JP5729754B2 - Seismic reinforcement structure for embankment and design method of underground wall used for it - Google Patents

Description

  The present invention mainly relates to a seismic reinforcement structure for embankments constructed on liquefied ground and a design method thereof.

  The ground liquefaction is caused by the fact that when horizontal force is applied to the ground during an earthquake, the pore water pressure between the sand particles increases due to the shear deformation of the ground, and the effective stress becomes zero as the pore water pressure increases. This is a phenomenon in which fluid transmission becomes impossible due to the inability to transfer stress between the two, and is likely to occur in loose saturated sandy ground (hereinafter, liquefied ground is referred to as liquefied ground).

  As liquefaction progresses, the ground loses its vertical bearing capacity, leading to collapse of the building, and damage to the piles due to lateral flow of the ground occurs. It has come to be clearly recognized.

  Various countermeasures have been researched and developed for such liquefaction damage. However, when embankment is constructed on liquefied ground, the method on both sides of the embankment is designed to sandwich the lower area of the embankment. A method is known in which steel sheet piles (sheet piles) are driven vertically downward from the bottom and their heads are connected to each other with a tensile material such as a tie rod.

  According to this countermeasure work, since the shear deformation of the ground spreading below the embankment is suppressed by the steel sheet pile, liquefaction of the ground is less likely to occur during an earthquake.

JP-A-10-131207 Japanese Patent Laid-Open No. 11-1926 JP 2009-79415 A

  However, if the earthquake significantly exceeds the scale assumed in the current design or the embankment scale is very large, the above countermeasure work may not always be sufficient. These studies revealed this.

  In other words, when liquefaction occurs, the bottom width of the embankment (horizontal distance between the buttocks) increases with the settlement of the embankment, and the top edge width (horizontal distance between the shoulders) of the embankment increases accordingly. It occurs, and tensile stress is generated at the top of the embankment, causing vertical cracks along the material axis direction of the embankment embankment.

  The extension at the top of the embankment means that if a railroad track is laid on the embankment, even if the embankment does not collapse, forced deformation will be applied to the track due to vertical cracks at the top of the embankment, and railway running safety The problem of causing trouble was caused.

  Such vertical cracking at the top of the embankment in liquefaction leads to a situation in which even when a road is laid on the embankment, vertical cracking occurs on the pavement surface and the vehicle cannot be driven safely.

  The present invention has been made in consideration of the above-described circumstances, and is a seismic reinforcement structure for embankments capable of preventing the extension of the embankment top and accompanying vertical cracks by a rational method, and the underground wall used therefor. The purpose is to provide a design method.

In order to achieve the above object, the earthquake-proof reinforcement structure for embankment according to the present invention has a structure in which a pair of underground walls extend downward from the vicinity of each bottom of the embankment, respectively. In the seismic reinforcement structure of the embankment formed by connecting the upper edges of the pair of underground walls with each other via a tensile material, so as to be opposed to the ground so as to sandwich the ground extending below the
The pair of underground walls are respectively inclined with respect to a vertical plane so that the mutual separation distance at the lower edge is smaller than the mutual separation distance at the upper edge , and the pair of underground walls are Supporting force of vertical upward component while restraining shear deformation of the ground along the horizontal direction in the region sandwiched between the pair of underground walls or the back region thereof by the supporting force of the horizontal component through the tensile material Thus, of the embankment, an increase in vertical load due to the looseness of the ground of each levee body sandwiching the central part of the dam body is supported .

  Moreover, the earthquake-proof reinforcement structure of the embankment which concerns on this invention uses the said ground as liquefied ground.

  Further, the embankment seismic reinforcement structure according to the present invention has an arrangement angle of the underground wall with respect to a vertical plane of 20 ° to 50 °.

  The embankment seismic reinforcement structure according to the present invention is such that the lower edge of the underground wall is not penetrated into a support base located below the ground.

  Moreover, the earthquake-proof reinforcement structure of the embankment which concerns on this invention makes the said embankment into the embankment formed by laying a railroad track or a road at the top.

