percent, respectively, in contrast to sample 30d10p with a 100 mm-bearing plate. In other words, the f_bu increased by 35.75, 113, and 280.54 percent, respectively, when the $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ climbed from 2.5 to 3.13, 4.17, and 6.25. The f_bu rose by 35.75, 113, and 280.54 percent when the c/b in samples 30d8p, 30d6p, and 30d4p changed from 0.75 to 1.06, 1.58, and 2.63 percent, respectively.

Effect of Concrete Age

Table 5. Effect of concrete age on the ultimate bearing capacity of the concrete samples.

Group	Specimen	Concrete Age (Day)	$\sqrt{\frac{{\mathit{A}}_1}{{\mathit{A}}_{\mathit{b}}}}$	c/b	fbu (Mpa)	Gain in fbu (%)
GI; plate 40 mm	3d4p	3	6.25	2.63	99.23	0.00
	7d4p	7	6.25	2.63	150	51.16
	15d4p	15	6.25	2.63	155.3	56.51
	28d4p	28	6.25	2.63	168.2	69.51
GII; plate 60 mm	3d6p	3	4.17	1.58	65.05	0.00
	7d6p	7	4.17	1.58	69	6.07
	15d6p	15	4.17	1.58	85.2	30.98
	28d6p	28	4.17	1.58	94.2	44.81
GIII; plate 80 mm	3d8p	3	3.13	1.06	39	0.00
	7d8p	7	3.13	1.06	43.3	11.03
	15d8p	15	3.13	1.06	51.2	31.28
	28d8p	28	3.13	1.06	60	53.85
GV; plate 100 mm	3d10p	3	2.5	0.75	28.1	0.00
	7d10p	7	2.5	0.75	31.2	11.03
	15d10p	15	2.5	0.75	34.1	21.35
	28d10p	28	2.5	0.75	44.2	57.30

lists effect of concrete age on the ultimate bearing capacity of the concrete samples. The samples were divided into groups (GI, GII, GIII and GV); each one included four samples subjected to same bearing plate area (A_b). For each group, the bearing plate area, concrete cover and square root of local area aspect ratio were stayed constant. The A_b was 40 mm, 60 mm, 80 mm and 100 mm in group GI, GII, GIII and GV, respectively. The $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ was 6.25, 4.17, 3.13 and 2.5 in group GI, GII, GIII and GV, respectively. Also, c/d was 2.63, 1.58, 1.06 and 0.75 in group GI, GII, GIII and GV, respectively. The concrete age was varied (3, 7, 15 and 28 d) in each group. In general, it was noticed that as the concrete age increased, the ultimate bearing strength (f_bu) improved more. The f_bu of the samples 3d4p, 7d4p, 15d4p and 28d4p was 99.23, 150, 155.3 and 168.2 MPa, respectively. In other words, the f_bu of was 99.23, 150, 155.3 and 168.2 MPa, respectively, when the concrete age reached 3, 7, 15 and 28 d in the samples 3d4p, 7d4p, 15d4p and 28d4p. The relationship between the f_bu and concrete age was drawn in Figure 10 for GI-samples. The f_bu of the samples 7d4p, 15d4p and 28d4p improved by 51, 56.5, and 69.5%, respectively, compared to sample 3d4p that tested at 3 days. When the concrete age climbed from 3 to 7, 15 and 28 days in the samples 7d4p, 15d4p and 28d4p, the f_bu improved by 51%, 56.5%, and 69.5%.

Samples 3d6p, 7d6p, 15d6p, and 28d6p in group GII had f_bu values of 65, 69, 85, and 94.2 MPa, respectively. To put it another way, the f_bu of samples 3d6p, 7d6p, 15d6p, and 28d6p was 65, 69, 85, and 94.2 MPa, respectively, when the concrete age reached 3, 7, 15, and 28 days. For GII-samples, the correlation between the f_bu and concrete age was depicted in Figure 10. In comparison to sample 3d6p, was tested after three days, the f_bu of samples 7d6p, 15d6p, and 28d6p improved by 6, 31, and 44%, respectively. The f_bu increased by 6, 31, and 44% in samples 7d6p, 15d6p, and 28d6p as the concrete age increased from 3 to 7, 15, and 28 days.

