In the design of a diaphragm wall, several factors come into play. However, which ones have the greatest impact on the sizing and subsequent behavior of the structure? In this article, we review some of them.

đź“˘ Before we begin! I wrote this text a few years ago, and naturally, it incorporates information from various sources. Unfortunately, I haven’t kept all the references, and I could only recover the ones included at the end of the article. If you recognize any unacknowledged source, please let me know so that I can incorporate it.

Returning to the topic of the article, when designing a diaphragm wall, we must pay special attention to the following factors:

- Soil parameters.
- Water table level.
- Soil pressures.
- Soil-wall friction.
- Loads from adjacent structures.
- Stability, capacity, and waterproofing checks.
- Movements.

### Soil parameters

The first topic to be studied when designing a diaphragm wall is the soil in which it will be constructed. The available geotechnical information is not always as extensive and precise as we would like, but it should be demanded that it is sufficient to define some fundamental soil parameters: density (apparent and submerged if there is a water table), internal friction angle, cohesion, elastic modulus, modulus of subgrade reaction, etc. If this information is lacking, it is advisable to carry out additional investigative campaigns.

The lack of geotechnical information can lead to considering overly conservative soil properties, which sometimes deviate from the actual behavior of the structure we are designing. It may be more advisable to use soil parameters adjusted to the available field data and subsequently apply overall safety factors directly proportional to the uncertainty of the geotechnical data. On the other hand, probabilistic analyses are increasingly used in the geotechnical field, and the quality of the existing data plays a fundamental role in them.

When calculating diaphragm walls, it is recommended to be cautious with the geotechnical data but not overly conservative to avoid erroneous modeling of the structure.

In the calculation of diaphragm walls in cohesive soils, a double verification should be carried out, considering total and effective stresses, and varying the internal friction angle and cohesion from their undrained values to the drained values. The selection of one set of values or the other depends mainly on the duration of the different phases of the construction process. However, the calculation based on effective stresses is usually on the side of safety in most cases and is often used as the sole model.

Regarding cohesion, it is not recommended to be overly optimistic in its assessment as it has a decisive influence on the magnitude of soil pressures.

If there are not enough characterization tests available, it is prudent to assign zero cohesion to granular soils and a maximum value of 2 to 3 T/m2 to cohesive soils.

As for the modulus of subgrade reaction, which is necessary to apply stress-deformation models based on the Winkler method, it is important to remember that it represents the relationship between the deflection of the wall and the pressure at the measurement point. There are numerous proposals to define this parameter by linking it to variables such as the elastic modulus, pressuremeter modulus, dimensions of the loaded portion, stiffness of the wall, etc. For example, Chadeisson’s chart relates the modulus of subgrade reaction to the internal friction angle and cohesion. The result obtained from this chart is usually conservative, so in the absence of experimental results, it can be used for an initial approximation of the modulus of subgrade reaction value.

The modulus of subgrade reaction is not an intrinsic property of the soil but depends on the load surface.

### Water table level

The pressure generated by water is perhaps the most important factor in the calculation of a diaphragm wall. While in the previous section, it was advised to adopt characteristic values for the parameters, when it comes to the water table level, it is advisable to be conservative.

The considered water table level should not be based on a single measurement but should encompass the possible fluctuations that may occur over a representative period of time.

When determining the water table level, historical records should be studied to account for exceptional situations, and in any case, its position should be raised at least 1 meter above the maximum level detected in the geotechnical investigation.

Regarding the laws of interstitial pressures on both sides of the wall, it is common to consider hydrostatic values. It is possible that sufficiently impermeable layers may interrupt the vertical transmission of pressures, resulting in a more favorable pressure distribution. This fact should be experimentally verified through the installation of piezometers. Otherwise, it may be risky to consider laws different from hydrostatic conditions.

### Soil pressures

As mentioned earlier, current calculation models take into account that soil pressures vary with the displacement of the wall according to an elastoplastic law. For zero displacements, the pressure value will correspond to the at-rest condition, and at limit states, passive and active pressures will be reached, depending on the direction of displacement.

It is common to apply a safety factor of 1.50 to 2.00 to the passive pressure since a significant displacement of the structure is required to mobilize it. This practice makes sense in limit equilibrium methods where the soil is always assumed to be fully yielded, regardless of the level of deformation. However, in stress-deformation models where the pressures are defined at each moment by the displacement of the wall, adopting a high safety factor for the passive pressure can be excessively conservative.

