Diaphragm wall-soil-cap interaction in rectangular-closed- diaphragm-wall bridge foundations

Abstract

Rectangular-closed-diaphragm-wall foundation is a new type of bridge foundation. Diaphragm wall-soil-cap interaction was studied using a model test. It was observed that the distribution of soil resistance under the cap is not homogeneous. The soil resistance in the corner under the cap is larger than that in the border; and that in the center is the smallest. The distribution of soil resistance under the cap will be more uniform, if the sectional area of soil core is enlarged within a certain range. Due to the existence of cap, there is a “weakening effect” in inner shaft resistance of the upper wall segments, and there is “enhancement effect” in the lower wall segments and in toe resistance. The load shearing percentage of soil resistance under the cap is 10%-20%. It is unreasonable to ignore the effects of the cap and the soil resistance under the cap in bearing capacity calculations.

Keywords

diaphragm wall / bridge foundation / low cap / interaction

Introduction

A new type of bridge foundation, called rectangular-closed-diaphragm-wall foundation, as shown in Fig. 1, is composed of a cap and diaphragm walls. The diaphragm walls under cap are connected with rigid joints, which form a rectangular frame in the horizontal section [1]. Because of its rectangular-tubular shape in structure form, rectangular-closed-diaphragm-wall foundation is also called “shaft-diaphragm-wall foundation” [2,3].

In 1979, rectangular-closed-diaphragm-wall foundation instead of open caisson foundation was used in viaduct engineering on the Northeast Shinkansen in Japan, which paved the way for diaphragm wall technique to be applied in bridge foundation engineering [4]. Thereafter, the rectangular-closed-diaphragm-wall foundation was developed rapidly in Japan [5-7]. But in China, diaphragm walls are mostly used in foundation pit support or seepage control. Recently, the diaphragm walls were also used as part of the main building structure, and the vertical load from the superstructure is supported directly by diaphragm walls [8,9]. However, it is just beginning in China that rectangular-closed-diaphragm-wall is used as bridge foundation and is bearing vertical load by itself [10,11].

During the construction of rectangular-closed-diaphragm wall, the center soil surrounded by trenches is kept undisturbed [12]. And a relatively closed “soil core” which is enwrapped by diaphragm walls and cap is formed, as shown in Fig.1. The working mechanism of closed-diaphragm-wall foundation is much more complex than the single-diaphragm-wall foundation under vertical loading. For closed-diaphragm-wall, the soil under cap, the soil core, the stratum under wall toes and the walls themselves are all bearing the vertical loads; and there is an interaction between bearing factors. But up to now, the systematic and deepening research on closed-diaphragm-wall soil interaction is still quite insufficient [12].

The development and engineering application of bearing capacity theory for rectangular-closed-diaphragm wall are restricted, because of the complexity of rectangular-closed-diaphragm-wall soil interaction. Therefore, a model test for rectangular-closed-diaphragm-wall bridge foundation was conducted for the first time in China, and the diaphragm wall-soil-cap interaction was studied by the model test.

Model test

In order to compare the bearing behaviors of rectangular-closed-diaphragm-wall and that of single-diaphragm-wall, a closed-diaphragm-wall model and a single-diaphragm-wall model were installed simultaneously at the same model tank. Besides, for investigating the influence of soil core area on the diaphragm wall-soil-cap interaction, two groups of closed- and single-diaphragm-walls with different sectional dimensions were made and tested in turn.

Model making

The diaphragm wall models were made of 32-mm-thick organic glass boards which were custom-made from the manufacturer. The sectional dimension of the single-diaphragm-wall model in group A was 280 mm×32 mm and that of the single-diaphragm-wall model in group B was 380 mm×32 mm. The height of both the single-diaphragm-wall models was 770 mm. The outer sectional dimension of the closed-diaphragm-wall model in group A was 280 mm×280 mm and the inner sectional dimension was 216 mm×216 mm. In addition, the outer sectional dimension of the closed-diaphragm-wall model in group B was 380 mm×380 mm and the inner sectional dimension was 316 mm×316 mm. The height of both the closed-diaphragm-wall models was 720 mm. And the thickness of all diaphragm wall models is 32 mm.

The surface of all the diaphragm wall models was glued with fine sand for the sake of increasing the roughness [13]. The diameter of the fine sand was controlled within the range of 1-3 mm. The glue was a mixture of epoxy resin and 650 curing agent with a proportion of 1∶1.

Model soil

The disturbed loess Q₄, carried from Wanrong County of Shanxi Province, was used as model soil. The layout of the soil in the model test is shown in Fig. 2. At first, the 10-cm inverted filter, composed of gravel whose particle size is less than 12 mm, was installed at the bottom of the model test tank. Over the inverted filter, there is double steel wire mesh with pore size of 0.4 mm and 10 cm sand layer overlying on the mesh. Subsequently, the prepared model soil was filled layer by layer with required density.