Moreover, the design method of the underground wall used for the earthquake-proof reinforcement structure of the embankment according to the present invention is such that the pair of underground walls extend downward from the vicinity of each method bottom of the embankment, respectively. In addition, the ground extending below the embankment is disposed so as to be sandwiched between the grounds, and the pair of underground walls are separated from each other at a lower edge thereof so that a distance between them is smaller than a distance between the upper edges. Each of the pair of underground walls is connected to each other via a tension member , and the pair of underground walls are By the supporting force of the vertical component while restraining the shear deformation of the ground along the horizontal direction in the region sandwiched between the pair of underground walls or the back region thereof by the supporting force of the horizontal component via the tensile material , Out of the embankment Create a 2-dimensional FEM model for vibration analysis of earthquake-proof reinforcement structure of embankment adapted to support the increase in vertical load due to soil loosening of the bank side side portion sandwiching the dam central portion,
Using the two-dimensional FEM model for vibration analysis, the calculation of the deformation of the embankment with respect to a predetermined input seismic wave and the calculation of the extension amount at the top of the embankment from the deformation of the embankment are performed. As a parameter,
The arrangement angle of the underground wall that minimizes the extension amount of the embankment top is obtained from the result of the parameter analysis.

  When railway tracks and roads are laid on the embankment, from the viewpoint of running safety of vehicles such as railways and automobiles, the extension at the top of the embankment that causes vertical cracking is more effective than the settlement of the entire embankment. Suppression can be important.

  However, for earthquakes and normal-scale embankments that are assumed in the current design, the conventional seismic reinforcement structure that drives steel sheet piles vertically downwards enables necessary and sufficient countermeasures, but exceeds the assumptions. When an earthquake of scale occurs or the embankment scale is very large, the embankment at the top of the embankment that causes vertical cracking is sufficiently stretched even though the settlement of the embankment due to liquefaction can be suppressed to some extent. The applicants' analysis revealed that there are cases where it cannot be prevented.

  If the scale of the earthquake or the embankment is small, even if it is a conventional seismic reinforcement structure, the pair of underground walls are connected to each other at their upper edges. The horizontal slope of the embankment and the accompanying extension of the embankment top width (horizontal distance between the shoulders) can be suppressed to some extent, but in the event of an earthquake, the slope is formed more than the center of the embankment bank. Since the strain increases at the side of the levee body, the vertical load that flows on the ground directly below the side of the dam body increases significantly when the scale of the earthquake or embankment increases.

  For this reason, the steel sheet pile driven vertically downward cannot support the increase in vertical load, and the side of the dam body sinks into the ground immediately below the embankment of the embankment. It is thought to cause vertical cracking.

  In other words, it has been found that the conventional seismic reinforcement structure may not be able to cope with a change in load transmission balance caused by an earthquake.

  The present applicants have made the above-mentioned invention by repeating research based on such knowledge, and in the seismic reinforcement structure for embankment according to the present invention, a pair of underground walls are connected to each bottom of the embankment. When facing the ground so that the ground extending downward from the vicinity and extending below the embankment is sandwiched between the ground, and connecting the upper edges of the pair of underground walls to each other via a tensile material, A pair of underground walls are inclined with respect to the vertical plane so that the distance between them at the lower edge is smaller than the distance between them at the upper edge, in other words, a reverse C shape. Deploy.

  In this way, each middle wall supports the increase in vertical load due to the loosening of the ground on the side of the levee body with the support force of the vertical upward component, and for shear deformation due to earthquake, the horizontal component via the tensile material This will be restrained by the support force of the ground, thus preventing liquefaction of the ground in the area sandwiched by the underground wall and the area extending to the back side of the underground wall, and by the looseness of the ground on the side of the levee body It is possible to reliably prevent the extension at the top of the embankment and, consequently, the vertical crack at the top of the embankment.

  If the underground wall can support the increased vertical load due to the looseness of the ground on the side of each embankment across the center of the embankment, the material, structure or construction of the underground wall The method is arbitrary, and it can be constituted by a columnar wall made of cast-in-place concrete or soil cement, including steel sheet pile (sheet pile), steel pipe sheet pile, precast concrete plate.

  As the ground on which the embankment is constructed, it can be applied to liquefied ground and ground having insufficient support for earthquakes, for example, soft clay ground.

  As described above, the pair of ground walls arranged in an inclined manner must support the vertical load from directly above while restraining the shear deformation of the ground along the horizontal direction in the region sandwiched between them and the back region. Therefore, the arrangement angle with respect to the vertical plane is appropriately determined in consideration of the action along the two directions. For example, the optimum arrangement angle of the underground wall can be obtained by the following calculation procedure.