Samples 3d8p, 7d8p, 15d8p, and 28d8p in group GIII had f_bu values of 39, 43.3, 51, and 60 MPa, respectively. To put it another way, the f_bu of samples 3d8p, 7d8p, 15d8p, and 28d8p was 39, 43.3, 51, and 60 MPa, respectively, when the concrete age reached 3, 7, 15, and 28 days. For GIII-samples, the correlation between the f_bu and concrete age was depicted in Figure 10. In comparison to sample 3d8p, was tested after three days, the f_bu of samples 7d8p, 15d8p, and 28d8p improved by 11, 31.28, and 53.85%, respectively. In samples 7d8p, 15d8p, and 28d8p, the f_bu increased by 11, 31.28, and 53.85% as the concrete age increased from 3 to 7, 15, and 28 days.

Samples 3d10p, 7d10p, 15d10p, and 28d10p in group GV had f_bu values of 28, 31, 34, and 44 MPa, respectively. In other words, when the concrete age reached 3, 7, 15, and 28 days in the samples 3d10p, 7d10p, 15d10p, and 28d10p, the f_bu was 28, 31, 34, and 44 MPa, respectively. For GV-samples, the relationship between the f_bu and concrete age was depicted in Figure 10. In comparison to sample 3d10p, was tested after three days, the f_bu of samples 7d10p, 15d10p, and 28d10p improved by 11, 21.35, and 57.3%, respectively. In samples 7d8p, 15d8p, and 28d8p, the f_bu increased by 11, 21.35, and 57.3 percent as the concrete age increased from 3 to 7, 15, and 28 days.

3.2.4. Ultimate Deformation

Slip under the bearing plate was recoded against the applied bearing load. For each sample, the corresponding slip (∂u) to ultimate bearing strength (f_bu) was obtained. Effect of both local area aspect ratio (A₁/A_b) and concrete age on the ultimate deformation (∂u) of all samples are discussed in the following sections.

Effect of Local Area Aspect Ratio (A₁/A_b)

Figure 11 shows deformation values under the bearing plates at the top of tested concrete pedestals at different concrete ages. In each group, there was a one sample was loaded by steel plate 100 mm at its top while there are three samples were tested under steel plates 80, 60 and 40 mm. generally, it is clear that the smaller the area of the loading plate, the smaller the bearing slip (∂u) significantly. In most codes, an equation is presented to calculate bearing resistance (f_bu) based on the square root of the A₁/A_b. So, the relationship between the ∂u and square root A₁/A_b was drawn in Figure 12 for all groups. It is clear that as the square root A₁/A_b increased, the ∂u noticeably declined. In groups G3, G7, G15, and G28, the samples were at the same age 3, 7, 15, and 28 days after casting. The same behavior occurred in all groups at different concrete ages (3, 7, 15, and 28 days).

The experiment revealed that as the bearing area ratio (A₁/A_b) increased, the bearing strength of the concrete improved while deformation decreased. To ensure safety, both bearing strength and deformation capacity must remain within acceptable limits. The maximum permissible resistance was determined to prevent exceedance, and the corresponding deformation of the loading plate at this value was calculated. Finally, the actual values were compared to the maximum allowable limits, incorporating safety factors.

At ages 3, 7, and 15 days, the deformation beneath the bearing plate varied with the square root of the local area aspect ratio. When the ratio was 2.5, deformation reached 2.7 mm; at 3.13, it was 2.6 mm; at 4.13, it decreased to 2.45 mm; and at 6.25, it further reduced to 2.1 mm. These results indicate that as the local area aspect ratio increases, deformation under the bearing plate decreases.

Effect of Concrete Age

Figure 13 illustrates how the age of the concrete affects the samples’ eventual bearing deformation capacity. Effect of concrete age on the deformation values under the bearing plates at the top of tested concrete pedestals at different plate areas was discussed. Each group (GI, GII, GIII, and GV) contained four samples that were exposed to the identical bearing plate area (A_b = 40 × 40 mm², 60 × 60 mm², 80 × 80 mm², and 100 × 100 mm²). The concrete age (3, 7, 15, and 28 days) was changed for each group, but the bearing plate area, concrete cover, and square root of local area aspect ratio remained unchanged. Overall, it was found that as the concrete aged, the ultimate bearing slip either remained constant or slightly decreased. In concrete samples, the bearing plate’s drop value varied with plate size. For a 40 mm plate, the drop was approximately 2.1 mm, increasing to 2.45 mm for a 60 mm plate, 2.67 mm for an 80 mm plate, and 2.78 mm for a 100 mm plate. These results indicate that larger bearing plates lead to greater deformation.