The embedded depth of all the diaphragm wall models was 72 cm. The stratum under the wall toe, with a thickness of 72 cm, was filled by 7 layers with a density of 1.5 g/cm³. The thickness of the soil layer around the diaphragm-wall models was also 72 cm, and the soil layer was filled by 7 layers with a density of 1.4 g/cm³. The physico mechanical characters of the soil are shown in Table 1.

Layout of testing elements

There were 2 dial indicators at the top of the single-diaphragm-wall and 2 at the top of the closed-diaphragm-wall respectively to measure the displacement of wall tops. And there were 2 miniature earth pressure cells under the single-diaphragm-wall and 2 under the-closed-diaphragm-wall respectively to measure the toe resistance. Besides, for the purpose of measuring the soil resistance under the cap, 3 miniature earth pressure cells were disposed under the cap to measure the soil resistance in the corner, in the border, and in the center respectively.

There were 42 foil strain gauges divided into 6 columns pasted on the surface of the diaphragm-wall-models, of which 2 columns were used for the single-diaphragm-wall and 4 columns used for the closed-diaphragm-wall as shown in Fig.3(b). The vertical layout of the strain gauges is shown in Fig. 3(a).

Loading device

The loading device of the diaphragm-wall models is a simple and convenient lever loading device (see Fig.4). The cast iron weights of 10 kg were used as lever loading. And the plate of the weights was made of 10 mm steel plate.

Data acquisition

The values of strain for the diaphragm wall shaft were collected automatically by the YE2539 static strainmeter. The values of strain, from the miniature earth pressure cells and measured by the YE2539 static strainmeter, could be obtained by a conversion coefficient. The displacement of the wall tops could be read from the dial indicators.

Test results

Load-settlement behavior of diaphragm wall

Figure 5 shows the load-settlement relationship of two groups of the diaphragm walls. The Q-s curves of the single-diaphragm-walls are abruptly decreasing, and their characteristics of breakage are much obvious. For the single-diaphragm-wall A (in group A), when the load increases to 3.0 kN, the settlement of the wall top obviously increases, and the shaft resistance inclines towards being fully mobilized. Thereafter, the increased load was born by the toe resistance. When the load increases to 4.8 kN, the single-diaphragm-wall A breaks with large settlement. The Q-s curve of the single-diaphragm-wall B is similar to that of the single-diaphragm-wall A. When the load increases to 3.3 kN, the settlement of the single-diaphragm-wall B increases obviously. And when the load increases to 4.8 kN, the single-diaphragm-wall B breaks with large settlement either.

Because the Q-s curves of the closed-diaphragm-walls decrease slowly, there is no obvious breakage characteristic. Because the load of the closed-diaphragm-walls was born by inner and outer shaft resistance, soil resistance is under cap and toe resistance. At the beginning of loading, the load was mainly born by outer shaft resistance. With increasing of the load and settlement of the closed-diaphragm-walls, the inner shaft resistance, soil resistance under the cap and toe resistance were mobilized gradually and bore the main increased load. Thereupon, under the interaction of the diaphragm-wall-soil-cap, the closed-diaphragm-walls exhibited good bearing capacity. Up to the last load grade, the Q-s curves of the closed-diaphragm-walls are slowly decreasing also.

Using the determination method of ultimate bearing capacity of pile foundation, the corresponding load at the starting point of abruptly decreasing in the Q-s curve is taken as the ultimate bearing capacity of the single-diaphragm-walls [14]. In this way, the ultimate bearing capacity of the single-diaphragm-wall A is 3.9 kN and that of the single-diaphragm-wall B is 4.2 kN.

Since the Q-s curves of the closed-diaphragm-walls are slowly decreasing, the ultimate bearing capacity of the closed-diaphragm-walls depends on the s-lgQ curve and the comprehensive consideration of settlement [15]. So, it can be determined that the ultimate bearing capacity of the closed-diaphragm-wall A is 9.6 kN while that of the closed-diaphragm-wall B is 18 kN.

Distribution of soil resistance under cap

Figure 6 shows the soil resistance under the caps dependent of load. Because of the difference of load magnitude for two groups of the closed-diaphragm-walls, the soil resistance under the cap at the corresponding load level (the ratio of i-grade load Q_i and the last grade load Q_last) was used for comparison and analysis. As shown in Fig.6, the distribution of the soil resistance under the cap is that the soil resistance in the corner under the cap is larger than that in the border, and the soil resistance in the center is the smallest. This is similar to the basic law for soil resistance under cap in pile group foundation that “the nearer to the edge of cap, the larger soil resistance under cap is” [16].