  First, a vibration analysis two-dimensional FEM model corresponding to the above-described embankment seismic reinforcement structure is created.

  Next, using the two-dimensional FEM model for vibration analysis, the deformation of the embankment for a predetermined input seismic wave is obtained, and the operation for obtaining the extension amount at the top edge from the deformation of the embankment is performed by the arrangement of the underground wall with respect to the vertical plane. The corner is used as a parameter.

  Next, from the result of the parameter analysis described above, an arrangement angle of the underground wall that minimizes the extension amount of the embankment top is obtained.

  Here, according to the analysis conducted by the present applicants, regarding the liquefied ground, the arrangement angle of the underground wall is set to 5 ° to 85 °, preferably 10 ° to 60 °, more preferably 20 ° to 50 °. It is good. If it is less than 20 °, it cannot sufficiently cope with the change in load transmission balance caused by an earthquake, and if it is less than 10 °, it becomes difficult to cope with the change in load transmission balance, and if it is less than 5 °, it becomes almost impossible. It is.

  On the other hand, if the angle exceeds 50 °, the horizontal shear constraint necessary to prevent liquefaction becomes insufficient, and if it exceeds 60 °, the shear deformation constraint becomes difficult, and if it exceeds 85 °, it becomes almost impossible. It is.

  In installing the underground wall, whether or not the lower end of the underground wall penetrates into the support base is arbitrary, but in the present invention, the lower edge of the underground wall can be made non-penetrating into the support base.

  If it does in this way, it will become possible to adopt the present invention regardless of the depth and presence of the support base, and the applicable embankment will be greatly expanded and the installation depth of the underground wall will be shallow. It is also possible to greatly reduce the cost of seismic reinforcement work.

  In the present invention, the use of the embankment is arbitrary and can be applied to a river embankment. However, when the embankment is constructed by laying a railroad track or a road at the top, vertical cracks at the top of the embankment occur. Therefore, it is possible to sufficiently ensure the running safety of railways and automobiles.

It is a figure of the earthquake-proof reinforcement structure 1 of the embankment which concerns on this embodiment, (a) is whole sectional drawing, (b) is a detailed perspective view which showed the connection condition with the tie rod 5 in the upper edge vicinity of the steel sheet pile 6. FIG. It is the figure which showed the effect | action of the earthquake-proof reinforcement structure 1 of the embankment which concerns on this embodiment, (a) supports the load increase part of the dam body side parts 22 and 22 with the support force of the vertical upward component of the steel sheet pile 6 (B) shows the state where the shear deformation of the liquefied ground 3 due to the earthquake is restrained by the support force of the horizontal components of the steel sheet piles 6 and 6 via the tie rods 5. The vertical sectional view shown. It is the graph which showed the shear deformation distribution of the embankment and the liquefied ground at the time of the earthquake, (a) when the arrangement angle of the steel sheet pile is 0 °, (b) is also 37 °, (c) Is a graph showing the case of 58 °. It is the graph which showed the deformation condition of the embankment by liquefaction, (a) is a hoshiri stretch, (b) is the amount of subsidence at the top, and (c) is a graph which shows the hoshi shoulder stretch.

  DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments of a seismic reinforcement structure for embankments according to the present invention and an underground wall design method used therefor will be described with reference to the accompanying drawings.

  FIG. 1A is an overall cross-sectional view showing an embankment seismic reinforcement structure 1 according to the present embodiment. As can be seen in the figure, the seismic reinforcement structure 1 of the embankment according to the present embodiment is applied to the embankment 2 on which a railroad track (not shown) is laid. It is constructed on the liquefied ground 3 stacked on top.

  On the liquefied ground 3, steel sheet piles 6, 6 as a pair of underground walls are arranged oppositely so as to extend downward from the vicinity of each method bottom of the embankment 2 and sandwich the liquefied ground 3. The steel sheet piles 6 and 6 are connected to each other via a tie rod 5 as a tensile material at their upper edges.

  Here, the steel sheet piles 6 and 6 are arranged in a vertical plane so that the mutual separation distance at the lower edge is smaller than the mutual separation distance at the upper edge. Are inclined by an arrangement angle θ.