4. Proposed Formulas

To calculate the concrete bearing resistance (${\mathrm{f}}_{\mathrm{b}\mathrm{u}}$), ACI code [15] induced the following Formula (1).

$${\mathrm{f}}_{\mathrm{b}\mathrm{u}}=0.7225{\mathrm{f}}_{\mathrm{c}}\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$$

(1)

where ${\mathrm{f}}_{\mathrm{c}}$ is concrete compressive strength of each concrete pedestal. ${\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}$ is ratio between the bearing area aspect ratio. For all tested concrete blocks, the ${\mathrm{f}}_{\mathrm{b}\mathrm{u}}$ was calculated using Equation (1) and predicted findings were compared to experimental values in Figure 14 and

Table 6. Comparison between experimental ultimate bearing strength (f_bu,E) and theoretical ones (f_bu,ACI) using ACI equation.

Specimen	fc (MPa)	fbu,E (MPa)	Concrete age T (day)	$\sqrt{\frac{{\mathit{A}}_1}{{\mathit{A}}_{\mathit{b}}}}$	fbu,ACI (MPa)	fbu,E/fbu,ACI
3d10p	11.2	28.1	3	2.5	20.23	1.39
3d8p	11.2	39	3	3.13	25.33	1.54
3d6p	11.2	65.05	3	4.17	33.74	1.93
3d4p	11.2	99.23	3	6.25	50.58	1.96
7d10p	18.5	31.2	7	2.5	33.42	0.93
7d8p	18.5	43.3	7	3.13	41.84	1.03
7d6p	18.5	69	7	4.17	55.74	1.24
7d4p	18.5	150	7	6.25	83.54	1.80
15d10p	23.6	34.1	15	2.5	42.63	0.80
15d8p	23.6	51.2	15	3.13	53.37	0.96
15d6p	23.6	85.2	15	4.17	71.10	1.20
15d4p	23.6	155.3	15	6.25	106.57	1.46
28d10p	31.2	44.2	28	2.5	56.36	0.78
28d8p	31.2	60	28	3.13	70.56	0.85
28d6p	31.2	94.2	28	4.17	94.00	1.00
28d4p	31.2	168.2	28	6.25	140.89	1.19

for all tested samples. The results indicate that the ACI code equation [15] is inaccurate for most samples. In 3-day-old specimens, the equation significantly underestimated the experimental values, likely because it is designed for samples older than 28 days. Additionally, the equation generally produced lower values than the experimental results due to its limitation on the area aspect ratio, which must not exceed $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ = 2. In contrast, all samples in this study had ratios greater than 2, further contributing to the discrepancy. Therefore, it is necessary to introduce an amendment to the ACI equation to be able to predict the bearing strength of the concrete, taking into account the effect of the age of the concrete and the ratio $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$.

In order to develop new formulae that could estimate the ultimate bearing strength for all examined samples, the study findings were submitted to linear multiple regressions. Excel data analytics was used to look into it. The bearing area ratio and the concrete’s age are the input factors that are taken into account for this study. The output parameters were determined to be the ultimate bearing strength.

Consequently, a new equation that can predict the bearing strength of the concrete while accounting for all of these variables was developed using the results of the samples examined in this study. After many mathematical trails, the Equation (2) was the best fit formula to estimate the ultimate bearing strength (${\mathrm{f}}_{\mathrm{b}\mathrm{u}}$) of the tested samples taking into account the effect of the age of the concrete (T) and the ratio $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$.

$${\mathrm{f}}_{\mathrm{b}\mathrm{u}}={\mathrm{f}}_{\mathrm{c}}\left[{\displaystyle \frac{3}{2}}\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}-{\displaystyle \frac{8\mathrm{T}}{103}}-1\right]$$

(2)

The inputs of the new proposed Equation (2) were listed in

Table 7. Comparison between experimental ultimate bearing strength (f_bu,E) and theoretical ones (f_bu,th).