### Soil-wall friction

Due to displacements and the roughness of concrete, the pressure exerted on the wall inclines at a certain angle with the horizontal, which promotes stability. The value of this angle (Î´) is always unknown and its influence in the calculation is crucial.

The Spanish Building Technical Code (CTE) limits the value of Î´ to 1/3Î¦ for passive pressure and 2/3Î¦ for active pressure (Î´=0 for active pressure if thixotropic slurries are used), where Î¦ is the internal friction angle of the soil. The Recommendations for Maritime Works (ROM), on the other hand, recommend moderate values of Î´, lower than Î¦ for both passive and active pressure. Other recommendations, such as those from the United States Army Corps of Engineers, indicate that Î´ should not exceed 1/3Î¦ for passive pressure and 1/2Î¦ for active pressure.

Considering a zero friction angle for the active pressure due to the use of thixotropic slurries overly penalizes the calculation and does not seem to align with reality if proper control of drilling slurries and the execution process of the wall is carried out. On the other hand, very high values of the friction angle can lead the calculation to the side of insecurity.

It is common to consider a friction angle between the diaphragm wall and the soil of 1/3Î¦ for both active and passive pressure.

### Overloads from neighboring structures

The effect of loads from neighboring structures on the diaphragm wall can be significant, especially if there are tall buildings or heavy structures nearby. In most calculations, solutions provided by elasticity theory are used for point loads, uniform loads, or strip loads.

It has been shown that, in some cases, the actual pressures are higher than the theoretical values provided by elasticity, so some authors recommend using a multiplication factor of up to 2.00 for these loads.

It is also true that when the loads are situated at a certain distance from the wall, the actual pressures can become negligible, while according to elasticity theory, they still have a significant effect. It is challenging to define from which point the loads have no influence on the wall. Some publications use the concept of the active wedge, such that any load located outside of it may not be considered in the calculation. It seems more prudent not to consider loads from neighboring structures when they are located at a distance from the wall greater than its depth, except for exceptional cases with significant loads (buildings with more than 15 floors).

If there is no information available regarding the type and configuration of the neighboring building’s foundation, it is common to consider an undefined load in the calculation located at the level of the last basement or at ground level if there are no basements, with a value of 1 T/m2 per floor of the building. If the actual soil volume occupied by the basements cannot be excluded from the calculation model, the weight of the soil located in that area should be subtracted from the obtained load. Such a load magnitude usually leads to conservative results. Obviously, if the location and shape of the foundation, as well as the load acting on it, are known, a more accurate calculation can be performed.

For example, a 10-story building on the surface with a single basement can be modeled by a load at approximately -3.00 meters level, with a value of 10.00 T/m2 minus the weight of the soil in the basement area. Assuming a soil density of 1.80 T/m3, the load generated by the building would be 10.00 – 1.80 x 3.00 = 4.60 T/m2.

In the calculation, the loads on the top of the diaphragm wall due to the superstructure must not be forgotten, nor the loads derived from supporting elements such as anchors, slabs, and beams.

To prevent piping, it is necessary to reduce the hydraulic gradient, so in normal situations, increasing the depth of the diaphragm wall is usually sufficient.

The water flow towards the excavation can also cause heave of the base. For this phenomenon to occur, there must be a relatively impermeable layer at the base, with an upward interstitial pressure greater than the weight of the soil above it.

In these cases, increasing the depth of the diaphragm wall is ineffective, and other possible solutions should be considered. It is common to improve the soil above the impermeable layer, for example, by using jet grouting columns, to increase the weight that resists heave. Bleeding wells can also be installed to release interstitial pressures in the problematic area.

The base of the shielded excavation should be thoroughly studied, and conservative calculation criteria are recommended for analyzing failure, piping, and heave phenomena.

### The stability, structural capacity, and impermeability of the diaphragm wall

The limit states of failure due to translation, rotation, or settlement must be properly studied.

The horizontal and bending moments generated by the external and internal sides of the wall must be balanced in all stages of construction, with an appropriate safety factor (typically between 1.50 and 2.00).