  In order to connect the steel sheet piles 6 and 6 to each other via the tie rod 5, the end of the tie rod 5 is inserted into an insertion hole 9 formed in the upper edge of the steel sheet pile 6 as shown in FIG. The contact surface with the steel sheet pile 6 may be inserted into a washer 7 formed in a tapered surface corresponding to the arrangement angle θ, and the nut 8 may be screwed and tightened.

  Prior to constructing the seismic reinforcement structure 1 for embankment according to the present embodiment, the arrangement angle θ of the steel sheet piles 6 and 6 is determined by the following procedure.

  First, a two-dimensional FEM model for vibration analysis corresponding to the above-described embankment seismic reinforcement structure 1 is created.

  Next, using the two-dimensional FEM model for vibration analysis, the deformation of the embankment 2 with respect to a predetermined input seismic wave is obtained, and the operation for obtaining the extension amount at the top edge of the embankment 2 from the deformation of the embankment is performed on the steel sheet pile with respect to the vertical plane. 6 and 6 are used as parameters.

  Next, the arrangement angle θ of the steel sheet piles 6 and 6 at which the extension amount at the top edge of the embankment 2 is minimized is obtained from the result of the parameter analysis described above.

  The arrangement angle θ varies depending on the scale of the embankment 2 and the nature of the input ground motion, but is preferably 20 ° to 50 °, and more preferably 30 ° to 40 °. If the angle is less than 20 °, the change in the load transmission balance caused by the earthquake cannot be sufficiently dealt with, and if the angle exceeds 50 °, the horizontal shear deformation constraint necessary for preventing liquefaction becomes insufficient. On the other hand, if it is in the range of 30 ° to 40 °, it is sufficient to cope with changes in load transmission balance caused by earthquakes and to prevent liquefaction when the scale of the embankment, stratum structure or input seismic motion is typical. This is because the horizontal shear deformation can be sufficiently restrained.

  In order to construct the embankment seismic reinforcement structure 1 according to the present embodiment, first, the steel sheet piles 6 and 6 are respectively applied to the liquefied ground 3 from the vicinity of the bottom of the embankment 2 at the arrangement angle θ determined by the above-described procedure. Include.

  The driving depth of each steel sheet pile 6 may be appropriately determined in consideration of the soil properties of the embankment 2 and the liquefied ground 3, the scale of the embankment 2, and the assumed seismic motion properties. As shown, the lower edge of the steel sheet pile 6 need not penetrate into the support base 4.

  Once the steel sheet piles 6 and 6 have been driven to a predetermined depth, the steel sheet piles 6 and 6 are then connected to each other at their upper edges via the tie rods 5.

  In the embankment seismic reinforcement structure 1 thus constructed, the steel sheet piles 6 and 6 have triangular shapes located on both sides of the central portion 21 of the levee body 2 as shown in FIG. The increased load of the dam body side portions 22 and 22 in the cross section is supported by the supporting force of the vertically upward component.

  That is, when the scale of the embankment 2 and the scale of the earthquake are large, the shear strain increases at the side portions 22 and 22 of the dam body at the time of the earthquake, and the vertical load flowing to the liquefied ground 3 immediately below them greatly increases.

  Here, when the steel sheet piles 6 and 6 are not provided, or when the steel sheet piles 6 and 6 are driven vertically, an increase in the vertical load from the side portions 22 and 22 of the levee body is not supported. The parts 22 and 22 sink into the liquefied ground 3, and as a result, it is assumed that a vertical crack occurs at the top edge of the embankment 2. In this embodiment, the steel sheet piles 6 and 6 are inclined by the arrangement angle θ. I'm allowed.

  Therefore, the increase in the vertical load from the dam body side portions 22, 22 is supported by the supporting force of the vertical upward component of the steel sheet piles 6, 6, and the elongation that causes vertical cracks at the top edge of the embankment 2. Does not occur at the top edge of the embankment.

  On the other hand, the shear deformation of the liquefied ground 3 due to the earthquake is reliably restrained by the supporting force of the horizontal component of the steel sheet piles 6 and 6 via the tie rod 5, as shown in FIG.

  In addition, when a steel sheet pile is driven vertically, the pair of steel sheet piles receives a force that causes the lower edge to open outward from the ground sandwiched between them as a reaction force that restrains shear deformation.

