1. Explanation of Relevant Code Provisions 

Article 5.2.4 of the 'Code for Design of Building Foundation' (referred to as the Code) states that the characteristic value of foundation bearing capacity determined by load tests or other in-situ test results, empirical values, etc., requires depth correction. Its provision explanation also includes a passage: "Currently, there are many structures with main building and podium integrated in construction projects. For the depth correction of the foundation bearing capacity of the main structure, the load within the range above the foundation base should preferably be considered as the surcharge on both sides of the foundation. When the surcharge width is greater than twice the foundation width, the surcharge can be converted into soil layer thickness as the foundation embedment depth. When the surcharges on both sides of the foundation are unequal, the smaller value should be taken."

Currently, the understanding of depth correction of foundation bearing capacity in the engineering field is still very confused. This article intends to further summarize the essence of depth correction of foundation bearing capacity, elaborate its application in several common foundation forms, and analyze several popular understandings in the engineering field, hoping to be helpful to the majority of designers.

2. Essence and Key Points of Depth Correction of Foundation Bearing Capacity 

2.1 Essence and Key Points of Depth Correction

References [1] and [2] point out that the depth correction of foundation bearing capacity is to consider the resistance effect of the surcharge q above the foundation base elevation on both sides of the foundation against the upward sliding of the sliding soil mass on both sides of the foundation. This surcharge can be intuitively understood as the pressure weight acting on the surface of the sliding soil mass, as shown in Figure 1. The surcharge q can be the soil self-weight q = rd; it can also be the continuous uniform pressure generated by the podium. The calculation formula can refer to the Code formula (5.2.2-1). Note that live loads should be reduced according to the requirements of Article 4.1.2 of the 'Load Code'.

Therefore, combining the foundation failure mechanism and the premise of establishing the calculation formula, several elements of depth correction of foundation bearing capacity are summarized as follows:

(1) The depth correction of foundation bearing capacity is actually the pressure weight effect of the surcharge. Whether using the natural embedment depth of the soil or converting other continuous uniform pressure weights such as the podium into soil thickness for depth correction of foundation bearing capacity, the essence is the manifestation of the surcharge on both sides of the foundation resisting the upward movement of the sliding soil mass.

(2) Requirements for continuity, uniformity, and a certain distribution width of the surcharge. The establishment of the foundation bearing capacity calculation formula is based on the premise that the surcharge q is a continuous uniform load acting on the entire surface of the sliding mass. According to the Code and the recommendations of Reference [2], the depth correction of foundation bearing capacity can be performed as long as the distribution width of the surcharge satisfies the requirement of being greater than (2~4) B (B is the foundation width). If the surcharge is formed by natural soil layers, this load is basically continuous and uniform. Pressure weights such as podiums may not necessarily form a continuous uniform surcharge; see the detailed analysis below.

(3) Requirement to take the minimum value. Foundation failure generally occurs at the weakest part, so the minimum value of the embedment depth (or converted embedment depth) around the foundation should be taken for depth correction.

Understanding the essence of depth correction of foundation bearing capacity, the problem of depth correction can be transformed into considering the magnitude and distribution of the surcharge within the range of 2~4 times the foundation side length around the foundation (indicated by the reverse diagonal lines in Figure 2). By grasping the above three elements, the problem of determining the depth correction value for general engineering can basically be solved.

Figure 2 Schematic Plan of Surcharge Action

2.2 Misunderstandings in Design and Explanations

(1) The "load within the range above the foundation base" in the provision explanation refers to the foundation pressure at the foundation base elevation of the podium on both sides of the main building.

"Load within the range above the foundation base" refers to the foundation pressure at the foundation base elevation of the main building on both sides of the main building (see Figure 1).

The problem arising from this misunderstanding is: when the foundation base elevation of the podium is above the foundation base elevation of the main building (as shown in Figure 3), the surcharge effect formed by the H-h thick soil is underestimated. In this case, the calculated embedment depth d used for depth correction = the average vertical pressure transmitted from the superstructure of the podium to the top of the foundation under standard combination of load effects plus the soil thickness d1 converted from the self-weight of the podium foundation + (H-h).

Figure 3 Calculated Embedment Depth When Podium Base Elevation Is Above Main Building Base Elevation

(2) "Surcharge" refers to the part of the foundation pressure that "exceeds" the self-weight stress of the soil layer at the embedment depth.

From the above analysis, it can be seen that "surcharge" is not additional stress.

(3) Determine the equivalent embedment depth of the foundation using the actual reaction at the foundation base elevation.

According to the Code formula (5.2.2-1), the foundation base reaction value p (see Figure 1) is related to the vertical force transmitted from the superstructure to the top of the foundation, the self-weight of the foundation, and the soil weight on the foundation. It has no direct relationship with the surcharge on both sides of the foundation. Therefore, doing so is unreasonable.

(4) Confusing the principle of depth correction of foundation bearing capacity with the long-term consolidation improvement effect of foundation bearing capacity.

Foundation bearing capacity is different from the bearing capacity of the superstructure; it is closely related to foundation deformation. Under long-term loading on the foundation, the foundation deformation and settlement tend to stabilize, so the foundation bearing capacity can be appropriately increased. It can be seen that the consolidation improvement mechanism of foundation bearing capacity is different from the pressure weight effect of the surcharge.

(5) When the foundation bearing capacity is determined by deep load tests, depth correction is still performed.

When the characteristic value of foundation bearing capacity is determined by deep load tests, the surcharge on both sides already exists, so the Code stipulates that depth correction is not required.