Besides, the soil resistance under the cap of the closed-diaphragm-wall B at the corresponding load level is larger than that of the closed-diaphragm-wall A. Because the sectional area of soil corn for the closed-diaphragm-wall B is 2.14 times than that of the closed-diaphragm-wall A, and the augmentation of sectional area of soil corn improved the development of soil resistance under cap.

Along with the increase of load, the increment of the soil resistance in the corner under the cap is larger than that in the border, and the increment of the soil resistance in the center is the smallest. The ratio of the soil resistance in the corner, border and center enlarge continuously. When the corresponding load level increases to 100%, the ratio of the soil resistance in the corner, border and center of the closed-diaphragm-wall A is 7.4∶3.2∶1, yet the ratio of the closed-diaphragm-wall B is 4.3∶2∶1. It is obvious that not only the average value of the soil resistance under the cap of the closed-diaphragm-wall B is larger than that of the closed-diaphragm-wall A, but also the distribution of the soil resistance under the cap of the closed-diaphragm-wall B is more uniform than that of the closed-diaphragm-wall A.

Figure 7 shows the relationship between the settlement and soil resistance under the caps of the closed-diaphragm-walls. With the development of wall-top displacement and slab deformation, the soil under the cap is compressed without lateral deformation, the soil is more compact and its compression modulus increases, so, the soil resistance under the caps increased too. It can be seen from Fig. 7 that the increasing rate of the soil resistance in the corner under the cap is the fastest, and that in the center is the slowest. The change curve of the soil resistance at the center becomes flat. When the wall-top displacement is less than 7 mm, the soil resistance in the corner under the cap of the closed-diaphragm-wall A is larger than that of the closed-diaphragm-wall B. But, with the development of wall-top displacement, the soil resistance in the corner under the cap of the closed-diaphragm- wall B increases more rapidly, when the displacement is greater than 7 mm, the soil resistance in the corner under the cap of the closed-diaphragm-wall B exceeds that of the closed-diaphragm-wall A. In addition, the soil resistance in the border and that in the center of the closed-diaphragm-wall B are larger than that of the closed-diaphragm-wall A. Therefore, the increase of the cap area is beneficial to the development of the soil resistance under the cap.

Influence of cap on shaft resistance

As shown in Figs. 8 and 9, the outer shaft resistance develops from top to bottom. When the load is small, the outer shaft resistance on the middle and upper wall segments is mobilized firstly, and the unit resistance value is much larger than that of the lower wall segments. With the increase of load and the development of wall-top displacement, the outer shaft resistance of the lower wall segments develops gradually. When the load increases to 60% of the last grade load, the outer shaft resistance of the closed-diaphragm-walls is fully mobilized. But, as shown in Fig. 6, when the load level reaches 60%, the soil resistance under the cap increases rapidly, which shows a characteristic of the closed-diaphragm-walls that the outer shaft resistance precedes the soil resistance under the cap to be mobilized.

However, the behavior of the inner shaft resistance is completely different from that of the outer shaft resistance. The outer shaft resistance develops from top to bottom, yet the inner shaft resistance develops from bottom to top. As shown in Figs.10 and 11, when the load is small, the inner shaft resistance of the wall segments with 0-40 cm embedded depth closes to 0. With the increase of load, the inner shaft resistance develops gradually, and, the deeper the wall segment is, the larger the increasing rate of inner shaft resistance is. The top soil of the soil core is compressed by the cap, and the soil core is dragged down by the inner shaft of the closed-diaphragm- wall. So, the diaphragm-wall-soil relative displacement is very small, which restricted the development of inner shaft resistance of the upper wall segments. Thus, the inner shaft resistance at the top of the soil core closes to 0. This is the “weakening effect” in the inner shaft resistance due to the cap.

With the increase of wall-top displacement, the soil core is compressed by the cap and could not produce lateral deformation for the role of circumjacent diaphragm-walls. Therefore, the relative density and internal friction angle of soil enlarges, the soil strength is improved, and the diaphragm wall-soil relative displacement increases. Otherwise, because of the compression of the soil, there was normal stress produced in the inner wall shaft. So the inner shaft resistance of the wall segments with 40-70 cm embedded depth is obviously greater than that of the upper wall segments. In other words, there is “enhancement effect” in the inner shaft resistance due to the cap. This effect is very obvious near the wall toe, and the unit inner shaft resistance even exceeds the unit outer shaft resistance with the same depth.