The diaphragm wall must be reinforced according to the stress envelope obtained in the calculation for all stages of the construction process, from the start of excavation to serviceability.

Regarding permeability, it should be noted that diaphragm walls are not completely impermeable structures. It is common for moisture to appear and minor water seepage to occur during excavation, through joints, connections, or even through the concrete of the diaphragm wall itself. This is also reflected in international standards, such as the European Standard EN 1538: “Execution of special geotechnical works: diaphragm walls.”

### Movements

The design of diaphragm walls must take into account the acceptable threshold of displacements in the surrounding area. The maximum level of displacements that can be tolerated depends on the proximity, typology, and condition of neighboring buildings, structures, and utilities.

Stress-strain methods allow for the calculation of deformations in the diaphragm wall during soil excavation. However, even with accurate knowledge of the movements, it is challenging to determine the induced settlements in the vicinity. On the other hand, current finite element/difference programs are capable of calculating settlements as they can include both the structure and its surroundings in the modeling.

Some authors have defined settlement distribution laws based on the maximum settlement of the diaphragm wall, which can be estimated as 75% of the maximum deflection value in the absence of specific information. Generally, beyond a distance from the diaphragm wall equal to twice the excavation depth, the settlements that occur are relatively small and have a lesser influence on neighboring constructions.

There are extensive inventories of measured deflections and settlements in diaphragm walls, relating the movements to the excavation height. However, the specific characteristics of each case require these values to be treated with a certain degree of skepticism.

When the surroundings of the diaphragm wall are sensitive, it is common to use angular distortion criteria to assess the potential harm caused by the settlements during excavation. There is no clear and universal limit for angular distortion that avoids damage to the surroundings, although a threshold of 1/1000 is often used as a reference (angular distortion is defined as the differential settlement recorded between two points divided by the distance between them).

As a summary of the above, a simple criterion is provided to limit the deflections of the diaphragm wall during the design phase. If Î´H represents the maximum deflection in the wall, H is the excavation height, and D is the distance between the diaphragm wall and neighboring buildings, the allowable deflections are indicated in the following figure.

Deflections below 15 mm in a diaphragm wall are typically indicative of minimal impact on buildings, structures, and utilities located in the vicinity.

These values are based on construction experience and the findings of significant studies in this field. However, each project requires a detailed study of the influence of diaphragm wall movements on the surrounding area.

### Conclusions

The design and calculation of diaphragm walls require careful consideration of various aspects due to their significant impact on the structural behavior. Soil parameters, such as strength and stiffness, must be accurately determined to assess the wall’s performance under different loading conditions. The water table level is crucial in evaluating potential groundwater effects, including uplift pressures and seepage forces. Soil pressures acting on the wall need to be analyzed to ensure stability and proper design of reinforcement.

Additionally, the soil-wall friction plays a vital role in the transfer of loads and overall stability of the wall. The interaction between the wall and adjacent structures must be carefully assessed to account for any additional loads imposed on the wall and potential differential movements.

Furthermore, it is essential to conduct thorough stability, capacity, and waterproofing checks during the design phase. These include evaluating global stability against sliding and rotation, examining the stability of the excavation bottom, and considering the potential for seepage and material drag due to water flow. The structural capacity of the wall and its elements must be verified to ensure it can withstand the applied loads and meet safety requirements.

Lastly, the assessment of movements is critical. Predicting and limiting displacements induced by the wall’s construction and subsequent loading is necessary to prevent detrimental effects on adjacent structures and ensure overall stability. Monitoring and managing these movements are essential to minimize any adverse impacts.

By addressing these aspects comprehensively, engineers can develop well-designed diaphragm walls that effectively support excavations, provide structural stability, and maintain their waterproofing properties. Consideration of soil parameters, water table level, soil pressures, soil-wall friction, loads from adjacent structures, stability, capacity, and movements collectively contribute to the successful performance of diaphragm walls in diverse geotechnical and construction scenarios.

**References**

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- RODRĂŤGUEZ ORTIZ, J.M. (2008). â€śAlgunos temas de interĂ©s en el diseĂ±o de muros pantallaâ€ť. Jornadas TĂ©cnicas SEMSIG â€“ AETESS. Muros Pantalla en Ăˇmbito urbano. Ed. Aetess.