(6) The converted thickness of the surcharge used for depth correction of foundation bearing capacity should not be greater than the natural embedment depth of the foundation.

As long as the surcharge satisfies the above three elements, it should be allowed for depth correction of foundation bearing capacity. It should not be limited by the natural embedment depth.

(7) Take the average or weighted average of the embedment depths (or converted embedment depths) on both sides of the foundation for depth correction of bearing capacity.

From the failure mode, when the pressure weights on both sides of the foundation are different, the sliding surface of failure naturally occurs first on the side with lighter pressure weight. The provision explanation of the Code "When the surcharges on both sides of the foundation are unequal, take the smaller value" reflects this concept. Before sufficient demonstration, taking the smaller value is safer.

(8) Only consider correction along the short side direction of the foundation, not the long side direction.

When the surcharges around the structure are similar and the length and width differ greatly, failure generally does not occur along the long side. In this case, it is acceptable to consider the short side (B direction). However, when the length-to-width ratio of the structure is close to 1, it is safer to take the minimum embedment depth (converted embedment depth) around the foundation for depth correction.

3. Considerations and Suggestions When the Podium Side Length Is Less Than 2 Times the Main Building Side Length 

As shown in Figure 4, the podium side length is less than 2 times the main building side length. Two cases are considered.

(1) When the converted depth at the podium is greater than the natural embedment depth, according to the Code requirements, taking the natural embedment depth for depth correction is acceptable. However, the author believes that when the podium can form a relatively continuous uniform surcharge, the pressure weight effect of the podium can be appropriately considered, and the calculated embedment depth can be taken between the converted embedment depth of the podium and the natural embedment depth. Because there is no authoritative information in this regard, the specific value should be chosen carefully or refer to engineering experience.

(2) When the converted embedment depth at the podium is not greater than the natural embedment depth, the Code does not clearly specify. At this time, taking the converted embedment depth and considering the smaller value should be reasonable and safer. Of course, as mentioned above, from the pressure weight mechanism, the larger pressure weight of the natural embedment depth can also be appropriately considered, but it should also be done with caution.

Figure 4 Case Where Podium Side Length Is Less Than 2 Times Main Building Side Length

4. Examples of Calculated Embedment Depth for Various Foundation Types

4.1 Strip or isolated foundations are shown in Figure 5 (a), (b).

4.2 Integral foundations such as box foundations or raft foundations are shown in Figure 5 (c).

4.3 Isolated foundation + waterproof slab is shown in Figure 5 (d).

The magnitude of the foundation reaction of the waterproof slab is closely related to its construction [3]. When a soft cushion is set under the waterproof slab to ensure that the waterproof slab does not bear or bears the minimum foundation reaction, the foundation reaction q under the soft cushion can consider the self-weight of the waterproof slab, the weight of the basement floor construction, etc. If a general cushion is used under the waterproof slab, the waterproof slab and the foundation will jointly bear the force transmitted from the superstructure, and the foundation reaction is obtained by analysis and calculation.

Figure 5 Schematic of Calculated Embedment Depth in Various Cases (d in the figure represents calculated embedment depth)

For column spacing of 6~8m and slab thickness plus plain concrete cushion of about 500mm, the foundation reaction of the waterproof slab cannot form a uniform load, so the average foundation pressure q cannot be fully used as a surcharge for depth correction of the bearing capacity under the isolated foundation. Many designers reduce the average foundation pressure as a surcharge, i.e.,

(1) In the formula, a is the reduction coefficient. The value of the reduction coefficient depends on the column span, slab thickness, and soil properties. The smaller the column spacing, the thicker the raft, and the better the foundation soil, the less the reduction. However, due to the lack of information in this regard, the magnitude of the bearing capacity correction is highly empirical; related discussions are in Reference [1]. However, the reduction coefficient should not be too small; otherwise, the calculated converted depth de is less than the distance d1 from the podium indoor floor to the foundation base, which is meaningless.

The calculated embedment depth is taken as the smaller of the outdoor embedment depth and the converted embedment depth.

5. Examples of Depth Correction of Foundation Bearing Capacity for Main Building with Podium 

To highlight the problem, only the case of the short side direction of the structure, the same natural embedment depth on both sides of the foundation, the podium side length greater than 2 times the main building side length, and the main building foundation being a box or raft foundation with good integrity is explained.

5.1 Main building and podium integrated

The calculated embedment depth is taken as the minimum converted embedment depth on the left and right sides, as shown in Figure 6 (a).

5.2 Joint set between main building and podium, filled with coarse sand to compact the ground

Since coarse sand can transmit horizontal forces, the depth correction of the foundation bearing capacity of the main building can refer to the case of main building and podium integrated, as shown in Figure 6 (b).

5.3 Podium with isolated foundations

Because the isolated foundations of the podium cannot form a continuous uniform distributed load, the contribution of the podium load to the surcharge cannot be considered. The calculated embedment depth should be the natural embedment depth measured from the podium indoor floor, as shown in Figure 6 (c).

5.4 Podium with isolated column foundations + waterproof slab

As analyzed in 4.3, the waterproof slab cannot form a uniform load. It is advisable to conduct reaction tests under the waterproof slab, accumulate certain measured data, and then reduce the foundation reaction according to formula (1) as a surcharge, as shown in Figure 6 (d).

Figure 6 Schematic of Depth Correction of Foundation Bearing Capacity for Main Building with Podium (d in the figure represents calculated embedment depth)