In contrast, the values of inner shaft resistance for the two closed diaphragm walls in 0-30 cm depth parts are very close. But in 30-70 cm depth wall segments, the unit inner shaft resistance of the closed-diaphragm-wall B is much larger than that of the closed-diaphragm-wall A. It is shown that the development of the inner shaft resistance improved by the increase of wall spacing. Meanwhile, the increase of sectional area of cap impels the corresponding increment of soil resistance under the cap, and the additional stress generated by the cap also increases, then the normal stress produced in the inner wall shaft is enlarged. So, the sectional dimension of the closed-diaphragm-wall is increased to some extent: the “enhancement effect” on the inner shaft resistance due to the cap is strengthened.

Influence of cap on toe resistance

Figures 12 and 13 show the relationship between the unit toe resistance of two groups of the diaphragm walls and wall-top displacement. Although the unit toe resistance of the closed-diaphragm-wall A is less than that of the single-diaphragm-wall A, with the increase of displacement, the unit toe resistance of the closed-diaphragm-wall A increases much more rapidly, and when the displacement is greater than 11 mm, the unit toe resistance of the closed-diaphragm-wall A exceeds that of the single-diaphragm-wall A. Yet the unit toe resistance of the closed- diaphragm-wall B is always larger than that of the single-diaphragm-wall B, and with the increase of displacement, the difference of the unit toe resistance continues to enlarge.

In general, there is a “settlement hardening” phenomenon in the toe resistance of the closed-diaphragm-walls. Because of the vertical overlapped stress caused by the soil resistance under the cap and the shear stress of the inner wall shaft at the wall toe level, the principal stress difference is narrowed at the wall toe level and the lateral deformation of the soil at the wall toe is restricted by the circumjacent diaphragm walls. Besides, it is similar to the low cap composite pile foundation, that the diaphragm wall-soil relative displacement and penetration of the wall toe are restricted by the cap’s effect, which improved the toe resistance of the closed-diaphragm-walls. So, there is a certain “enhancement effect” on the toe resistance for the existence of the cap.

Load shearing behaviors

Figures 14 and 15 show the load shearing behaviors of the closed-diaphragm-walls. It is observed that the laws of the load shearing magnitude for the two closed-diaphragm-walls are very similar. At the beginning of loading, the magnitude and increasing rate of the soil resistance under the cap and toe resistance are small, yet the shaft resistance develops very well and the increasing rate of that is fast. With the increase of load, the increasing rate of the shaft resistance becomes slow, and the increasing rate of the soil resistance under the cap and toe resistance is fast.

Figure 16 shows the load-load shearing ratio curves of the closed-diaphragm-walls. Obviously, with the increase of load, the load shearing percent of the shaft resistance decreases gradually, while the load shearing percent of the soil resistance under the cap and toe resistance are increased continuously. With the relatively small sectional dimension of the closed diaphragm wall A (the cap area is small too), the soil resistance under the cap could not develop well, and the load shearing percent of the soil resistance under the cap of the closed-diaphragm-wall A was less than that of the closed-diaphragm-wall B. In addition, the inadequate development of the soil resistance under the cap weakened the “enhancement effect” on toe resistance, so, the load shearing percent of the toe resistance of the closed-diaphragm-wall A is less than that of the closed-diaphragm-wall B, too [17].

When the wall-top load reaches limited load, the load shearing percent of the soil resistance under the cap of the closed-diaphragm-wall A is 11.3%, and that of the closed-diaphragm-wall B is 17.8%. Therefore, as a part of the vertical load bearing capacity of the closed-diaphragm-wall foundation, the soil resistance under the cap is indispensable. But in current calculation method of bearing capacity of the closed-diaphragm-wall foundation in Japan [18], the role of cap and soil resistance under cap was ignored. This is unreasonable because the calculated results are less than the practical ones, and the design based on the calculated results would be conservative. Thus, found waste would be produced to a certain extent for the design size (sectional dimension or embedded depth) of closed diaphragm wall which is too large, and which will decrease the economic benefit of closed diaphragm wall foundation.

Conclusions

Using a model test, the diaphragm-wall-soil-cap interaction was studied. The following conclusions can be made as follows:

1) The distribution of the soil resistance under the cap is not uniform. The soil resistance in the corner under the cap is larger than that in the border, and the soil resistance in the center is the smallest. The distribution of soil resistance under the cap will be more uniform, if the sectional area of soil core is enlarged to a certain extent.

2) Due to the existence of the cap, there is “weakening effect” on the inner shaft resistance of the upper wall segments, and there is “enhancement effect” on the lower wall segments.

3) There is “enhancement effect” on the toe resistance also for the existence of the cap. And the larger the cap area is, the more obvious the enhancement effect is.

4) The load shearing percentage of the soil resistance under the cap is 10%-20%. It is unreasonable to ignore the effect of the cap and the soil resistance under the cap in bearing capacity calculations.

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