  Therefore, when the steel sheet pile is placed vertically, it is necessary to penetrate the lower edge of the steel sheet pile into the support base. However, the steel sheet piles 6 and 6 of the present embodiment are arranged so as to be narrowed in the depth direction. Therefore, even if the lower edge does not penetrate into the support base 4, it is not necessary to worry that the lower edge opens outwardly and the action of the shear deformation restraint is lowered as in the case of vertical driving. .

  As explained above, according to the seismic reinforcement structure 1 of the embankment according to the present embodiment, the pair of steel sheet piles 6 and 6 extend downward from the vicinity of each method bottom of the embankment 2 and liquefied ground 3. The steel sheet piles 6 and 6 are connected to each other via the tie rods 5 so that the steel sheet piles 6 and 6 are vertically shaped so as to have a reverse C shape. Since it is inclined with respect to the surface by each arrangement θ, the shear deformation of the liquefied ground 3 in the region sandwiched between the steel sheet piles 6 and 6 and the region extending to the back side of the steel sheet pile is constrained to prevent liquefaction. However, it is possible to reliably prevent the embankment 2 from extending at the top end position of the embankment side portions 22 and 22 at the top end of the embankment, and consequently the vertical crack at the top end of the embankment 2.

  Moreover, according to the embankment seismic reinforcement structure 1 which concerns on this embodiment, since the pair of steel sheet piles 6 and 6 were made non-penetrating into the support base 4, even if the support base 4 is deep, the steel sheet pile 6 Since it is sufficient to drive 6 into the liquefied ground 3 by a predetermined depth, it is possible to significantly reduce the cost of the seismic reinforcement work.

  In the present embodiment, the embankment 2 constructed on the liquefied ground 3 is targeted. However, the seismic reinforcement structure of the embankment according to the present invention is not limited to the liquefied ground, and the supporting force against the earthquake is not sufficient. It can also be applied to the ground, for example, soft clay ground.

  Moreover, in this embodiment, the arrangement angle of the steel sheet piles 6 and 6 with respect to the vertical plane is set to 20 ° to 50 °. However, this is a case where the stratum structure, the soil condition, or the input ground motion is typical, and the shoulder stretch Can be arbitrarily determined in the range of, for example, 10 ° to 60 °, or 5 ° to 85 °, instead of the above angle range.

  Moreover, in this embodiment, although the underground wall of this invention was comprised with the steel sheet pile 6, it replaced with this, and it comprises it as a steel pipe sheet pile, a precast-concrete plate, or it comprises the column row wall which consists of spot cast concrete or soil cement. be able to.

  Moreover, in this embodiment, although the steel sheet pile 6 was made non-penetrating to the support base 4, it does not mean that it should not be made non-penetrating until the support base is shallow, but the lower edge of the steel sheet pile is made to penetrate the support base. Thus, the shear deformation may be restrained more reliably.

  Further, in this embodiment, it is assumed that the embankment 2 in which the railroad track is laid at the top end is seismically strengthened. As long as it is necessary to prevent the vertical crack at the top, it may be applied to banking for other purposes, for example, river embankments.

  In the present embodiment, the optimum underground wall arrangement angle is obtained by analysis. However, it goes without saying that the underground wall arrangement angle can be determined by a test or experiment instead.

  FIG. 3 shows the embankment seismic reinforcement structure 1 according to the present embodiment as a two-dimensional FEM model for vibration analysis so that the arrangement angle of the steel sheet pile can be arbitrarily set as a parameter. Figure (a) shows a steel sheet pile driven vertically downward, and (b) shows a steel sheet pile arrangement angle θ of 37 °. FIG. 4C shows the steel sheet pile having an arrangement angle θ of 58 °.

  In the modeling, the embankment is 28 m in width, 10 m in shoulder width, 6 m in height, and soil is sandy, the liquefied ground is 10 m in thickness, soil is sandy, N value is 8, the support base was 5 m thick, the soil was sandy soil, the N value was 50 or more, the steel sheet piles 6 and 6 were 6 m high, and the embedding depth was 5 m.

