*2.2. Calculation Method*

The most important link of FCB displacement control of a subgrade is to identify the replacement thickness of the roadbed. This currently relies heavily on the layerwise summation method for estimation of total deposition, as well as comparative analysis with settlement monitoring data available before improvement, leading to the determination of the replacement thickness [18] in the transverse hole for the filling of the road embankment stage, which mainly depends on the layerwise summation method. When this method is used to calculate the settlement under complex loading and unloading conditions, it produces large errors.

For easier calculation of displacement thickness. Chen [19] had proposed a calculation formula of unloading quantity, but it is necessary to be combined with engineering practice to determine the parameters, which has a high cost. Thus, based on the formula proposed by Chen and the ratio variation between load and settlement, a method for calculating unloading according to the settlement is proposed as follows:

$$P\_{\mathbf{c}} = \mathbf{h} \cdot (\gamma\_1 - \gamma\_0) \tag{1}$$

where *γ*<sup>1</sup> is the embankment unit weight that generally ranges between 19.0 and 21.0 kN/m3, and *γ*<sup>0</sup> is the foamed lightweight concrete embankment wet unit weight ranging between 5.5 and 6.0 kN/m3; *Pc* is the embankment unloading amount, and *h* is the replacement thickness.

At present, the existing settlement data is mainly used to predict the settlement curve, and the replacement thickness is determined according to the result. The weight of embankment was reduced by replacing the undisturbed soil, which can reduce settlement. Therefore, when the monitored settlement data does not meet the requirements, the embankment should be improved. The unloading value is mainly determined by the difference between the bulk density of the replacement material and the undisturbed soil mass. Thus, the method proposed in this paper has an advantage of calculating the unloading value of the overload embankment to a certain extent, even though there is a difference in establishing the initial expression. To devise an expression that can calculate the replacement thickness under different conditions, including overload, equivalent load, and under load conditions (i.e., after embankment soil replacement with FCB), further research on the relationship between foundation consolidation settlement and pressure must be conducted.

Based on the assumption that unloading construction is not performed on the embankment, the embankment ultimate settlement under pressure *<sup>P</sup>*<sup>0</sup> is *<sup>S</sup>p*+Δ*<sup>p</sup>* <sup>∞</sup> , and the observed foundation settlement before unloading construction is *Sm*. If embankment unloading construction is implemented and the unloading amount is *Pc*, the embankment residual weight *P*<sup>1</sup> *<sup>u</sup>* induces the ultimate settlement *S<sup>h</sup>* <sup>∞</sup>, and a formula for settlement calculation can be given as follows:

$$\frac{S^{p+\Delta p}\_{\infty}}{S^{\rm h}\_{\infty}} = \frac{P\_0}{P^1\_{\mu}}\tag{2}$$

Owing to the fact that the settlement calculation considers rebound under unloading conditions, the following concepts should be clarified. When unloading *Pc* in FCB embankment replacement is completed, the load *Pc* · *Sm*/*SP*+Δ*<sup>P</sup>* <sup>∞</sup> had converted into effective load, unloading this part of the load will cause rebound. As a result, this part of the capacity should take the swelling index caused by unloading into account, the swelling index is usually taken as *δ* times the compression settlement (engineering empirical suggested range of values: 0.05–0.03). Meanwhile, the other part of the load that is not converted is *Pc* · (<sup>1</sup> <sup>−</sup> *Sm*/*SP*+Δ*<sup>P</sup>* <sup>∞</sup> ), and its settlement computation is suggested to confirm normal compression settlement. Therefore, the settlement caused by unloading is expressed as:

$$S\_c = \frac{\left[1 - (1 - \delta)\frac{S\_{\rm tr}}{S\_{\rm co}^{P + \Delta P}}\right]}{P\_0} \cdot P\_c \cdot S\_{\rm co}^{P + \Delta P} \tag{3}$$

After unloading construction, the actual remaining consolidation settlement *S*<sup>1</sup> *<sup>m</sup>* is expressed as:

$$\mathbf{S}\_{m}^{1} = \mathbf{S}\_{m} - \mathbf{S}\_{c} = \mathbf{S}\_{m} - \frac{[1 - (1 - \delta)\frac{\mathbf{S}\_{m}}{S\_{\infty}^{P + \Delta P}}]}{P\_{0}} \cdot P\_{c} \cdot \mathbf{S}\_{\infty}^{P + \Delta P} \tag{4}$$

Considering the allowable post-construction settlement Δ*S* in design work, by summing the actual remaining settlement *S*<sup>1</sup> *<sup>m</sup>* and allowable post-construction settlement Δ*S*, the total ultimate settlement *S<sup>h</sup>* <sup>∞</sup> induced by the residual embankment load after moving the load *Pc* is obtained:

$$S\_m^1 + \Delta S = S\_\infty^h \tag{5}$$

$$P\_{\mathcal{E}} = \frac{P\_0 \cdot (S\_{\infty}^{P + \Delta P} - S\_{\text{m}} - \Delta S)}{(1 - \delta) \cdot S\_{\text{m}}} = \theta \cdot P\_0 \cdot (\frac{S\_r - \Delta S}{S\_{\text{m}}}) \tag{6}$$

where *Sr* is the residual settlement before improvement with FCB, *Sr* <sup>=</sup> *<sup>S</sup>P*+Δ*<sup>P</sup>* <sup>∞</sup> <sup>−</sup> *Sm*; *Sm* is the monitoring data during construction; *SP*+Δ*<sup>P</sup>* <sup>∞</sup> is the computed ultimate settlement under the embankment load *P*<sup>0</sup> function; *P*<sup>0</sup> is the embankment gravity load, and Δ*S* is the design-allowable post-construction settlement for which a local standard is suggested for determining its value. *ϑ* is the rebound correction factor expressed as *ϑ* = 1/(1 − *δ*), where *δ* is the swelling index within the range 0.05–0.3.

Under the condition that the embankment design applies overload pre-loading, if the calculated subgrade unloading confirms that *Pc* ≤ *P*<sup>0</sup> − *Pu*, *Pu* is the amount of overload, the post-construction settlement requirement can be satisfied after removing the overload pressure. When *Pc* > *P*<sup>0</sup> − *Pu*, except for removing overload, it is necessary to apply FCB to process the excess load, *Pc* − (*P*<sup>0</sup> − *Pu*). If equivalent load pre-compression is applied in embankment reinforcement, the computation of FCB replacement thickness should take the unloading value *Pc* into account. If the embankment design condition is under load pre-compression (*P*<sup>0</sup> ≤ *Pu*), computation of the FCB replacement thickness should confirm the expression: *Pc* + *Pu* − *P*0.

In order to use equation (6) to calculate unloading value, parameters *P*<sup>0</sup> and *Sm* can be acquired by measuring before unloading, and *δ* is determined either by laboratory sample testing or by practical engineering empirical estimation. Δ*S* is allowable postconstruction settlement decided by local standard regulations [20]. The ultimate settlement *SP*+Δ*<sup>P</sup>* <sup>∞</sup> contributing to the pre-loading effect before unloading, it can be obtained by conventional layerwise summation method or by prediction of measured settlement during preloading construction.

## **3. Field Study on Shen-Jia-Hu Highway**