Specimen	fc (MPa)	fbu,E (MPa)	Concrete age T (day)	$\sqrt{\frac{{\mathit{A}}_1}{{\mathit{A}}_{\mathit{b}}}}$	fbu,th (MPa)	fbu,E/fbu,th
3d10p	11.2	28.1	3	2.5	28.19	1.00
3d8p	11.2	39	3	3.13	38.77	0.99
3d6p	11.2	65.05	3	4.17	56.25	0.86
3d4p	11.2	99.23	3	6.25	91.19	0.92
7d10p	18.5	31.2	7	2.5	40.82	1.31
7d8p	18.5	43.3	7	3.13	58.30	1.35
7d6p	18.5	69	7	4.17	87.16	1.26
7d4p	18.5	150	7	6.25	144.88	0.97
15d10p	23.6	34.1	15	2.5	37.40	1.10
15d8p	23.6	51.2	15	3.13	59.71	1.17
15d6p	23.6	85.2	15	4.17	96.52	1.13
15d4p	23.6	155.3	15	6.25	170.15	1.10
28d10p	31.2	44.2	28	2.5	17.95	0.71
28d8p	31.2	60	28	3.13	47.43	0.79
28d6p	31.2	94.2	28	4.17	96.10	1.02
28d4p	31.2	168.2	28	6.25	193.45	1.15

. The last column of Table 7 shows experimental-to-theoretical bearing strength ratio (f_bu,E/f_bu,th) of tested samples using proposed equation. This ratio was approximately equal to 1 in all samples, which indicates that the predicted values were close to experimental ones. Structural designers will benefit from this equation, as it provides a valuable tool for determining early-age concrete strength. This is particularly useful for projects requiring early loading due to time constraints, ensuring safe and efficient construction.

5. Conclusions

The local compressive strength of the concrete supports at various ages under 28 days is the main subject of this work. Concrete’s load-bearing strength is crucial for reducing construction risks and enhancing building safety. Size of concrete pedestals was constant (250 × 250 × 200 mm) while the bearing plate’s area (A_b) was varied. A steel bearing plate was positioned in the center of each block’s top surface to provide bearing stress to that area. The bearing plate’s area measured 100 × 100 mm, 80 × 80 mm, 60 × 60 mm, and 40 × 40 mm. sixteen concrete supports were tested under local compressive stresses. The bearing area aspect ratio or unloaded-to-loaded area (A₁/A_b) was 6.25, 9.76, 17.36, and 39. The bearing tests were conducted at concrete age equal 3, 7, 15, and 28 days. Effect of both bearing area aspect ratio and concrete age on the collapse, bearing stress–slip response, ultimate bearing strength and ultimate deformation of the tested concrete supports was studied in details. The results confirm the following observations:

• Compared to 3 days-concrete, the compressive strength increased by 65, 110 and 178% while the tension strength increased by 94, 151 and 244% when the concrete age climbed to 7, 15 and 28 days, respectively.
• The concrete samples failed due to concrete splitting near the contact bearing area’s outer border.
• The bearing stress–plate slip curve of the samples with a small plate area, such as 40 mm, showed the highest bearing capacity values and the least deformations. As A₁/A_b increased, the sample resisted higher bearing stresses.
• At the same level of the bearing plate area, the bearing stress of the samples having high age was higher than that of the samples having little age.
• At concrete age equals 3 days, when the $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ increased from 2.5 to 3.13, 4.17, and 6.25, the ultimate bearing strength of the samples increased by 38.79, 131.5, and 253.13%, respectively. At all concrete ages, as the $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ increased, the ultimate bearing strength of the samples improved more.
• When the concrete age of the samples climbed from 3 to 7, 15 and 28 days, the ultimate bearing strength improved by 51 %, 56.5 %, and 69.5 % at $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ equals 6.25. Additionally, it was found that as the concrete age of the samples increased, the ultimate bearing strength whatever $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$ is varied.
• A new equation was proposed to be able to predict the bearing strength of the concrete, taking into account the effect of the age of the concrete and the ratio $\sqrt{{\displaystyle \frac{{\mathrm{A}}_1}{{\mathrm{A}}_{\mathrm{b}}}}}$.

Limitations of this investigation are: size of concrete pedestals was 250 × 250 × 200 mm, the bearing plate’s area (A_b) was varied (100 × 100 mm, 80 × 80 mm, 60 × 60 mm, and 40 × 40 mm), the steel bearing plate was positioned in the center of each block’s top surface, and the bearing tests were conducted at concrete age equal 3, 7, 15 and 28 days.