  Comparing Fig. 3 (a) and Fig. 3 (b), the shear strain of the liquefied ground just below the hind butt seen when the steel sheet pile is driven vertically is observed when it is driven diagonally at an arrangement angle of 37 °. Is almost zero, and in the case of vertical placement, the increase in vertical load due to the loosening of the side of the levee body causes shear deformation of the liquefied ground directly below the heel, whereas the placement angle is 37 °. In the case of slanting, the increase in the vertical load due to the looseness of the side of the levee body is supported by the steel sheet pile, so that it can be seen that the liquefied ground just below the heel is hardly sheared.

  On the other hand, when the arrangement angle of the steel sheet pile is set to 58 °, the shear strain is increased in the back region of the steel sheet pile, and it is understood that the horizontal shear deformation cannot be suppressed if the inclination angle is too large.

  Fig. 4 is calculated using the above-mentioned analysis results. Fig. 4 (a) shows the amount of change in horizontal distance between the buttocks (leg butt stretch), and Fig. 4 (b) shows the amount of crest depression. FIG. 4C shows the amount of change in the horizontal distance between the shoulders (the shoulder stretching).

  From these graphs, it is expected that when the steel sheet pile is not driven in, both the top sinking amount and the hoshiri stretch are very large, and excessive deformation and vertical cracking will occur in the embankment.

  On the other hand, when steel sheet piles are driven in, the sinking amount of the top edge is greatly reduced in all cases, but for the shoulder stretch, there is a difference depending on the arrangement angle of the steel sheet pile, and the arrangement angle is 0 °. Is 0.11 m for 21 °, 0.11 m for 37 °, 0.09 m for 58 °, and 0.16 m for 58 °. Stretch was minimized.

1 Seismic reinforcement structure of embankment 2 Embankment 3 Liquefaction ground (ground)
4 Support base 5 Tie rod (tensile material)
6 Steel sheet pile (underground wall)

Claims (6)

A pair of underground walls are arranged opposite to the ground so as to extend downward from the vicinity of each bottom of the embankment and sandwich the ground extending below the embankment, and above the pair of underground walls. In the seismic reinforcement structure of embankments, where the edges are connected to each other via a tensile material,
The pair of underground walls are respectively inclined with respect to a vertical plane so that the mutual separation distance at the lower edge is smaller than the mutual separation distance at the upper edge , and the pair of underground walls are Supporting force of vertical upward component while restraining shear deformation of the ground along the horizontal direction in the region sandwiched between the pair of underground walls or the back region thereof by the supporting force of the horizontal component through the tensile material By the above-mentioned, the seismic reinforcement structure of the embankment characterized by supporting the increase of the vertical load by the looseness of the ground of each embankment side part across the embankment middle part among the embankments. The earthquake-proof reinforcement structure for embankments according to claim 1, wherein the ground is liquefied ground. The seismic reinforcement structure for embankments according to claim 2, wherein an arrangement angle of the underground wall with respect to a vertical plane is set to 20 ° to 50 °. The seismic reinforcement structure for embankments according to claim 2 or 3, wherein a lower edge of the underground wall is not penetrated into a support base located below the ground. The earthquake-proof reinforcement structure of the embankment according to any one of claims 1 to 4, wherein the embankment is an embankment in which a railroad track or a road is laid at the top. A pair of underground walls are arranged opposite to the ground so as to respectively extend downward from the vicinity of each bottom of the embankment so that the ground extending below the embankment is sandwiched, and the pair of underground walls are Inclined with respect to the vertical plane so that the mutual separation distance at the lower edge is smaller than the mutual separation distance at the upper edge, and the upper edges of the pair of underground walls are connected to each other via a tensile member A seismic reinforcement structure for embankment , wherein the pair of underground walls are supported by a horizontal component through the tension member, or in a region sandwiched between the pair of underground walls or a back region thereof. While restraining the shear deformation of the ground along the horizontal direction, the support force of the vertical upward component supports the increase in vertical load due to the looseness of the ground on each side of the bank body across the bank center part of the embankment. Is supposed to To create a two-dimensional FEM model for vibration analysis of seismic reinforcement structure of the embankment,
Using the two-dimensional FEM model for vibration analysis, the calculation of the deformation of the embankment with respect to a predetermined input seismic wave and the calculation of the extension amount at the top of the embankment from the deformation of the embankment are performed. As a parameter,
An underground wall design method used for a seismic reinforcement structure for embankments, wherein an arrangement angle of the underground wall that minimizes the extension amount of the embankment top is obtained from a result of the parameter analysis.